International Edition in English

Optical Spectroscopy of Single Impurity Molecules in Solids

By W. E. Moerner" and Thomas Baschk*

Optical spectroscopy of a single impurity molecule provides the first truly local probe of host-guest interactions in doped solids. In conventional optical high-resolution experiments with many molecules only ensemble averages of the microscopic parameters can be obtained. In the single-molecule regime, the exquisite sensitivity of an individual dopant molecule to both the local environment and to external perturbations has been exploited in recent experi- ments to reveal a wealth of fascinating novel phenomena such as spectral diffusion in crystals and polymers, optical modification of a single impurity molecule (spectral hole-burning), local field measurements at the site of a single impurity molecule, and quantum optics in a solid.

Volume 32 - Number 4 April 1993

Pages 457-628

1. Introduction[**'

Significant progress in the optical spectroscopy of single quantum systems confined in traps or on surfaces has oc- curred in the last decade. For example, imaging and spec- troscopy of single ions confined in electromagnetic traps has led to novel measurements that test the foundations of quan- tum physics. In particular, various workers have reported direct measurement of quantum jumps, Doppler sidebands, photon antibunching, extremely narrow optical linewidths, and other fundamental phenomena such as ion crystalliza- tion and chaos.['-31 The original work on trapped single electrons and on the Paul trap led to the Nobel Prize in physics for Dehmelt, Paul, and Ramsey in 1989.[41

At the other extreme, recent advances in various near-field spectroscopies such as scanning tunneling microscopy

~

[*I Dr. W. E. Moerner IBM Research Division, Almaden Research Center San Jose. CA 95120-6099 (USA) Dr. T. Basche lnstitut fur Physikalische Chemie der Universitdt Sophienstrasse 11, D-W-8000 Munchen 2 (FRG)

the end of the review. [**I Important terms and abbreviations are listed in a glossary (Section 10) at

(STM)''. 7bl have provided detailed images of single atoms, of single molecules of benzene and CO on Rh and of liquid crystal molecules on graphite"] to name only a few examples. The invention of STM earned Binnig and Rohrer''' the Nobel Prize in physics in 1986, and many workers around the world are applying this technique to a large variety of systems. Moreover, the STM work has in- spired a broad array of sensitive surface measurements based on the atomic force microscope.[7b9s1 A requirement of STM is the need for a strong bond between the molecule of interest and the underlying surface so that the molecule can remain in a fixed configuration long enough for the tunneling spec- trum to be obtained.

By contrast, the relatively new field of single-center optical spectroscopy in condensed matter is only now beginning to provide novel chemical and physical insights. For single mol- ecules in liquids, the emphasis has been on the detection of single molecules labeled with fluorophores for analytical ap- plications without recording detailed spectra. In the early work, use of laser-induced fluorescence and a hydrodynami- cally focused flow to reduce the scattering volume allowed the detection of single molecules of the protein B-phycoery- thrin, whose fluorophore is equivalent to 25 rhodamine 6G molecules.[9* lo] Recent enhancements of the method have

Angrw. C'lrem. l n t . Ed. Engl. 1993, 32. 451 -416 8 VCH Verlugsgesellsrhuft mhH, W-6940 Weinhrim, 1993 OS?0-0833/93/0404-0457 $ 10.OOf .2SK 451

allowed the detection of single molecules of rhodamine 6G in a flowing liquid.[”% 12] One distinct advantage here is that the experiments are usually conducted at room temperature; however, the fluorescent molecule and the solution must be chosen carefully to maximize photostability. In the first work to go beyond digital (present/not present) detection of a molecule, two fluorescent species were distinguished by the difference in fluorescence lifetime.“ 31

This review concerns single-center spectroscopy when the center of interest is a molecular or ionic dopant (defect) hidden deep inside a solid. The detection and spectroscopy of a single absorber in a solid (in the case of a molecular impu- rity called single-molecule detection, SMD) provides a natu- ral complement to the earlier hole-burning and coherent transient spectroscopy of impurities in solids.[’4- ”I Single- center spectroscopy in solids provides a useful tool for the study of local host-guest interactions where the absorbing center is essentially a t rest, confined by the host lattice, and where the normal averaging over many “equivalent” centers is removed. Although this paper focuses on molecular impu- rity centers, the physical concepts apply equally well to ions, color centers, and other defect absorptions in solids.

As an important first step toward single-molecule detec- tion (SMD), it was necessary to make a very detailed exam- ination of the inhomogeneously broadened optical absorp- tion line of a defect in a solid with large numbers of absorbers (the usual regime). In this limit, a fundamental effect called statistical fine structure (SFS) was observed for the first time.[’8’ 19] SFS results from (static) fluctuations in the spectral density of absorbers with optical wavelength, and therefore scales as the square root of the number of absorbers in resonance. The observations of SFS and other steps toward SMD will be described in Section 2. Crucial to these measurements was the use of a powerful zero-back- ground laser technique called frequency modulation (FM) spectroscopy, first described by Bjorklund[’O1 in 1980.

With a firm understanding of SFS in inhomogeneous lines, it became possible to approach the ultimate limit of

single-molecule detection (SMD) and spectroscopy. One motivation for the development of S M D comes from the fact that for an inhomogeneously broadened line, the centers located within a homogeneous width of a given laser fre- quency are located at that particular spectral position for a variety of possible reasons. This intrinsic multidimensional inhomogeneity cannot be removed with spectral hole-burn- ing or coherent transient techniques. However, with SMD the absorption spectrum of a unique individual absorber in its particular environment can become directly accessible, as long as no other centers absorb at the same frequency. This is the primary reason for pursuing the spectroscopy of indi- vidual centers in condensed matter. The use of powerful spectroscopic methods (FM spectroscopy) and the proper- ties of the inhomogeneous line itself make SMD feasible; the first successful SMD experiments[21 241 will be described in Section 3.

The advent of a superior technique, fluorescence excita- tion with extremely high collection efficiency,[251 allowed greatly increased signal-to-noise ratio (SNR) for single- molecule spectra. Examples of precise measurements of the optical linewidth[261 and other phenomena which then be- came observable will be presented in Section 4. In studies of pentacene molecular defects in crystalline para-terphenyl, a novel physical effect called spectral diffusion was ob- ~ e r v e d , [ ~ ’ , ~ ~ ] which will be summarized in Section 5. Sec- tion 6 describes how extensions of SMD to polymeric hosts[29, 301 allow direct observations of hole-burning and stochastic kinetics for an individual center. Section 7 pre- sents results of very recent single-molecule spectroscopy in which spectral shifts due to external electric fields (the Stark effect) have been measured in both crystalline and amor- phous 321 Finally, Section 8 reviews a novel new experiment on quantum optics in solids, where the fun- damental photon antibunching expected for the fluorescence emission from a single molecule in a solid has been ob- served.[331 With these results, a new regime of optical spec- troscopy may be envisioned in which some of the scientific

W. E. Moerner was born in 1953 in Pleasanton, California. After receiving three Bachelor’s degrees in 1975,from Washington University, St. Louis, he obtained M . S. (1978) and Ph.D. (1981) degrees in physics from Cornell University, where he worked with A . J. Severs. He joined the IBM Research Division, Almaden Research Center in 1981, and worked extensively in the area of spectral hole-burning. He received the Roger I . Wilkinson Outstanding Young Electrical Engineer Awardfrom the Eta Kappa Nu Honorary Electrical Engineering Society of the U S . in 1984 and an Outstanding Technical Achievement Awardfrom IBM in 1988 and in 1992. He is a Fellow of the Optical Society of America and the American Physical Society, a Senior Member ofthe Institute of Electrical and Electronics Engineers, and a member of the American Chemical Society. His current interests include single-molecule spectroscopy in solids, optical storage, and polymeric photorefractive materials.

Thomas BaschP, born 1959 in Bingen, Germany, did his undergraduate studies in chemistry at the University of Munich where he received his Ph.D. in 1990,for his work with C. Brauchle. In 1991 and 1992 he was a postdoctoralfellow with W E. Moerner at the IBM Almaden Research Center in Sun Jose. His current research interests include optical line-narrowing experiments with adsorbed molecules and single-molecule spectroscopy in condensed phases.

458 A n p w . Chem. In[ . Ed. Engl. 1993, 32, 451-476

advances and observations of physical effects made possible by the ion trap and STM techniques may be applied to con- densed matter.

2. First Steps toward Single-Molecule Spectroscopy

2.1. Background on Inhomogeneously Broadened Optical Lines

It is well known that absorbing guest centers in solids with zero-phonon transitions give rise to inhomogeneously broadened 351 where the overall line profile is caused by an approximately Gaussian distribution of center fre- quencies for the individual absorbers that is broader than the (usually Lorentzian[”]) homogeneous lineshape of the indi- vidual absorbers. This situation is shown schematically in Figure 1 and by simulation in Figure 2, which will be de- scribed in Section 2.2. The distribution of center frequencies is caused by dislocations, point defects, or random internal electric and strain fields and field gradients in the host mate- rial. Inhomogeneous broadening is not only a universal fea- ture of high-resolution laser spectroscopy of defects in soIids.1’5,371 but it also appears in a fundamental way in other spectroscopies of impurity centers such as NMR, ESR, and Mossbauer spectroscopy. Inhomogeneous broadening also occurs in amorphous hosts, where the (generally broad) center frequency distribution is caused by the large multiplic- ity of local environments. Although the work reviewed here is focused mainly on the lowest electronic transition of the

inhomogeneous line IGaussionl

1

line Lorentzionl

n-

line center wings of line

Fig. 1. Top: Schematic representation of an inhomogeneous absorption band at low temperatures and the principle of single-molecule detection in solids. The entire band is formed as a superposition of Lorentzian profiles of the individual absorbers, a distribution of center resonance frequencies is caused by random strains and imperfections. The lower part of the figure shows how the number of impurity molecules in resonance in the probed volume can be varied by changing the laser wavelength. The laser linewidth (1 3 MHz) is negligible (after ref. [ 2 3 ] ) .

absorbing molecule, all of the concepts apply equally well to inhomogeneously broadened vibronic lines as well as to in- homogeneously broadened purely vibrational zero-phonon lines.

Inhomogeneous broadening generally dominates a t low temperatures, because the homogeneous zero-phonon lines become much narrower than the inhomogeneous distribu- tion of center frequencies only when the host phonons are quenched. For example, for pentacene in p-terphenyl, the homogeneous width of the lowest electronic transition at 593 nm is 7.8 MHz at 1.5 K,[381 while the overall inhomoge- neous line is 42 G H z in width in crystals grown by the Bridg- man method.[391 In the single-molecule spectroscopy to be described in Section 3, inhomogeneous broadening will be used to select one single absorber for study by proceeding out into the wings of the inhomogeneous line as shown on the right side of Figure 1 .[401 Since the center frequencies for these absorbers are displaced very far from the most com- mon center frequencies near the center of the inhomoge- neous line, such absorbers have highly unique and strained sites. For this reason, various recent SMD experiments have also considered the situation where the concentration of im- purity centers is lowered and single molecules are measured much closer to the center of the inhomogeneous line.

2.2. Statistical Fine Structure

Before the single-molecule limit can be approached, how- ever, it is necessary to review the statistical properties of inhomogeneous lines. To quantify the number of impurity centers absorbing at a particular frequency or wavelength, it is useful to define the quantity HH, which is the average number of centers in the probed volume whose center fre- quencies are within one homogeneous width of the laser wavelength. Due to the unavoidable randomness associated with the imperfections in solid hosts even for a single molec- ular orientation or “site”, inhomogeneous absorption lines (at least where E, $ 1 ) are often approximated by smooth, Gaussian profiles.r34. 391 However, since the inhomogeneous line on a microscopic scale is simply a superposition of dis- crete homogeneous lines with widths as much as 1000 times narrower than the overall inhomogeneous profile, the true shape of the inhomogeneous line cannot be a smooth func- tion. In fact, unavoidable fluctuations in the number of ab- sorbers per unit wavelength interval should give rise to a “spectral noise” on the overall Gaussian background that scales as the square root of the mean number of centers in resonance. In other words, there should be a statistical fine structure (SFS) present on the absorption profile scaling in absolute magnitude as (in the limit of EH $1). Since SFS arises from the absorption of many overlapping impuri- ty absorptions, the absolute magnitude of the SFS is clearly larger than a single-molecule absorption signal (where EH z 1) . Therefore, observations of SFS would be expected to precede true single-molecule or single-center detection. This is more than just a pedagogical point: in fact, in any experiment with sensitivity capable of reaching the single- molecule limit, SFS should be observed first and used as a “test signal” to optimize the detection conditions.

Figure 2 shows a computer simulation of an inhomoge- neous lineshape for various total numbers of centers N and

AnRim Chern. Int. Ed. Engl. 1993. 32, 451-476 459

30 I I I I I

A 20

A

10

0 -4 -2 0 2 4

V-

Fig. 2 . Simulated absorption spectra with different total numbers of absorbers N . A Gaussian random variable was used to select center frequencies. The homogeneous linewidth is one-tenth of the standard deviation of the inhomoge- neous distribution. A = absorption in arbitrary units, v = frequency in units of u,,~ (see text).

hence different values of N,. Here yH is the (assumed Lorentzian) homogeneous width (full width at half-maxi- mum absorption, FWHM), and din,, is the standard devia- tion of the normally distributed distribution of center fre- quencies. For clarity, a small value of the ratio cinh/yH = 10 was chosen for the simulation; in real solids, this ratio usual- ly ranges from 102-105. The main point here is that even though the center frequencies were chosen by sampling from a (smooth) normally distributed random variable, the actual center frequencies never form a smooth uniform covering of the allowed frequency space. This is merely a statement that the usual number fluctuations encountered in many areas of physics and chemistry must occur here as well. As Figure 2 shows, the average absorption ct grows linearly with N,, while the relative fluctuations in absorption Aa/ct decrease with (NH)-’12. Therefore, in terms of relative changes in absorption it appears that low-concentration samples (N, < 10, for example) might be expected to be optimal for the observation of SFS. While this is true for most tech- niques, SFS was in fact first observed in a different regime.

2.3. Detection of Statistical Fine Structure with Laser Frequency Modulation Spectroscopy

The limit NH -+1 is in fact the single-molecule regime itself. In the early work, it was realized that statistical fine structure could be measured without completely solving the problem of single-molecule detection. The zero-background tech- nique of laser frequency modulation (FM) spectroscopy[201 provides a solution, because the variable measured is Aa itself, which increases with (N,)’”. In other words, statistical fine structure is easier to detect a t large ZH if F M spec- troscopy is used. A glance a t Figure 2d verifies that the size of the absorption variations due to SFS in terms of depar- tures from the average absorption is indeed far larger than the size of the absorption signal from a single molecule. Rather than describe the details[41] of F M spectroscopy here, it is more useful to describe the characteristics of the method: 1) The laser is phase-modulated at the radio fre- quency v,, and the transmitted beam is detected with a radio

frequency lock-in amplifier a t v,. 2) The background is zero in the absence of residual amplitude modulation (RAM). 3) The noise on the signal is derived from the laser noise a t v,, which may be at the quantum limit if no excess noise is introduced by the detector. 4) The signal is largest when the width of the spectral feature is comparable to or less than v,; broad spectral features produce no signal. More precisely, in F M spectroscopy the detected signal (in the cosine phase) is proportional to [a(v + vm) - a(v - v,)]L, where v is the laser frequency and L is the sample thickness. Thus the F M signal measures the difference in stL a t the two sideband frequen- cies. It can easily be shown[’91 that as long as the optical density is not too large the F M signal resulting from statisti- cal fine structure is described by Equation (a), where c is the

(Acc)L = O ( N ~ ) ” ~ / A = c(p,L/A)”’ (a)

peak absorption cross section, A is the beam area, and the volume density per homogeneous linewidth is given by pH = NH/AL. Therefore, the F M signal increases if the con- centration of absorbers or the sample length increases, and increases for smaller laser spots. Further, centers with higher cross section lead to larger F M signals.

For the well-studied model system“ 5 3 4 2 1 pentacene in p- terphenyl crystals statistical fine structure can be easily de- tected by F M spectroscopy at 1.5 K.[’’? A schematic illus- tration of the location of the pentacene molecules in the p-terphenyl host crystal is shown in Figure 3. Pentacene can

Fig. 3. Schematic representation of the crystal struture ofp-terphenyl showing one possible location for a pentacene dopant molecule. This depiction of the pseudomonoclinic crystal structure (projected onto the ab plane) was adapted from ref. [43]

substitute for any one of the four p-terphenyl molecules in the low-temperature unit 431 giving rise to four S, + So optical absorption origins near 593 nm, called O, , O,, O,, and 0,. It is convenient to focus on the inhomoge- neously broadened origins 0, and 0, , because the homoge- neous linewidths are smaller here than for the other origins.

An example of the static nature (and repeatability) of the SFS spectra measured with F M spectroscopy is shown in Figure 4, where the bottom panel shows a 5-GHz-wide scan near the peak of the 0, line. The spectra were acquired by

460 Angeu Chem. Ini. Ed. Engf. 1993, 32,451-416

pentacene para-terphen yl

perylene terry 1 en e

repeatedly scanning the desired frequency range with a Rho- damine 6G single-frequency dye laser (2.8 MHz linewidth). Contrary to what the reader might think, this is not a record- ing of some noisy signal. The many peaks and valleys are actual, repeatabfe fine structure as is demonstrated by the two expanded traces in the top panel of Figure 4, the lower

r 0.2

1 0.1

IIVI

-0.1 I 1

r - ? O F

-2000 -1000 0 1000 2000 Auk IMHzl -

Fig. 4. Frequency modulation spectrum over a wide scan range showing statis- tical fine structure. The lower panel shows the result of 64 averages of a 5 GHz region of the inhomogeneous line of pentacene inp-terphenyl ( T = 1.4 K). The upper panel shows a portion of the same spectrum on an expanded frequency- scale together with another acquisition of the spectrum taken 20 min later, offset for clarity. Laser power 3 pW, focal spot diameter 20 pm (after ref. [19]). I is the intensity of the SFS signal in Volts.

of which is an expansion of the trace in the bottom panel and the upper of which is a subsequent acquisition of the same spectral region more than 20min later. The agreement is quite good, indicating that at 1.4 K there is little or no re- arrangement or annealing of the strains and other imperfec- tions in the p-terphenyl crystal which defined the inhomoge- neous distribution when the crystal was cooled. Most, if not all, of the slight differences between the spectra are due to the quantum and avalanche noise of the detection system. As expected from Equation (a), the root mean square amplitude of the SFS spectra should grow as (NH)’I2, and indeed a measured dependence of (NH)0.54’ ‘ . O 5 h as been observed experimentally.[’ ‘1

More insight into the source of SFS can be derived from spectra from different sample volumes. The formation of a specific set of center frequencies for a given sample volume is a random process which reflects the underlying probability distribution for center frequencies; thus SFS should be dif- ferent for different sample volumes. A “SFS landscape” of the sample can be generated by acquiring multiple SFS spec- tra as a function of the position of the laser spot, as shown in Figure 5. This display allows one to search for “mi-

Fig. 5. Statistical fine structure (SFS) versus laser spot position d and laser frequency uL (0 MHz = 592.32 nm) near the inhomogeneous line center for pentacene in p-terphenyl. A sequence of 100 spectra were obtained; the 20 pm laser spot was moved by 2 pm after each spectrum, and the results plotted as a three-dimensional plot of the SFS signal to show the SFS “landscape” (after ref. ~ 9 1 ) .

crosites”, special (more probable) frequencies that would appear as ridges in this three-dimensional plot. No evidence for microsites or departures from the statistical source for SFS have been observed in this system. As a final point, the value of the underlying homogeneous linewidth can be deter- mined directly by an autocorrelation analysis of the SFS spectra.“9’ In systems with weak spectral hole-burning and weak spectral diffusion, this method of obtaining the homo- geneous width should work as well as the older, more estab- lished techniques of coherent transients or hole-burning, as long as the signal-to-noise ratio of the SFS spectrum is rea- sonable.

2.4. Further Steps Toward the Single-Center Limit

Subsequent to the first observations of statistical fine structure, other researchers utilized both FM spectroscopy and fluorescence excitation to observe SFS in other classes of materials at smaller and smaller values of NH. Lange et al.[441 relied upon fluorescence excitation of Sm2+ ions in CaF, at 77 K with a fixed-frequency laser in tightly focused spots. They saw Poisson fluctuations in the detected fluorescence as a function of the position of the focal spot, and concluded that they had reached the level NH = 5. In a particularly novel approach, developed by the Yen group at the Universi- ty of G e ~ r g i a , ~ ~ ’ . ~ ~ ] laser fluorescence excitation was used in a glass fiber doped with Nd3’ ions. Here the fiber geometry effectively maintained a small focus and a small sample vol- ume, and background signals from the host were reduced. The measured SFS led these researchers to conclude that they had reached SH values on the order of a few tens of ions,

AngrM. Chem. Int. Ed. Engl. 1993, 32. 451-416 46 1

although the spectral features were somewhat broad. In both of these cases, special detection geometries were required to reduce interfering background fluorescence from Rayleigh and Raman scattering.

Equation (a) shows that SFS becomes harder and harder to detect when cr decreases. The drop in signal can be partial- ly offset by increasing the concentration of centers, but for constant optical density the signal still suffers as the square root of the cross section. Nevertheless, F M techniques with the addition of secondary Stark modulation to remove resid- ual amplitude modulation (RAM) allowed the observation of SFS for Cr3+ ions in ale~andrite.[~’I Another approach when cr is low is maintaining a focused spot over a long distance in an optical fiber. In this case the SFS signal in- creases as the square root of the fiber length, as long as the optical density is less than unity. Using this approach and F M spectroscopy techniques, Brocklesby et al.[481 observed SFS for Nd3’ ions in a silica fiber. These experiments demonstrated that SFS can indeed be detected for absorbers in amorphous hosts and for relatively weakly absorbing cen- ters.

3. Detection of Single Molecules in Solids with Absorption Techniques

3.1. Detection with FM Double-Modulation Techniques

Compared to the previous single-absorber experiments on ions in traps, molecules on surfaces, and molecules in hydro- dynamic flows, single-molecule detection in solids provides a different set of experimental challenges. The problem can be likened to finding a needle in a haystack, because unlike the ion-trap experiments, for example, the molecule of inter- est is hidden within a solid containing a large number ( z 10’’ - of nonabsorbing, potentially interfering host molecules within the laser focal volume. If laser-induced fluorescence excitation were used for S M D and the host molecules had appreciable Raman (or Rayleigh) scattering cross sections, the signal from the one absorbing molecule could be swamped by the scattering signal from the host.

The first successful S M D experiment,[2 ‘I also performed on the pentacenelp-terphenyl system, avoided the problem of fluorescence background from the host “haystack” by using the powerful zero-background properties of F M spec- troscopy.[201 This method also has the advantage that it is sensitive only to spectral features with widths on the order of the modulation frequency v,. Therefore, any impurity mole- cules in the host matrix with wide absorption lines as a result of stronger electron-phonon coupling or much shorter excit- ed state lifetimes than that of pentacene d o not contribute to the observed signal. In this method narrow spectral features in the sample are used to convert the frequency- (phase-) modulated light beam into an amplitude-modulated beam. Since the method directly measures the conversion of fre- quency into amplitude modulation, any residual amplitude modulation (RAM) from imperfections in the modulator can give rise to a spurious background signal. To overcome this, a secondary modulation of the spectral feature itselfwas implemented by using oscillating Stark (or separately, ultra- sonic) fields.

In the case of pentacene, the applied secondary Stark modulation with oscillating electric fields at frequency f( in the kHz range) shifts the absorption profile twice each cycle by the quadratic Stark effect.[49* 501 The secondary modula- tion with demodulation at 2fgenerates the first derivative of the F M signal. Because the physical effects giving rise to the RAM are insensitive to the Stark modulating field, this detection system yields a signal that is free from RAM back- ground. It is clear that other local perturbations of the impu- rity molecule might also be used for double-modulation de- tection. Other RAM suppression methods that d o not require secondary modulation could also be utilized.[5’. 5 2 1

The size of the expected absorption signal from a single molecule in an F M spectrum is straightforward to esti- mate.[”] The change in absorbance, (Aa)L, is given by the probability of absorption of a photon in the incident beam by the molecule, a / A , where cr is the peak absorption cross section and A is the area of the laser beam. Clearly, then, one would prefer tightly focused laser spots and molecules with strong absorptions. In the first experiments, the focal spot was N 3 pm in diameter, and the peak (low-temperature) absorption cross section for pentacene is 9.3 x lo-’’ cm’, yielding an absorbance change of This is not an extremely small signal, but detection must be performed with a light intensity that does not produce extreme power broad- ening. To meet this constraint in a tightly focused spot, the measurements were performed with only 0.1 pW of light a t the detector, which is an extremely small laser power for F M spectroscopy. Such a low light level required an avalanche photodiode to avoid detector Johnson (thermal) noise and resulted in detection approximately 3 dB above the quantum limit.

In spite of these limitations, the FM/Stark and FM/ultra- sound methods can be used to detect the optical absorption of a single molecule of pentacene in a solid crystal of p-ter- pheny1.[21*231 Figure 6 shows examples of the spectra for the FM/Stark case. The first three traces are simulations to illus- trate the expected single-molecule lineshape for either Stark or ultrasonic double-modulation. Trace a shows a Lorentzi- an absorption profile of width y , trace b the expected simple F M signal:[411 two copies of the absorption line with oppo- site sign, spaced by 2v, =I50 MHz (in the limit y << v,, where v m is the rf modulating frequency). With secondary modulation that causes frequency shifts less than the linewidth, the resulting double-modulation lineshape is the derivative of the simple F M lineshape (trace c). Thus the signature of a single molecule is a W-shaped feature with a large negative slope and a large positive slope separated by

In a typical experiment, the laser frequency was set near the center of the inhomogeneous line, and the resulting strong SFS signal was used to optimize the optical and elec- tronic configuration. Then as the laser wavelength was moved out into the wings of the line, the SFS amplitude dropped uniformly. Eventually spectra that appear to be superpositions of two to five single-molecule spectra were observed. Finally, sufficiently far out into the wings of the line, true single-molecule spectra could be recorded. Trace d in Figure 6 shows a set of eight FM/Stark double-modula- tion spectra of a strong in-focus molecule far out in the long-wavelength edge of 0, , along with several unavoidable,

2v,.

462 Angew. Chem. Int. Ed. Engl. 1993, 32, 451-416

I I I V 1

0

-0.8

0 200 400 600 Av, [MHzl -

Fig. 6. Single-molecule spectra obtained with the FM/Stark technique (quadratic Stark effect) for pentacene in p-terphenyl. a) Simulation of the ab- sorption line. b)Simulation of the FM spectrum with v, =75 MHz. c) Simulation of FM/Stark double-modulation lineshape. d) SMD spectra at i. = 592.423 nm, 512 averags, 8 traces overlaid; the bar corresponds to 2 Y, = 150 MHz. (0, line center is at 592.326 nm.) e) Average of traces in (d) and the fit to the in-focus molecule (smooth curve). f ) Signal at i. = 597.514 nm very far from the line center; same conditions. g) Traces of SFS at the 0, line center, i. = 592,186 nm. 128 averages each. The vertical scale is correct for traced; the other traces have the same scale but are offset vertically for clarity (after ref. [21]). I = intensity of the double-modulation signal.

weak, repeatable features from out-of-focus molecules at the left and right edges of the laser scan range. These out-of- focus features were caused by molecules not located at the peak of the laser intensity profile. The fiducial bar in Fig- ure 6 marks a spectral range equal to 2v,. Trace e shows the average of the eight scans in trace d, along with a fit to the central feature generated by a simple model for the double- modulation process.[231 The fit to the essential features of the SMD lineshape is reasonable, and the homogeneous width required by the fitting process is somewhat larger than the low-power homogeneous width, as expected.

Trace f in Figure 6 shows the detected signal from a laser wavelength so far away from the pentacene site origins that no absorptions are expected to lie in the laser scan range; this is the background shot and avalanche noise. In samples of undoped pure p-terphenyl, only a baseline noise level similar to the off-line data in trace f was observed, even near the center of the inhomogeneous line. Trace g shows spectra of the strong SFS observed near the center of the inhomoge- neous line for which a smaller number of averages were used. This spectrum is composed of a superposition of many W profiles similar to trace d in Figure 6 with many different center frequencies, illustrating the qualitative difference be- tween spectra of large numbers of molecules (trace g) and spectra of one molecule (trace d). By using the related FM/ ultrasound technique and both longitudinal and transverse (shear) ultrasonic waves,[z’’ 231 single-molecule detection was confirmed.

In summary, the shape of the observed features, the posi- tion relative to the pentacene in p-terphenyl origins, the lack

of such signals in undoped samples, and the appearance of single-molecule spectra with both the FM/Stark and FM/ul- trasound techniques, led to the conclusion that the recorded spectra were indeed due to single molecules of pentacene. However, in both cases, the signal-to-noise ratio (SNR) was only approximately 3 - 5 , and further improvements in this SNR proved difficult since the measurements were already performed near the quantum limit and power broadening was already present. Indeed, one cannot underestimate the difficulty in acquiring spectra like those in Figure 6 , especial- ly since later work to be described in Section 4 showed that many molecules spectrally diffuse within seconds. The single molecules observed by FM spectroscopy must have been class I (see Section 4) stable pentacene molecules with no spectral diffusion.

3.2. Signal-to-Noise Limits in FM Detection

The characteristics of the signal-to-noise ratio (SNR) for nonsaturating absorbers in FM spectroscopy have been de- scribed in ref. [41]. We will outline here the additional com- plications of avalanche photodiode detection and saturation of the optical transition as they affect single-molecule detec- tion.[*’ The analysis in this section is the result of unpub- lished work by W. P. Ambrose and one of the authors (W. E. M.). For simplicity, the signal-to-noise ratio for simple frequency modulation will be presented, with the as- sumption that the principal effect of the double-modulation is to remove residual amplitude modulation (RAM) and that the secondary modulation is strong enough to provide max- imal signal.

The signal-to-noise ratio (SNR) of simple frequency mod- ulation (FM) can be expressed in terms of a voltage or cur- rent ratio [Eq. (b)], where the (homogeneous) saturation of the absorption is described by Equation (c). Po is the laser

G2(AccL)’ ‘ I 2 SNR = [C ]

& + J

power at the detector, cro is the unsaturated peak cross sec- tion, I, is the saturation intensity, and I , = p2Po/4AT, is the laser intensity in the first-order sideband at the sample, f l is the modulation index, and T, is the total transmittance of all optical components between the sample and the detector.

The SNR limits of FM spectroscopy derive from the two noise terms in the denominator of Equation (b), which repre- sent the contributions of the shot noise of the laser beam (carrier) and the Johnson (thermal) noise of the detector, respectively. The constant J i s given by 4kT/2eRLRG:F, with k Boltzmann’s constant, T the absolute temperature, e the electron charge, R, the load resistance, R the detector re- sponsivity in AW-’, G, the avalanche gain, and F, the avalanche excess noise factor. As one can see, the effect of the Johnson noise in reducing SNR is suppressed due to the

[*] Readers not interested in this particular problem may move on to the next section.

Angew C‘hm?. Int . Ed. EngI. 1993. 32, 457-476 463

gain of the avalanche photodiode. Similarly, the constant C is given by Rp2/16eBF,, with B the detection bandwidth. While FM spectroscopy has been shown to be capable of detecting absorption changes as small as in a 1 Hz bandwidth if several mW of power is available at the detec- tor, the severe limitations on the laser power in single- molecule detection greatly reduce the sensitivity of the tech- nique. When the best possible gains for Si avalanche detectors of approximately 100 and F, factors near 2.2 are used, the peak FM SNR is on the order of 1 for a saturation intensity of 70 mWcm-’, which is the value for pentacene in p-terphenyl including triplet saturation. This SNR is consis- tent with the observed SNR in the FM experiments, and can be improved only by the use of laser beams with reduced quantum noise. As will be shown below, many pentacene centers have smaller values of saturation intensity and thus were probably not observable in the FM experiments.

4. Improvements in Signal-to-Noise Ratio by Fluorescence Excitation

4.1. Signal-to-Noise Limits in Fluorescence Excitation

The relatively low signal-to-noise ratio (SNR) availabIe from FM absorption spectroscopy and the high powers re- quired to attain this SNR placed severe limits on the physical and chemical information that could be obtained. The demonstration by Orrit et al. (see Section 4.2) that fluores- cence excitation with high collection efficiency can be ac- complished with acceptable background scattering levels provided greatly increased SNR at lower probing intensity, thus opening the door for additional detailed spectroscopic studies. In the fluorescence excitation method the frequency of a single-mode laser is tuned across the molecular absorp- tion line, and the Stokes-shifted fluorescence intensity is

M C Fig. 7. Experimental set-up for single-molecule fluorescence excitation spec- troscopy in a solid at liquid helium temperatures. The excitation laser beam enters from the left and is focused by a lens (L) with a 10 mm focal length into the sample (S), which is mounted on an alkali metal halide plate. The excitation beam is terminated with a piece of black tape (B). The fluorescence from the sample is collected by a parabolic mirror (P). which collimates the emission into a beam propagating to the right in the figure. Fine positioning of the lens (L) relative to the sample is accomplished with an electromagnetic actuator consist- ing of a coil ( C ) and magnet (M). Vertical displacement of the sample relative to the laser focal spot (resolution: 10 fim) is performed with a translation stage and micrometer screw (not shown) (after ref. [28]).

monitored as a function of the excitation wavelength. The fluorescence excitation spectrum then represents an image of the absorption spectrum. An example of the experimental arrangement used by the IBM group is shown in Figure 7. (In the original setup by Omit et al. a focusing lens was not used and the sample was placed at the end of a single-mode optical fiber.) For optimal collection of the emitted photons, the sample is placed at the joint focus of a lens focusing the laser beam and a paraboloid with numerical aperture near 1 .O. The sample is mounted on a transparent substrate made of an alkali metal halide to reduce the possibility of first- order Raman scattering from the substrate. The emitted ra- diation passes through a long-pass color filter before detec- tion with photon-counting apparatus.

The attainable signal-to-noise ratio (SNR) for single- molecule detection in a solid by fluorescence excitation can be approximated by Equation (d), where S, is the peak fluo-

S, D Qccr P,z I A h v L U , ~- -

(noise),,, D Qf cr Po z + CbP07 + N d z [ A h v

D Qf cr POT/ A h v ~- - S, (noise),,, D Qf cr Po z + CbP07 + N d z [ A h v

rescence signal from one molecule, Qf is the fluorescence quantum yield, cr ist the peak absorption cross section on resonance, Po is the laser power, z is the integration time (counting interval), hv is the photon energy, Nd is the dark count rate, and C, is the background count rate per Watt of excitation power. The factor D = qQFp4F$ describes the overall efficiency for the detection of emitted photons, where ‘lo is the photomultiplier tube quantum efficiency, F, is the fraction of the total emission solid angle collected by the paraboloid, 4 is the fraction of emitted fluorescence which passes through the long-pass filter, and E; is the total trans- mission of the windows and collection optics along the way to the photomultiplier. The three terms in the denominator of Equation (d) represent shot noise contributions from the emitted fluorescence, background, and dark signals, respec- ti vel y .

According to Equation (d) there are several important criteria that have to be fulfilled for optimum SNR, once the collection efficiency D is maximized. First, the peak absorp- tion cross section cr and the fluorescence quantum yield Gf of the impurity in the matrix should be as high as possible. Further, the area of the laser spot at the sample plane should be as small as possible, which requires tight focusing of the probing laser beam. The power Po cannot be increased arbi- trarily because saturation causes the peak absorption cross section to drop,[s31 cr + a(Z) = cr,/(l + Z/fs), where I is the laser intensity. For maximum fs for organic molecules, it is favorable to have the triplet quantum yield low and the triplet lifetime short (expressions for I, are given in ref. 1541).

To give a concrete example of the application of Equa- tion (d) to a specific material we now consider the parame- ters appropriate for the model system pentacene in p-ter- phenyl at 1.5 K. Prior work has established that QF = 0.78[”] and that cr,, = 9 x 10-l’ cm2.1231 For is we use the measured[551 value of 2.5 mW crK2 , which is lower than the value one would calculate using published photophysical parameters.’”. 571 The collection optics and GaAs photo- multiplier tube yielded a collection efficiency of D = 0.01, and background and dark count parameters of C, = 7 x lo1’

464 Angeu,. Chem. Ini. Ed. Engl. 1993. 32, 457-476

SNR

20

15

10

5

0 I (

Fig. 8 . Signal-to-noise ratio (SNR) for fluorescence excltation of pentacene in p-terphenyl versus laser power P and laser beam cross-sectional area A .

counts W - ' s - ' and Nd = 30 cps, respectively. With these values. a three-dimensional plot of SNR for an integration time of 1 s versus laser power and beam area can be produced (Fig. 8). It is clear that for a fixed laser spot area, an optimal power exists which maximizes the tradeoff between the satu- rating fluorescence signal and the linearly increasing (with P) background signal. The lens focusing arrangement shown in Figure 7 produced a spot size of = ( 5 pm)' located at the midpoint of the area axis. The SNR values predicted by Equation (d) are in reasonable agreement with the experi- mentally obtained values. One final fact to recognize from Figure 8 is that the best-case SNR at smaller and smaller beam areas levels off. This is due to the effect of saturation and shot noise; at smaller and smaller areas the power must be reduced eventually to the point where the SNR is con- trolled by the shot noise of the detected signal [first term in the denominator of Eq. (d)].

Of course. in single-molecule studies in solids, a crucial physical effect not included in Equation (d) must be taken into account. Persistent spectral hole-burning (PSHB), which can be observed for certain impurities in crystals and which is a more or less general phenomenon in amorphous hosts."41 can cause the single impurity to change its absorp- tion frequency before it emits enough photons to be detected above the noise level. The amount of hole-burning that can be tolerated depends upon the total number of molecular excitations required to achieve adequate SNR. A general rule of thumb for practical situations with collection efficien- cy D near 1 % is that approximately lo5 excitations are re- quired to achieve a SNR on the order of 10 with 1 s integra- tion time. This means that the hole-burning quantum efficiency should be This indeed may be the most important factor limiting the number of materials systems suitable for single-molecule studies.

4.2. Fluorescence Excitation Measurements for Pentacene in p-Terphenyl

Recognizing from the S M D experiments using F M detec- tion that pentacene in p-terphenyl is nearly ideal for such

studies, Orrit et al. were the first to apply fluorescenceexcita- tion with high-efficiency collection to this system.[''] Fig- ure 9 shows the first spectra generated with apparatus simi- lar to that in Figure 7 except that an optical fiber rather than a lens was used. The sample itself was a thin sublimed platelet which helped to reduce the volume available for scattering. In the upper traces, the single-molecule signals appear as isolated dots; expansion of the scan range in the lower trace shows a clear, well-defined single-molecule pro- file with much improved SNR. These results led most inves- tigators to subsequently use the fluorescence excitation method.

The entire inhomogeneous line may now be measured over a wide wavelength range in order to provide specific data that can be contrasted with the schematic picture in Figure 1. Figure 10 shows data for a ~10-pm-th ick , low-concentra- tion, sublimed sample of pentacene in p-terphenyl at 1.5 K,12'] which was carefully mounted to avoid strain. This 18 GHz spectrum, obtained by scanning a 3 MHz linewidth dye laser, contains 20000 points; showing all the fine struc- ture usually requires several meters of linear space. Figure 10 top shows the frequency region covering the central part of the inhomogeneous line for the 0, site a t 592.321 nm. The structures appearing to be noise are not; they are direct measurements of the statistical fine structure (SFS) as de- scribed in Section 2. This structure is static and repeatable and arises directly from statistical variations in the spectral density of absorbers with laser frequency. It is immediately obvious that the inhomogeneous line is Par from Gaussian in shape and that there are tails extending out many standard deviations from the center both to the red and to the blue.

More interesting are the spectral features in the wings of the inhomogeneous line (Fig. 10 bottom). At a detuning of - 2.7 G H z and elsewhere, clearly resolved, individual single- molecule peaks can be observed. Similar single-molecule peaks are present on the blue edge of the inhomogeneous line. There is a slight variation in the height of the single- molecule peaks since some molecules are not exactly in the center of the Gaussian intensity profile of the laser beam.

A n p i . C/iw7i. 1171. Ed. EngI. 1993, 32, 451-416 465

16

12

8

l 4 NFl 0

15

10

5

n - -3 -2 -1 0

Av, IGHz 1 - Fig. 10. Fluorescence excitation spectrum of pentacene in p-terphenyl ( T = 1.5 K). The value of 0 on the frequency axis corresponds to a wavelength of 592.321 nm, which is near the center of the 0, site inhomogeneous distribution. N,, = Fluorescence count rate, Av,, = laser detuning. The unit lo3 s - ’ means lo3 counts per second. Top: An excitation spectrum obtained over 10 min with 2 nW of laser power. Bottom: Two spectra on an expanded scale (the upper trace is displaced from the lower) in the wing of the 0, site inhomogeneous distribution. The isolated peaks out in the wing are excitation peaks for single pentacene defects (after ref. [28]).

The total pentacene concentration for the sample can be estimated directly by counting the number of molecules in the spectrum; a value of 1 . 7 ~ 1013cm-3 or 8 x

molmol- ’ is obtained. At different concentrations and in samples with differing levels of strain from mounting, the inhomogeneous linewidth can be varied over a wide range. It has been observed (as in Fig. 9 and confirmed by the IBM group) that in some samples epoxied to the end of an optical fiber the strain can become so great as to spread out the inhomogeneous line over several hundred GHz in frequency space.

Upon close examination of an individual single-molecule peak, the lifetime-limited linewidth of 7.8 f 0.2 MHz can be observedIZ6l (Fig. 11). This value is in excellent agreement with previous photon echo measurements on large ensem- bles of pentacene molecules.‘38* ’*I The single-molecule exci- tation profile is well described by a Lorentzian function, as would be expected, since all inhomogeneous broadening has been removed. The laser intensity required for this measure- ment was 0.5 mWcm-2 (laser power 89 pW), and special care was required to remove the interfering effect of laser frequency drift during the measurements.

In general the homogeneous linewidth (full width at half- maximum, FWHM) of an optical transition in a solid is given by Equation (e), where TI is the excited state lifetime

and T? is the (pure) relaxation time (dephasing time). Pure dephasing effects alter the phase of the excited transition

without causing excited state decay, as for example when a lattice phonon scatters off the impurity molecule. In the pen- tacenelp-terphenyl system T: goes to infinity for low tem- peratures ( T < 4 K), because the host phonons and local modes are essentially quenched. Therefore, the homoge- neous width as shown in Figure 11 is given solely by the

NF, 300 7.8 + 0.2 MHz

IS-’]

200

100

t O L I ’ I ’ ’ ‘ ’ ‘ I I

-40 -20 0 20 40 AvL lMHzl -

Fig. 11. Low-power fluorescence excitation spectrum for a single pentacene molecule in a sublimed crystal of p-terphenyl ( T = 1.5 K). 0 MHz = 592.407 nm, which is in the wing of the 0, site inhomogeneous line. The solid line is a Lorentzian fit to the data (after ref. [26]).

lifetime contribution TI. It is important to recall that in hole-burning experiments[161 the width of a spetral hole is given in principle by twice the homogeneous width, because a spectral hole is a convolution of the population hole (with width Av,, produced during the burning step) and the homo- geneous lineshape (produced during the readout step). In many real (especially amorphous) systems, the hole width, however, can be much larger than 2Av, due to spectral diffu- sion occurring on a broad range of time scale^.['^^ The effect of spectral diffusion on the single-molecule lineshape in a polymeric host is described in Section 6. The point here is that the lineshape in Figure 11 shows neither spectral diffu- sion nor pure dephasing effects; the width has reached the smallest value allowed by Equation (e) and thus is the true homogeneous linewidth.

By slowly translating the laser focal spot across the face of the crystal and obtaining spectra at each position, one may observe single-molecule peaks localized in both frequency and position. It is thus possible to acquire a “spectral land- scape” from the fluorescence excitation spectrum of the sample similar to that obtained for the statistical fine struc- ture at high concentration near the inhomogeneous line cen- ter (see Fig. 5). Figure 12 shows a three-dimensional color plot of spectra taken at a series of overlapping laser spots 0.568 pm apart, in which the displacement was accomplished by translating the incident laser beam across the sample.[2s’ Within the 300 MHz tuning range shown, isolated single- molecule excitation peaks occur at laser detunings of + 20, + 130, and - 120 MHz (relative to the center of the scan) at different positions in the crystal of 30, 35, and 40 pm. The shape of an excitation peak along the position axis is a direct measure of the (Gaussian) intensity profile of the laser beam in the crystal, as probed with the fluorescence emitted by a single molecule. In Figure 12, the spatial width (FWHM) of

466 Angew. Chem. Int. Ed. Engl. 1993. 32, 457-476

Fig. 1 2 “Spectral landscape” of the fluorescence excitation of a single pen- tacene molecule in a crystal of p-terphenyl (T=1.5 K). The horizontal axis covers 300 MHz: the center of the axis corresponds to 592.544 nm. The axis extending into the page was generated by measuring successive, excitation spec- tra (scan time 2 min). The laser focal spot was displaced laterally by 0.57 pm between each measurement to cover a total distance of 40 pm. The intensity of the fluorescence is plotted on the vertical axis.

a single-molecule peak, and hence that of the laser focal spot is ~5 _+ 0.5 pm. The fluorescence peaks have different sizes because the molecules do not pass directly through the center of the laser focus and “experience” different peak laser inten- sities. The frequency widths of the peaks in Figure 12 are slightly larger than the lifetime-limited width (Fig. 11) due to the higher probing intensity used. The other oddly shaped peaks in the figure result from molecules that are spectrally diffusing. This effect will be discussed in more detail in the next section.

Spectra like those shown in Figure 11 are ideal for detailed measurements. For example, the intensity saturation behav- ior of both the linewidth and the emission rate for several single molecules in the wings of the inhomogeneous line was

yielding a (free-space) value for the saturation intensity of I, = 2.5 mWcm-’. Usually, absolute intensity measurements are difficult because of the Gaussian shape of the laser spot and the difficulty in determining the size of the laser spot in the sample. Here, however, the laser spot diame- ter may be easily determined simply by using the single mol- ecule as a probe. In the high-intensity limit, the peak fluores- cence emission rate saturates at (7.2 0.7) x lo5 photons per second. As the peak emission rate saturates, the emission rate in the wings of the line continues to increase with inten- sity, and the homogeneous linewidth broadens according to the expected form [Eq. (f)].1601 It is remarkable that the value

of I, expected based on previously determined photophysical parameters for pentacene in p-terphenyl is larger than the measured value by more than a factor of 20. The exact rea- son for this discrepancy is unknown, although it is reason- able that some of the photophysical parameters are modified for the single molecules located in the wings of the inhomo- geneous line. It is likely that the intersystem-crossing rate and/or triplet lifetime are affected rather than the fluores-

cence lifetime, since the intersystem-crossing process is more likely to be affected by strain.[561

It is also possible to measure the linewidths (FWHM) of the signals of single pentacene molecules as a function of temperature. Such data have been acquired at temperatures up to 10 K where the linewidth increases by almost a factor of 100 compared to the value at low temperatures.[28] The data are in excellent agreement with previous photon echo experiments“’. 61, 621 in which the temperature dependence of the echo decay time was found to follow a form described by dephasing via a single pentacene librational moder6’] with librational energy AE/k = 38 _+ 1 K = 27 If: 0.7 cm-’. To date, this same temperature dependence was found for all single molecules studied, indicating that the local mode is intrinsic to the defect center and is not influenced by the specifics of the local environment. This is to be contrasted with the local electric fields which do show a distribution (Section 7).

5. Detection of Spectral Diffusion of a Single Molecule in a Solid

In the course of the fluorescence excitation studies by Am- brose et al. on pentacene inp-terphenyl, an unexpected phys- ical effect was observed : spectral diffusion of individual pen- tacene impurity molecules in a crystal at 1.5 K.[”I Here, spectral diffusion means changes in the resonance frequency of a defect at low concentration due to changes in the nearby host, rather than the energy transfer effects that can occur for impurity centers at high con~ent ra t ion .~~’~ Two distinct classes of impurity molecules were identified: class I, which have center frequencies that are stable in time, and class 11, which show spontaneous, discontinuous jumps in resonance frequency of 20-60 MHz on a timescale of 1-420 s. Class I1 molecules were responsible for the distorted single-molecule peaks in Figure 12 which appeared to change shape between the individual laser scans. Figure 13 shows the behavior of a particular class I1 defect more clearly; the laser scan speed was increased to 1 scan every 2.7 s so that the spectral posi- tion of the molecule could be recorded with improved time resolution. The upper part of the figure shows how the reso- nance frequency of a spectrally “jumping” class I1 defect evolved with time, where each trace was digitally smoothed. A digital waveform recorder located the peak in each scan and recorded this resonance frequency as a function of time in the lower part the figure. For this defect, the optical tran- sition energy appears to have a preferred set of values, and the defect performs spectral jumps between these values that are discontinuous on the one-second timescale of the mea- surement. This type of jumping behavior occurred for some tens of class I1 defects. In one case, one single molecule was observed that discontinuously jumped between only two al- lowed frequencies, but spectral jumps between a larger num- ber of allowed frequencies was much more common (see below).

Before summarizing other types of behavior, we should present two crucial observations: First, the occurrence of class I1 defects was quite common in the wings of the inho- mogeneous line (increasing to 40 YO of the studied molecules at a distance of + 0.23 nm from line center), but only class I

Angcw. Chem. Int. Ed. Engl. 1993,32,451-4?6 467

200

1 100

Y O

[MHz] 0

-100

- -200 -100 0 100 200

Av, [MHz] -

t I i

t k.1-

Fig. 13. Spectral jumps in the resonance frequency Y” of a class I I single pen- tiicene defect in p-terphenyl ( T = 1.5 K). In the upper half of the figure are individual excitation spectra measured successively (scan time 2.7 s). The peak i n each spectrum is represented a s a function of time I in the lower half of the figure (after ref. 12x1). A!,, is the laser detuning.

defects were observed in a spectral region from 0.003 to 0.01 nm from line center. The fraction of pentacene mole- cules showing class 11 behavior increased for wavelengths further and further from line center, suggesting that disorder in the crystal is partially responsible for the spectral migra- tion. Second, the jumping rate did not depend upon the laser power used to measure the fluorescence excitation spectrum. This is the main reason that the observed changes in reso- nance frequency were attributed to a spontaneous process rather than a light-induced spectral hole-burning ef-

The behavior shown in Figure 13 shows relatively discon- tinuous resonant frequency changes, but in fact a wide array of characteristics was observed. Figure 14 provides an ex- ample that also illustrates the general effect of increasing temperature. These measurements of the time dependence of the resonance frequency of a single molecule were taken on a sample mounted on the end of a single-mode optical fiber placed at the focus of the collection paraboloid. This “wan- dering” defect spectrally diffused rapidly, and was found at a new frequency in every laser scan. During the 1600-second measurement a t 1.5 K (Fig. 14 top), the spectral wandering for this defect was confined to a 500 MHz region. At 4.0 K (Fig. 14 bottom), the wandering range expanded to 700 MHz, and the spectral diffusion rate also appears to be higher. This could have been due to a larger number of small jumps between the laser scans, or the spectral jump sizes may have increased with temperature.

Of course, a detailed study of the temperature dependence of an appropriately defined average jumping rate would help to identify the source of the spectral diffusion effect. Such data have not been obtained to date for technical reasons relating to the difficulty of following the same single mole- cule over the entire temperature range. In samples attached to the end of the optical fiber molecules with wandering

behavior like that in Figure 14 were found almost exclusive- ly, which reflects the increased disorder in these samples. In future work, it should be possible to obtain useful tempera- ture-dependence data even with the lens arrangement (Fig. 7) by cooling below 1.5 K with 3He or a dilution refrig- era tor.

r 1

Fig. 14. Qualitative increase in spectral diffusion rate with temperature. In both traces the resonance frequencies v g for a spectrally jumping molecule near the 592.582 nm excitation wavelength are shown. This molecule jumps often. ap- pearing at a new frequency in each spectrum (scan time 2.7 s). Raising the temperature from 1.5 K (top trace) to 4.0 K (bottom trace) appears to increase the spectral diffusion rate and jumping range (after ref. 12x1).

As a final illustration of the fascinating spectral diffusion phenomenon, Figure 15 shows the peak frequency trend of another pentacene defect over 1.6 h at 1.5 K. For this defect, which is on the low-frequency side of the inhomogeneous distribution, the overall trend can be described as “creeping” by successive jumps towards higher optical frequencies. As

400

* ____--~.__L_-L--

t Is1 - Fig. 15. Frequency “creep” of a spectrally jumping pentacene defect over an extended time. The peak frequency tlo of a class 11 defect near 592.544 nm (on the long-wavelength side of the 0, inhomogeneous distribution) spectrally jumps no more than 100 MH7 on short timescales. hut tends towards higher frequencies over 1 .h h. The inset. an expansion of the trace recorded over 600s. shows the individual jumps <80 MHz. (after ref. (281).

shown in the inset, there are residence times on the order of 30 s. and the molecule appears a t new, higher frequencies a t later times. This “creeping” pentacene defect may be in an environment that is structurally relaxing at 1.5 K into a n environment more typical of those found at the center of the inhomogeneous line.

The resonance frequency of an impurity molecule in an inhomogeneously broadened line is extremely sensitive to the strain a t the position of the molecule. Thus the spectral jumps appear to occur because the class I1 pentacene mole- cules are coupled to an (unidentified at present) ensemble of two-level systems (TLS) in the host crystal undergoing phonon-assisted tunneling or thermally activated barrier crossing. One possible source for the tunneling transitions could be discrete librations of the central ring of the nearby p-terphenyl molecules about the molecular axis. As Figure 3 shows, the p-terphenyl molecules have a particular dihedral angle between the central and outer phenyl rings, depending upon the specific position in the When the mono- clinic, room-temperature crystal strucure becomes triclinic below 170 K, it is not unreasonable to postulate that the sample may contain several single-crystal domains even though the phase transition is not destructive to the sam- ple.[h31 Thep-terphenyl molecules in a domain wall may have lowered barriers to such central-ring tunneling motions, and the pentacene molecules near the domain walls would “sense” such local motions and show class I1 behavior. Further experiments are necessary to conclusively identify the molecular motions responsible for the effect. Of course, the spectral diffusion surprisingly observed here in a crys- talline system is analogous to spectral diffusion processes that play a crucial role in the physics of glasses and other amorphous materials.[h41 Most importantly, with the single- molecule detection technique the spectral changes can be followed in real time for each individual impurity molecule; n o ensemble averages over “equivalent” centers need be made.

6. Single-Molecule Spectroscopy in Polymeric Hosts

6.1. Physical Properties of Glasses and Polymers at Low Temperatures

The experiments described so far were performed with single impurity molecules doped into a crystalline matrix. Amorphous systems such as glasses and polymers have a number of interesting physical properties a t low tempera- tures that are quite different from those for crystalline

A wealth of information on the low-tempera- ture dynamics of amorphous systems was obtained by dop- ing these materials with optical impurities and probing them with optical line-narrowing techniques such as fluorescence l ine-nar r~wing , [~’~ persistent spectral h~le-burning,[’~] and photon

To understand the optical properties of these systems, a brief description of the amorphous state is in order. A glassy or amorphous material is characterized by a complex, multi- dimensional potential energy surface. According to the two- level system (TLS) model, the potential energy surface can be

approximated by a distribution of asymmetric double-well potentials or so-called two-level systems. The TLS model assumes that a t low temperatures only the two lowest energy levels of each double-well are important. Transitions from one side of the double-well to the other occur by phonon- assisted tunneling and represent changes in the local struc- ture of the glass. As a result of the broad distribution of barrier heights and well-asymmetries, structural relaxation processes can occur on a wide distribution of timescales. When an impurity molecule is doped in an amorphous solid, its optical transition can couple to the TLSs (e.g. by dipole- dipole coupling), and the lineshape of the optical transition reflects the dynamicdl processes of the host.‘“’

One important physical effect that occurs often in amor- phous hosts is persistent spectral hole-burning (PSHB). In PSHB experiments, narrow bandwidth laser irradiation is used to select a reasonantly absorbing subensemble of molecules out of the inhomogeneously broadened absorp- tion band. The optical excitation induces either photochem- ical changes in the excited centers or photophysical (non- photochemical) alterations in the nearby host, and a narrow spectral hole can develop in the absorption because the al- tered centers no longer absorb at the laser wavelength. While photochemical hole-burning can occur in amorphous or crystalline systems, the nonphotochemical process is an al- most general phenomenon in amorphous systems and is most likely caused by TLS transitions induced by the laser e~citation.’~’] By measuring the hole-shape as a function of temperature and/or thermal cycling,[16] information on the host dynamics can be obtained.

6.2. Detection of Single Perylene Molecules in Pol yet h y lene

Aromatic hydrocarbons in non-hydrogen-bonding ma- trices are systems that show nonphotochemical hole-burning and have low PSHB quantum efficiencies. Taking this im- portant prerequisite into account, perylene in a polyethylene matrix was found to be a suitable candidate for single- molecule d e t e ~ t i 0 n . l ~ ~ ~ Furthermore, the photophysical parameters for this system are favorable: the homogeneous linewidth of the optical transition is narrow, the absorption cross section ((r, = 3.5 x 10-l‘ cm2) and the fluorescence quantum yield (P, = 0.98 are high, and the triplet yield and lifetime are low.

The maximum of the inhomogeneous line for the lowest electronic transition of perylene in polyethylene lies at ap- proximately 440 nm. The width of the inhomogeneous distri- bution is much larger than in a crystalline system, and single molecules were detected in the red wing of this distribution between 445 and 450 nm. In Figure 16 a fluorescence excita- tion “spectral landscape” of a perylene-doped thin film of polyethylene is shown at 1.5 K. This picture was taken with the same procedure as Figure 12. The signal sizes of the six strong single-molecule fluorescence peaks are again differ- ent, partly because the molecules “experience” different peak laser intensities. In an amorphous matrix, however, the orientations of the impurity transition dipoles are statistical- ly distributed, and with a fixed polarization of the incoming laser the single molecule fluorescence intensities vary as

AngiJ!t,. (’licm. int. Ed. EngI. 1993, 32, 451-476 469

Fig. 16. “Spectral landscape” of the fluorescence excitation of single perylene defects in a polyethylene film. Each “mountain” represents the fluorescence from an individual molecule as the probing laser scans the frequency (6.1 GHz, horizontal axis) and is translated spatially across the face of the sample (23 pm, axis extending up and right).

cos2H, where H is the angle between the laser polarization and the transition dipole axis. Hence, in this case there are two mechanisms that can lead to varying signal intensities. A close examination of the signal shapes along the frequency axis reveals that these shapes are slightly distorted. This dis- tortion is due to a real physical effect, namely spectral diffu- sion, the various manifestations of which will be described in the next section.

6.3. Spectral Diffusion in a Polymeric Host

In the pentacenelp-terphenyl system the observation of spectral diffusion of single molecules was quite surprising, as the phenomenon occurred in an ordered crystalline material. By contrast, in disordered, amorphous matrices spectral dif- fusion is a well-known p h e n ~ m e n o n . [ ~ ~ ~ “ * ] In the TLS pic- ture spectral diffusion occurs due to spontaneous (phonon- driven) transitions in the double-well potentials of the host when the impurity molecules are in their electronic ground states. In hole-burning experiments spectral diffusion is ob- servable by the time-evolution of the hole shapes (broaden- ing) after the burning process.[691 How does spectral diffu- sion manifest itself in single-molecule experiments in a polymer?

In the perylene/polyethylene system spectral diffusion ap- peared in two ways in single-molecule spectra.[701 First, dis- continuous jumps in frequency space on the scale of several hundred MHz between or during consecutive laser scans (scan time 2.86 s) were observed which were similar to the effects observed with pentacenelp-terphenyl (Section 5). Sec- ond, a broadening of the single-molecule Iineshape was ob- served which varied from molecule to molecule. The ob- served linewidths ranged from 52 MHz to 142 MHz, and all these values were larger than the lifetime-limited width of 22.7 MHz. It should be mentioned that part of the observed line-broadening could be due to pure homogeneous dephasing by fast, global (non-local) TLS transitions. Ac- cording to standard theories, this contribution to the width, however, is generally assumed to be the same for all mole- cules.

These results give direct evidence that spectral diffusion may occur over a range of frequencies and timescales. When

the TLS model is employed, the experimental findings can be qualitatively explained by a hierarchy of TLSs surrounding the impurity. Distant TLSs produce fast shifts that are small in magnitude; in this case spectral diffusion appears as a broadening of the linewidth on the one-second timescale of the measurement. The closer TLSs produce larger shifts that are more infrequent; in this case spectral diffusion appears as frequency jumps which can be resolved on the experimental timescale.

6.4. Spectral Hole-Burning of a Single Molecule

A spectral hole usually refers to a dip in the inhomoge- neously broadened absorption spectrum of many molecules when light irradiation alters the absorption frequencies of a portion of the resonant absorbers. In the single-molecule regime, however, only the isolated absorption profile of a single center is present. When photochemical or photophys- ical changes occur as a result of optical excitation, the ab- sorption line simply appears to vanish as the resonance fre- quency of the single center shifts away from the laser frequency. As the underlying mechanisms are the same in both cases, we will continue to use the term persistant spec- tral hole-burning (PSHB) even for the single-molecule case.

An example of spectral hole-burning of a single perylene molecule in a polyethylene host is presented in Figure 17.

1200

1 n

600 A 400

-1000-500 0 500 1000 AuL [MHzl -

Fig. 17. Persistent spectral hole-burning (PSHB) of a single perylene molecule in a polyethylene film at 1.5 K (see text). 0 MHz = 488.021 nm. The laser power for burning and scanning is 9 nW, and the scan time is 25 s (after ref. [29]). The vertical scale is correct for trace a, the other traces have the same scale but are offset vertically for clarity.

Before the traces shown in the figure were recorded, the molecule was scanned five times, and no significant changes were observed. Traces a, b, and c show three additional scans of the molecule. After trace c the laser was tuned into reso- nance with the molecule until the fluorescence decreased suddenly. Trace d was then acquired, which showed that the resonance frequency had shifted by more than f 1.25 GHz

470 Angew. Chem. inr . Ed. Engi. 1993,32,457-476

as a result of the light-induced change; in other words, PSHB had occurred. A further scan some minutes later (trace e) showed that the molecule surprisingly returned to the burn- ing frequency. After trace g the molecule was “burnt” again, and the whole sequence could be repeated several times.

The exact location of the new resonance frequency, how- ever, could not be determined in these experiments. By anal- ogy with previous nonphotochemical hole-burning studies of large ensembles of molecules,” ’I the shift may be expected to be as much as IOOcrn-’. Besides the reversible single- molecule hole-burning illustrated in Figure 17, it was pos- sible to observe other single molecules where the light- induced change was irreversible on the timescale of the ex- periment. The irreversible process was more common at high light power levels.

The possibility of burning one and the same molecule sev- eral times was used to determine the power dependence of single-molecule PSHB and to measure the kinetics of this process. Figure 18 shows that with increasing power, the burning time, although stochastically distributed, decreases. The power dependence of the hole-burning process was con- firmed in this way for many single molecules. The experi- ments unambiguously showed that the single-molecule hole- burning is truly a light-driven process in contrast to excitation-power-independent spectral diffusion.

400 1 I

350

300

t 250 200

NFI

[IOS”I 150

1800

1600

1400

1200

.. . 1000 1

0 200 400 600 t IS1 -

Fig. 18. Illustration of the power dependence of the hole-burning process for a single perylene molecule in a polyethylene film. a) The laser is tuned to reso- nance (i = 448.159 nm) with the single molecule in the first 10 sat a power level of 4.5 nW. The abrupt drop of the fluorescence signal at 260 s is the hole-burn- ing event; the return of the fluorescence signal indicates that the molecule has returned to its original frequency, only to be burnt again, and so on. b) The laser power level was increased to 27 nW; now the time in resonance, although stochastic. is clearly shorter (after ref. [29]).

In Section 6.3 two types of TLSs interacting with the im- purity were discussed, those producing broadened single- molecule lineshapes, and those producing resonance fre- quency jumps. There are, however, also the so-called external TLSs which are created by doping the host with the impurity molecules.1711 These TLSs are thought to be in the close vicinity of the impurity and effectively locked because the barrier to configurational changes is too high. A com- mon model for nonphotochemical hole-burning” 71 assumes that by optical excitation of the impurity this barrier is low-

ered and a transition of the TLS can take place. The sponta- neous return of perylene molecules after a burning event to exactly the same wavelength was somewhat surprising, though not absolutely unexpected. It suggests that coupling to exactly one dominant nearby TLS, rather than a succes- sion of TLS configurations, is involved in the hole-burning process. In this picture optical excitation induces a (phonon- assisted) transition in the double-well potential in one direc- tion which is reverted by a spontaneous (phonon-assisted) transition at some time later when the molecule is in its electronic ground state.

6.5. Measurement of the Stochastic Phototransformation Kinetics of a Single Molecule

The single-molecule hole-burning experiments are mea- surements with a single quantum system, although the mole- cule and its surrounding matrix cage have to be regarded as a kind of “supermolecule”. Therefore, it is not surprising that the burning time for one molecule a t a fixed power level is a stochastic quantity. By measuring a large number of burning events for one and the same perylene molecule in a polyethylene host it was shown that the burning times are exponentially distributed (Fig. 1 9).I7O1 This may be under- stood by the following simple argument.

ts Is1 - Fig. 19. Histogram of a random sample of 54 burning events measured for a single perylene molecule in a polyethylene matrix by using a power level of 4.5 nW ( T = 1.5 K, 1 = 448.156 nm). The plotted curve is the result ofan expo- nential fit to the data (after ref. 1701). N is the number of events per time interval.

Single-molecule hole-burning is an example of a Poisson random process. The probability distribution for r successes (hole formation) in a finite time interval 7 is therefore given by P(r,7) = exp( - Az)/(Azyr!. In the hole-burning experi- ment, however, the waiting time before the first burning event (ix. r = 0) was measured, and this waiting time there- fore has the probability distribution P(O,r) = exp( - 1-7). This corresponds to the familiar result that the distribution of waiting times between Poisson random events is exponen- tial. The smooth curve in Figure 19 is a result of a fit of a simple exponential to the data. The histogram of the random sample of burning times is reasonably well approximated by an exponential distribution function with rate parameter A = 0.18 s-I. This also means that the single perylene mole- cule investigated has an average hole-burning quantum efi- cieny of 2.9 x per photon absorbed.

A n j y w . Chein. In [ . Ed. EngI. 1993. 32, 457-476 47 1

It is interesting to point out a formal analogy between these experiments and “quantum-jump” measurements with single trapped ions in a vacuum. In the latter investigations the bright fluorescence from a strong (allowed) transition ceases when the single atom “‘jumps” into a dark state which is weakly coupled to the ground state by a forbidden transi- tion. In this case the number of quantum jumps per unit time is given by a Poisson distribution and the waiting times be- tween quantum jumps by an exponential distribution as we.l,172, 731

7. Stark Effect Studies with Single Molecules

The fact that spectra of a single molecule in a solid can be obtained with high signal-to-noise ratios naturally leads to measurements of such spectra under the influence of external fields. One can imagine that Zeeman effects, Stark effects. and stress-induced splittings and shifts can be observed. In recent work, two groups have completed Stark effect studies on single molecules, in one case in a crystalline host and in the other case, a polymeric host.

7.1. Pentacene in p-Terphenyl Crystals

The first single-molecule Stark effect studies of the pen- tacenelp-terphenyl system were performed by Wild et al. us- ing a longitudinal geometry in which the sample was held between a thin metal plate with a 5 pn pinhole and a Sn0,- coated glass plate.[311 (In fact, both the linear and quadratic Stark effects for this single-molecule system were utilized in the double-modulation scheme reported in Section 3 for the initial detection of single molecules with F M absorption.) In the recent work, fluorescence excitation spectra of single molecules were recorded with various DC external electric fields applied in order to determine specific values for the polarizability change and the internal field. In all cases. only shifts and no splittings of the single molecule spectra were observed.

Figure 20 shows the energy shifts recorded for four single molecules, along with best-fits to the data using second-

€ [kV crn-’l - Fig. 20 Stark shift of four molecules of pentacene A-D in p-terphenyl as ii function of electric field The plotted curves are the result of second-order polynomial fits to the data (after ref. [ i l l ) .

order polynomial^.[^ In general, a quadratic shift was ob- served with an offset from zero which was different for dif- ferent molecules. The high symmetry of the pentacene mole- cule is consistent with a quadratic shift, and the linear term was attributed to different internal crystal fields a t the

positions of the various single molecules. The data were used to determine that the internal fields ranged from - 1.6 x lo3 kVcm-’ to +0.8 x lo3 kVcm-’, and that the polariz- ability change Ax ranged from 1.1 x Fm2 to 2.5 x

Fm2. The unambiguous observation of a quadratic shift, which was relatively constant from molecule to rnole- cule, and a first-order shift, which varied considerably from molecule to molecule, gives direct evidence for one underly- ing source of inhomogeneous broadening that has been long postulated -randomness in the local crystal field.

7.2. Terrylene in Polyethylene

Numerous Stark effect studies of impurity molecules in amorphous materials have been performed over the last decade by using hole-burning technique^."^. ”I Even with centrosymmetric molecules, only linear Stark effects were observed, due to the reduction of symmetry caused by local fields. To address the important question as to whether or not linear Stark effects persist down to the single-molecule level, Orrit et al. have recently studied a new system com- posed of terrylene molecules in low-density polyethylene.1321 The terrylene molecule is similar to perylene, except that three rather than two naphthalene molecules are condensed at the peri positions. This modification conveniently shifts the first electronic transition to longer wavelengths. The thin films were sandwiched between two transparent conducting plates for the optical measurements. As with pentacene in p-terphenyl, only shifts of the single-molecule lines were ob- served.

Figure 21 shows the observed frequency shifts for a selec- tion of six single molecules. Only linear Stark shifts were detected, suggesting that the local fields were quite effective

1.0 -

d U

[GHzl 0.0 --

E IkV cm-‘] - Fig. 21. Stark shift o f single terrylene molecules 111 polyethylene as a function of electric field. The plots are linear to within experimental error; the magnitudes and signs of the slopcs depend upon the orientation of the field relative to the molecule and the matrix cage. The largest slope corresponds to a change in dipole moment of several Debye (after ref. [ 3 2 ] ) .

472 Angeu. Chrm. hi. Ed. Engl. 1993, 32, 457 -476

in lowering the molecular symmetry. By studying a large number of single molecules, the distribution of Stark coeffi- cients could be sampled, and positive coefficients were found to be more common than negative coefficients. It is certainly clear that these results provide individual measurements of the local fields, and that such perturbations are averaged in the conventional measurements at large values of NH. If it will be possible to measure the splitting coefficients for a single molecule with several directions of applied field, more specific information about the local symmetries may be ob- tained.

8. Measurements of Quantum Effects with Single Molecules in Solids

In all the experiments described in the preceding sections the single molecule served as an ultrasensitive probe for mea- suring truly local host-guest interactions. A single molecule can also be used to study the fundamental interaction of light and matter in experiments in which the fully quantum- mechanical nature of this interaction is revealed. So far in- vestigations of this type with single particles were limited to single atoms stored in radio-frequency traps by photon- recoil cooling. A variety of fascinating experiments such as quantum jumps, quantum collapse and revival, photon anti- bunching, and many others were realized with laser-cooled ions.“. However, for all molecules, even diatomic species, the internal degrees of freedom prevent laser-cooling, and therefore trapping of a single molecule in a vacuum has not been achieved to date. As illustrated in the earlier part of this paper, however, single molecules can be easily “trapped” and observed optically in a solid. When the molecules are impurities in a solid and the samples are cooled to liquid- helium temperatures, the solid acts as a “trap” for the single impurity molecules. They are effectively held at rest, and in many cases, rotation of the impurity molecule is quenched and recoil effects are usually small (less than the optical line~idth).‘~’. 761

One interesting aspect of the interaction of light and mat- ter concerns the correlation between photons radiated by a single atom or molecule. As was shown for Na atoms in a weak atomic beam177J or a single trapped Mg’ ion,[781 the correlation between successive photons emitted by a single atom (ion) decreases near t = 0 (photon antibunching). This is in marked contrast to the case for coherent light, where the correlation is independent of the time separation between photons, and for thermal light, which shows an increase in correlation (photon bunching) near t = 0.

Photon antibunching in the resonance fluorescence of a single atom was predicted by Carmichael and Walls.[791 This phenomenon is a true signature of a quantum-mechanical radiation field which can be nicely rationalized with the fol- lowing simple picture. In the correlation measurement the joint probability for the arrival of a photon at time t = 0 and the arrival of a photon at t > 0 is recorded. After emission of a photon at i = 0 the quantum system is in its ground state since it just emitted the photon. The probability of emitting a second photon at t = 0 is zero because the molecule cannot emit from the ground state. On the average, a time of half a Rabi period must elapse for the molecule to have a finite

probability of being in the excited state and hence emitting a second photon.

Photon antibunching must be observed on a short time- scale comparable to the excited singlet-state lifetime. Corre- lation measurements on the nanosecond timescale, or to be more specific, measurements of the second-order or intensity correlation function g(”(2) were performed with single pen- tacene molecules in a p-terphenyl host.[331 The exciting laser pumped the lowest zero-phonon purely electronic transition S, + So, and the photon correlation properties of the vibron- ically shifted fluorescence from the excited singlet state S, were analyzed. As in the single-atom experiments. the delay time distribution of consecutive pairs, N(z) , which is propor- tional to g”)(T), was measured in a Start-Stop experiment, that is, by using a beamsplitter and two photomultipliers (PMTs) to record the emitted fluorescence. Detection of a photon from the first PMT starts a delay time counter, and the detection of a photon by a second PMT stops the coun- ter. The distribution of such delay times is recorded for many Start-Stop pairs.

Plots of N(z) are shown in Figure 22 for different levels of Rabi frequency (which is proportional to the square root of the intensity). The antibunching in the correlation function is clearly evident at short times t -+ 0. With increasing power the background due to accidental pair correlations increases, leading to an increasing deviation of N(2) from zero at the origin. The solid lines in Figure 22 show the resuIts of numer- ical fits to the data using the solutions of the optical Bloch equations for a three-level system. At the highest power level (Fig. 22 c) the correlation function shows, besides the anti- bunching, the expected Rabi oscillations which are damped out during the excited state lifetime.

40

30

20 N I’d

10

12

1 8 N I T )

4

0 -100 0 100 200

ths l - Fig. 22. Measured intensity correlation N(T) (in counts per 0.9 ns] for a single pentacene molecule ( A % 593.4 nm). The antibunching is clearly seen for f -t 0. Rabi frequencies SZ: a) 11.2 MHz; b) 26.2 MHz; c) 68.9 MHr. The solid lines are fits to the data with $2 = I -10 MHz (a), 25.5 MHz (b), and 71.3 MHz (c) (after ref. [33]).

Angew. Chrm. Inr. Ed. Engl. 1993, 32, 451-476 473

Since pentacene in p-terphenyl is effectively a three-level system when lowest triplet state is included, photon bunch- ing should be observed for much longer times, comparable to the 40 ps triplet lifetime. This is a consequence of the fact that on average, the pentacene molecule emits roughly 200 photons due to singlet-singlet excitation before intersys- tem crossing into the “dark” triplet state occurs (the triplet yield is 0.0047[57]). This purely classical effect was observed clearly by Orrit et al.[251 and used to prove that the spectra in the early experiments arose from single molecules.

These first results on quantum optics in a solid demon- strate that single-molecule spectroscopy in solids can be used to investigate truly quantum-mechanical effects for multi- atom molecules with zero-phonon optical transitions. Here the experimental data were not affected by transit time or secular motion effects as are the beam or ion-trapping meth- ods. However, background signals and intersystem crossing into the triplet state did limit the single-molecule antibunch- ing signal and must be controlled in each specific case. As long as the lowest electronic transition of the molecule is pumped, the presence of vibrational levels in the ground state and the detection of nonresonant fluorescence does not prevent the observation of photon antibunching.

9. Summary and Outlook

By utilizing the near-quantum-limited performance and low background of laser frequency modulated (FM) spec- troscopy, the intrinsic fine structure on inhomogeneous lines in solids, statistical fine structure (SFS), was detected for the first time. With a detailed understanding of SFS and im- provements to FM spectroscopy to remove residual ampli- tude modulation (RAM), it thus became possible to measure the optical absorption spectrum of a single molecule of pen- tacene in p-terphenyl. Dramatic improvements in the signal- to-noise ratio resulting from the use of fluorescence excita- tion with high-efficiency collection led to the observation of lifetime-limited widths, to saturation and dephasing studies, and to the surprising observation of spectral diffusion for a single impurity molecule in a crystal. Extensions of these investigations to systems with polymeric hosts allowed study of the spectral diffusion process widely postulated in amor- phous materials, as well as to the observation of spectral hole-burning and stochastic kinetics for a single molecule. Stark effect studies in both crystals and polymers have yield- ed important new information about local symmetries and local fields. Fially, single-molecule techniques in recent work have led to the first quantum optics in a solid-the detection of photon antibunching for a single molecule.

The success of single-molecule detection and spectroscopy in solids opens up a new frontier of single-absorber experi- ments in which the measured properties of the absorbing center are not averaged over many “equivalent” absorbers. Here the absorbing entity is exquisitely sensitive to the sym- metry and perturbations introduced by the local environ- ment such as the local vibrational modes and the true local fields. While as a general technique the method presented here is not applicable to all molecular impurities, it can be applied to the large number of absorbing ions and molecules in solids that have zero-phonon transitions, reasonable ab-

sorption strength, and efficient fluorescence. The detectabil- ity of the resulting single-center signal, which ultimately de- pends upon the specific sample and weak or absent spectral hole-burning, must be evaluated in each case.

A number of fascinating future experiments based on the single-molecule detection techniques presented here may be contemplated. The temperature dependence of the spectral diffusion process in crystals may help to identify the source of the effect. It would be particularly interesting to measure the temperature dependence of the linewidth in a polymeric host to attempt to resolve the current controversy about dephasing processes in these systems. Nonlinear spec- troscopy to measure the dynamic Stark effect for a single isolated molecule may also be performed. With the proper choice of lifetimes, one would expect quantum jumps and other processes observed for single ions in vacuum electro- magnetic traps to become directly observable. The door is also open to true photochemical experiments on single ab- sorbers, measurements of the dispersed fluorescence from a single molecule, and the possibility of optical storage with single m o I e c u I e ~ . [ ~ ~ ~

In one novel experiment now possible the emission from a single molecule could be used as a light source of sub- nanometer-dimensions for near-field optical microscopy. Another possibility would be to perform cavity quantum electrodynamics studies with a single molecule in a solid. It is to be expected that single-molecule spectra will be ob- tained at higher and higher temperatures to extend the appli- cability of these studies to a wider range of materials. In all cases, improvements in the signal-to-noise ratio would be expected to open up a new class of applications. Because this field is only in its infancy, the possibilities are only limited at present by the imagination and the persistence of the exper- imenter and the continuing interest of the theoretician in the properties of single-quantum systems in solids.

10. Glossary

Coherent transient spectroscopy and photon echoes: In the present context we will limit our short explanation to the case of optical coherent spectroscopy where only two levels, the ground and excited electronic state of an atom or mole- cule, are involved. Coherent excitation of such a system with sufficiently high intensity lasers creates a coherent superposi- tion of the ground and excited state wave functions. The coherent superposition, which is characterized by a well- defined phase relation between the two levels, leads to inter- ference effects whose time evolution can be monitored with special spectroscopic techniques. The coherent state is de- scribed by the off-diagonal elements of the two-level density matrix in the optical Bloch equation formalism. The coher- ence is a transient phenomenon which is destroyed rapidly by population and phase relaxation processes. One example of coherent transient spectroscopy is the photon echo where the decaying coherence initially created by a first intense light pulse can be reestablished by a properly timed second light pulse. The photon echo can be formally described by the time evolution of a pseudo-spin vector in a fashion equiv- alent to the spin echo in magnetic resonance spectroscopy.

474 Angew. Chem. h i . Ed. Engl. 1993,32,457-416

The time decay of the photon echo amplitude also gives information about the underlying homogeneous width when inhomogeneous broadening is present. See for ex- ample, L. Allen, J. H. Eberly, Optical Resonance and Two- Level Atoms, Dover, New York, 1987.

Electron-phonon coupling and zero-phonon transition : When an impurity molecule in a solid matrix is electronically excited, the host vibrations (phonons) can couple to the elec- tronic excitation (electron-phonon coupling) in the same way as is well known for the intramolecular vibrations of the impurity. Linear electron-phonon coupling, where the cou- pling strength is given by the displacement of the excited state potential surface with respect to the ground state poten- tial surface, gives rise to phonon sidebands of the purely electronic transition line in absorption and emission. The purely electronic transition with no net creation or destruc- tion of phonons is called the zero-phonon transition and can be viewed as the optical analogue of the recoil-free Mossbauer line. Quadratic electron-phonon coupling leads to a broadening of the zero-phonon line by phonon scatter- ing. See for example, A. M. Stoneham, Rev. Mod. Phys. 1969, 41, 82; R. H. Silsbee, in Optical Properties of Solids, (Eds.: S . Nudelman, S. S. Mitra), Plenum, New York, 1969, p. 607; K. K. Rebane, Impurity Spectra of Solids, Plenum, New York, 1970, p. 99.

Frequency modulation (FM) spectroscopy: In FM spec- troscopy the laser is frequency-modulated at a high frequen- cy, narrow spectral features in the sample convert the fre- quency modulation into amplitude modulation, and the amplitude modulation of the light beam is detected with a high-speed detector and a lock-in amplifier. See G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 1983, 32, 145.

FWHM: Full width at half-maximum; a convention for measuring the width of spectral lines or of laser beam pro- files.

Photon antibunching: A purely quantum-mechanical cor- relation property of a light beam which states that the prob- ability of detecting two photons separated by a small time interval At approaches zero as At --f 0. See for example, R. Loudon, The Quantum Theory of Light, Clarendon, Oxford, 1983, pp. 226-229.

Rabi period: In the time evolution of a two-level atomic system pumped by light, the Rabi period is the time required for the superposition of the two states to go from pure ground state, through the excited state, and back to the pure ground state again. See L. Allen, J. H. Eberly, Optical Reso- nance and Two-Level Atoms, Dover, New York, 1987.

Residual amplitude modulation (RAM): Unwanted ampli- tude modulation of the laser beam in FM spectroscopy which represents a spurious background signal that can limit sensitivity. See for example, E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, J. Opt. SOC. Am. B 1985, 2, 1320.

Statistical fine structure (SFS): This effect refers to the intrinsic variations in absorption coefficient versus wave- length which occur for inhomogeneously broadened transi- tions due to number fluctuations in the spectral density of absorbers. See T. P. Carter, M. Manavi, W. E. Moerner, J. Chem. Phys. 1988, 89, 1768.

SMD: Single-molecule detection. SNR: Signal-to-noise ratio.

Spectral hole-burning: In spectral hole-burning experi- ments, narrow-bandwidth laser irradiation is used to select the resonantly absorbing subensemble of molecules out of an inhomogeneously broadened absorption profile. The optical excitation induces either photochemical changes in the excit- ed centers or photophysical (nonphotochemical) alterations in the nearby host, and a narrow dip (spectral hole) can develop in the absorption spectrum because the altered cen- ters no longer absorb at the laser wavelength. The width of the spectral hole can provide information about the underly- ing homogeneous linewidth when spectral diffusion effects are absent. Peristent spectral hole-burning (PSHB) refers to the situation in which the spectral hole lasts longer than any excited state lifetime. See for example, J. Friedrich, D. Haarer, Angew. Chem. 1984, 96, 96; Angew. Chem. Int. Ed. Engl. 1984, 23, 113; R. Jankowiak, G. J. Small, Science 1987, 237, 61 8-625; Persistent Spectral Hole-Burning: Science and Applications (Top. Curr. Phys. 44), (Ed.: W. E. Moerner), Springer, Berlin, 1988.

We are grateful to the Research Division of International Business Machines Corporation and to the U. S. Office of Naval Research for support of this research. We also acknowl- edge our colleagues, Drs. PV P. Ambrose, T P. Carter, and L. Kador for their work which laid the,foundations for single- molecule spectroscopy in solids.

Received: August 13, 1992 [A 898 IE) German version: Angew. Chem. 1993, 105, 537

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