1706 OPTICS LETTERS / Vol. 17, No. 23 / December 1, 1992

Use of trapped atoms to measure absolute photoionizationcross sections

Timothy P. Dinneen, Christopher D. Wallace, Kit-Yan N. Tan, and Phillip L. Gould

Department of Physics, U-46, University of Connecticut, Storrs, Connecticut 06269-3046

Received June 29, 1992

We describe a new technique for accurate measurement of absolute photoionization cross sections. Bymeasuring the loss rate of atoms from a laser trap in the presence of ionizing light, we directly measure thephotoionization rate. The only quantities requiring absolute calibration are the ionizing laser intensity and thefractional population in the relevant state. Our technique is capable of detecting extremely small ionizationrates, which means that low-power cw sources can be used. We have applied this method to photoionizationfrom the 5P3/2 state of rubidium at wavelengths of 413 and 407 nm. The cross sections are 1.36(12) X 10-17and 1.25(11) X 10-17 cm2 , respectively.

Photoionization of atoms from excited states is a fun-damental problem in atomic physics.' Predictionsof multiple minima in the photoionization cross sec-tion have drawn particular attention2 because thesefeatures depend sensitively on details of the atomicwave functions used in the calculations. Tests of thetheory require accurate cross-section measurementsthat are difficult to obtain in an absolute sense.

We present a new and rather general techniquefor the accurate and absolute measurement of pho-toionization cross sections. It is based on the abilityto cool and trap neutral atoms with laser light.3Because an atom is held in a laser trap by resonantlyenhanced radiative forces, if the atom is ionized, itescapes. Thus by measuring the loss rate of atomsfrom the trap that is induced by ionizing light, we aredirectly measuring the photoionization rate. Thisrate R, is given by the simple formula

R, = hPof, (1)

where Ip and v are the photoionizing intensity andfrequency, respectively, oC is the photoionization crosssection, and f is the excited-state fraction.

There are several obvious advantages to our tech-nique. First, because we measure the ionization rateper atom, we do not need to know the absolute atomicdensity. Second, we measure this rate by monitoringthe fluorescence of the trapped atoms, so we need notdetect ions. Third, because the confinement time ofatoms in the trap is rather long (e.g., 50 s), we canmeasure extremely low ionization rates and thereforeemploy extremely low intensities of ionizing light.In fact, experiments with spectrally filtered white-light sources should be possible. We note that atechnique similar to ours has been exploited to mea-sure ground-state photodetachment cross sections fornegative ions held in a Penning trap.4

We briefly compare our technique with previouslyused methods in order to demonstrate its advantages.The most straightforward way to observe photoion-ization from an excited state is to illuminate the

sample with two radiation fields, one to populate theexcited state and one to ionize it. The resulting ionsignal, properly calibrated, yields the photoionizationcross section. The major difficulty with this tech-nique is in calibrating the excited-state population,although ion detector efficiency can also be a concern.Nevertheless, reasonable results have been obtainedwith this method.' Calibration of the excited-statepopulation by measuring the fluorescence has beenshown to improve the accuracy.5 A technique thatavoids these calibration problems is the saturationmethod.6-9 Here, the intensity of the ionizing lightis varied and the cross section is deduced from theintensity at which the photoionization process sat-urates. Unfortunately, very high intensities (i.e., ofthe order of megawatts per square centimeter) are re-quired to reach saturation. A recently demonstratedfluorescence reduction technique'0 measures the de-pletion (by photoionization) of the excited-state pop-ulation. Atomic density and ion collection efficiencycalibrations are avoided, but competition with spon-taneous decay requires rapid photoionization and atime-resolved measurement.

Our experiment employs a magneto-optical trap"with diode lasers (see Fig. 1) to confine the rubidiumatoms.'2 The important aspects of the trap for thephotoionization measurements are as follows: (1)The cold atoms are confined until knocked out of thetrap by a collision with a hot background gas mole-cule. The average confinement time at our operatingpressure of 10-10 Torr is approximately 50 s. Thissets the scale for the minimum ionization rate thatwe can observe. (2) The trapping laser repeatedlyexcites the atoms, thereby yielding a steady-stateexcited-state (5P3 /2) fraction. This continual excita-tion means that the photoionization does not haveto compete with spontaneous decay and can there-fore occur at a relatively low rate. The repeatedexcitation, and subsequent fluorescence, provides themeans for measuring the number of atoms in thetrap.

The experiment is performed by exposing a sampleof trapped rubidium atoms to ionizing light and

0146-9592/92/231706-03$5.00/0 © 1992 Optical Society of America

December 1, 1992 / Vol. 17, No. 23 / OPTICS LETTERS 1707

Fig. 1. Schematic of the magneto-optical trap. The sixcircularly polarized (&' and o-) trap beams intersectat the origin, where the magnetic field (axial gradient5 G/cm) from the two coils (current i) vanishes. The trapis loaded with cold atoms from the laser-slowed atomicbeam.

0.0 -

-0.2

-0.4-

5 -0.6 -)- -0.8 -0--1.0 -

-1.2 -

-1.4

-0.4 0.0 0.4 0.8Time (s)

Fig. 2. Typical decay of atoms (measured by fluores-cence) from the trap owing to photoionization. The arrowindicates the point at which the ionizing laser is switchedon. The solid curve is an exponential fit (R, = 3.85 s'l)to the data.

measuring the resulting loss of atoms from the trap.The trap is loaded from an atomic beam that is slowedby frequency-chirped diode-laser light.' 3 With thetrap fully loaded, the atomic beam and slowinglaser are blocked, and the number of atoms in thetrap begins to decrease. At low trap densities (i.e.,<109 cm-3) this exponential decay (50-s time con-stant) is due to collisions with background gas. Atsome point during this slow decay, ionizing light froma cw krypton-ion laser is switched on, and rapiddecay owing to photoionization follows. An exampleis shown in Fig. 2. Because we operate at extremelylow ionizing intensities (e.g., of the order of watts persquare centimeter), the ionization rate is linear inthis intensity.

The intensity of the ionizing light is measured byusing a 520-pum-diameter aperture and a calibratedthermal power meter. This beam has an approxi-mately circular Gaussian profile with a l/e 2 radiusof 3.2 mm. Because the trapped atoms are confinedto an approximately 200-Ium-diameter region, theyexperience only the intensity that we measure di-rectly. The photoionizing beam is linearly polarizedalong the (-1, 1, 0) direction and incident in the

(1.00, 0.47,0.47) direction, where the coordinate axes(x, y, z) are determined by the three pairs of trap laserbeams. The z axis is along the axis of the magneticfield coils.

The trap laser determines the excited-state frac-tion f. It is detuned slightly below the F= 3 -F = 4 transition of the 85RbD2 line (A = 780 nm) andhas a typical total intensity (sum of all six beams)of It = 20 mW/cm2. We calibrate the excited-statefraction by varying the trap laser intensity and fittingthe measured ionization rate to a saturation curve.Although saturation of a multistate atom' in thelaser field of the three-dimensional trap is complex,15our data fit rather well to the formula for a two-stateatom,

r_ It/I'Sf2I/IS + 4(A/r)2 + 1

if the effective saturation intensity Is is allowed tobe a free parameter. Here, A is the laser detuning(-A = 2fr X 5.1 MHz for our data) and r = 27r X5.9 MHz is the natural decay rate of the excitedstate. A saturation curve and a least-squares fitto Eq. (2) are shown in Fig. 3. This fit yields avalue of Is = 10.5 mW/cm2 , somewhat higher thanthe 7.6 mW/cm 2 expected for the case of equallypopulated mF levels. We have repeated the mea-surements with the 87Rb isotope, which has differenthyperfine structure (F= 2 - F = 3). The best-fitvalue is 9.1 mW/cm2, again higher than the expectedvalue of 6.9 mW/cm 2 . Such a systematic deviationcould arise from a small misalignment of the centersof the trap laser beams. This possibility is supportedby the fact that measurements with larger (6.3 mmversus 3.2 mm 1/e2 diameter), and hence more uni-form, trap beams did not display this discrepancy.In any event, the effect on the inferred excited-statefraction is small.

The photoionization cross section o is calculated bycombining the measured values of intensity, excited-state fraction, and ionization rate according toEq. (1). We have made measurements with two vio-let lines of the krypton-ion laser where A = 413.1 and406.7 nm. These are above threshold by 0.413 and

8

UC)

CL 4C:

2

40

30

20

10

04' 0 , , , . , , 00 40 80 120

Trap Laser Intensity (mW/cm 2 )

Fig. 3. Ionization rate (Rp) and excited-state fraction (f)versus trap laser intensity for 85Rb. The fit to Eq. (2)(solid curve) calibrates the f axis. Error bars are ap-proximately the size of the points. The ionizing laser(A = 413 in) intensity is fixed at Ip = 1.1 W/cm 2 .

kZ)

1708 OPTICS LETTERS / Vol. 17, No. 23 / December 1, 1992

0.460 eV, respectively. Our results are as follows:or = 1.36(12) x 10-1' cm2 for A = 413.1 nm and oa =1.25(11) x 10-17 cm2 for A = 406.7 nm. These crosssections should be interpreted as the average overinitial state mF levels and for linear polarization.The errors are dominated by the uncertainty indetermining the absolute ionizing intensity (±8%),with a smaller contribution (±4%) from fitting theexcited-state fraction. The only previous measure-ment from the Rb 5P state is that of Klyucharevand Sepman.16 The 5P fine-structure doublet wasnot resolved, and the photoionization cross sectionat A = 440 nm was measured to be 9.6 X 10-'8 cm2 ,with a quoted systematic error of less than 30%.There are several theoretical calculations'7-20 thatpredict 5P cross sections between approximately1.1 x 10-17 and 1.5 x 10-17 cm2 at our wavelengths.These agree quite well with our measurements.

In conclusion, we have demonstrated a new tech-nique for measuring absolute photoionization crosssections and applied it to the case of rubidium inthe 5P312 excited state. Once calibrated, photoion-ization is a useful tool for absolute measurementsof the excited-state fraction, ion detection efficiency,and number of trapped atoms. Our method can beapplied to any atom that can be trapped. The list,which will undoubtedly continue to grow, currentlyincludes the alkali metals lithium,2' sodium," rubid-ium, and cesium22; the alkaline earths calcium andstrontium2 3; and the metastable rare gases helium,24

neon,2 5 argon,2 6 and krypton. 2 6 The method is notrestricted to excited states that are populated by thetrapping process. The ground state can be selec-tively photoionized (one photon or multiphoton) byalternating the ionizing light with the trapping light.Other excited states can be populated with additionallasers. Experiments can be done with aligned atomsif trapping, alignment, and photoionization periodsare alternated in time.

In fact, the method is not even restricted to pho-toionization. Any process that results in an atom'sbeing lost from the trap can be similarly exploited.Examples include excitation to metastable states(long-lived enough for the atom to escape the trap)or collisions with applied beams of electrons, atoms,or ions. The feature that all these phenomenahave in common is that the rate of the relevantprocess is measured directly by means of the traploss rate. If the incident flux is measured andthe fractional population in the appropriate state isknown, then a measurement of the trap loss rateconstitutes an absolute measurement of the crosssection. In addition to the advantages for absolutemeasurements, our technique is capable of measuringextremely low rates. This is a direct result of thelong confinement time of the trapped atoms.

We acknowledge numerous discussions with JuhaJavanainen on the issue of saturation of multistateatoms. This study was supported by the National

Science Foundation (grant PHY-8857336). Phillip L.Gould is an Alfred P. Sloan Research Fellow.

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