Thin-cell sub-Doppler spectroscopy by spatially separatedbeam method and pump–probe method

Atsushi Mikata,1 Utako Tanaka,1,2,* and Shinji Urabe1,2

1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan2JST-CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

*Corresponding author: utako@ee.es.osaka-u.ac.jp

Received 12 October 2007; accepted 13 November 2007;posted 6 December 2007 (Doc. ID 88198); published 4 February 2008

We experimentally demonstrate two methods that improve the resolution of sub-Doppler spectroscopyusing a 1 mm thick vapor cell. The linewidths of the observed spectra are approximately 1 order ofmagnitude narrower than the Doppler width. The first method involves using a 1 mm thick cell filled withRb atomic vapor and two spatially separated laser beams. By employing the same principle, we alsodemonstrate that it is possible to achieve the same resolution by using the pump and probe pulses of asingle beam. The latter method enables us to construct a simple and robust optical setup for sub-Dopplerspectroscopy. © 2008 Optical Society of America

OCIS codes: 300.6210, 300.6260.

1. Introduction

Spectroscopy using a thin atomic vapor cell was the-oretically proposed by Izmailov in 1992–1993 as anovel method for performing sub-Doppler spectros-copy [1,2]. This proposed method involved detectingonly slow atoms generated by the optical pumpingprocess in a three-level system and collisions of theseatoms with the inner walls of a thin cell. In a pio-neering experimental study by Briaudeau et al. [3],this method was successfully demonstrated using athin cell of thickness L � 10–100 �m. Later, theydemonstrated a different scheme using a similar thincell, in which the sub-Doppler features were found tooriginate in the transient regime of the linear inter-action with a two-level system under conditions ofextremely weak light irradiation [4,5]. This restric-tion on the incident light intensity was overcome byusing a very thin cell �L � 150–300 nm� whose thick-ness was less than the optical wavelength � [6]. Var-ious high-resolution spectroscopy experiments usingextremely thin cells have since been reported [7–11].

In the regime in which the optical pumping processdominates, some new experimental configurationswere investigated [12–14] using relatively thick cells

�L �� ��, and the sub-Doppler spectrum of the D lineof Cs was observed even using a 10 mm thick cell [12].Based on the method described in Otake et al. [13],frequency stabilization of diode lasers was achievedby applying a frequency-modulation technique [15]and by using a dichroic-atomic vapor lock [16]. Inaddition to optical spectroscopy experiments, radio-frequency (rf) magnetic resonance experiments wereperformed using relatively thick cells [17,18].

This paper focuses on the resolution enhancementachieved in sub-Doppler spectroscopy when a rela-tively thick cell �L � 1 mm� is used in which opticalpumping generates sub-Doppler resonance lines. Re-cently, Izmailov proposed that a spatially separatedcentral beam and coaxial beam could be used to im-prove the resolution [19] and applied the scheme to a120 �m thick cell [20]; however, it did not lead to asubstantial improvement in the resolution. A similarscheme using two spatially separated beams, namely,a central pump beam and a coaxial probe beam wasused with a 20 �m cell [21]. We demonstrate exper-imentally that an improvement in resolution of sub-Doppler spectroscopy using a relatively thick cell�L � 1 mm� can be achieved by using spatially sepa-rated beams that are not two coaxial beams but are apair of parallel beams. Additionally, we demonstratea method (hereafter referred to as “the pump–probemethod”) in which a single beam is introduced into a

0003-6935/08/050639-05$15.00/0© 2008 Optical Society of America

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thin cell, and which can also improve the resolution ofsub-Doppler spectroscopy. The latter method greatlysimplifies the optical setup.

2. Spatially Separated Beam Method and Pump–ProbeMethod

As mentioned above, we consider sub-Doppler spec-troscopy using a thin cell whose thickness is muchgreater than the wavelength of the resonance opticaltransition �L �� ��. The thin cell was 34 mm long and1 mm thick. To detect only slow atoms, we first irra-diated the optical-pumping beam tuned between theground state |a� and the excited state |c� to transferthe population to the |b� state (see Fig. 1). However,the population relaxation process redistributes theatoms in the |b� state to thermal equilibrium. Thedominant factor of the population relaxation processis collisions with the inner walls of the thin cell. Thecollision rate is proportional to the atomic velocityand inversely proportional to the distance betweenthe cell walls. Therefore, atoms with low z-componentvelocities tend to remain in the |b� state, whereasatoms with high velocities tend to return to the |a�state. Consequently, the number of very slow atomsin the velocity distribution for atoms in the |a� stateis less than that in the thermal equilibrium distribu-tion. Detecting the difference from the thermal equi-librium distribution is equivalent to detecting onlyatoms with a small velocity component, which is es-sential for thin cell sub-Doppler spectroscopy.

In the case of the spatially separated beam method,atoms that contribute to the sub-Doppler spectrumare those traveling from the pump beam region to theprobe beam region without colliding with the walls.This implies that the population of slow atoms de-tected by the probe beam depends on the distancebetween the two beams. Greater resolution is antic-ipated as this distance is increased.

The principle of observing sub-Doppler spectra bythe spatially separated beam method may be re-garded as analogous to atomic beam spectroscopy.Atoms that have thermal velocity along the cell di-ameter and a low velocity along the z axis generate

sub-Doppler spectra. Thus, only atoms that interactwith both the pump and probe beams within a certaintime interval provide sub-Doppler spectra. The sameinteraction could be achieved if we irradiate an entirecross section of the thin cell with the pump and probepulses of an expanded laser beam. First, a pumpbeam is irradiated to pump the atoms from oneground state to another ground state. Next, we turnoff the pump beam for a while. We then irradiateatoms with the weak probe beam and detect thetransmitted light intensity. By using this process, itis possible to observe the velocity distribution of theground state |a� from which slow atoms are selec-tively removed.

The advantages of the pump–probe method arelisted below:

(i) The principal advantage of the spatially sepa-rated beam method over the pump–probe method isthat no delay time is necessary, since the probe beamis continuously irradiated and detected.

(ii) The velocity selectivity along the z axis is bet-ter than that of the spatially separated beam methodsince the x and y components of velocity contributeless to the observed spectra. In the case of the spa-tially separated beam method, when atoms travelbetween two beams very fast, they are detected withthe probe beam even though the velocity along the zaxis is not small, thus reducing the velocity selectiv-ity along the z axis.

(iii) In the pump–probe method, a long intervaltime can be employed provided the signal-to-noiseratio is sufficiently high. By contrast, in the spatiallyseparated beam method, the cell diameter restrictsthe interval time, i.e., the resolution of spectra.

(iv) Only a single beam is necessary, enabling asimple optical setup to be used.

3. Experimental Results and Analysis

A. Spatially Separated Beam Method

Figure 2 shows the experimental setup for the spa-tially separated beam method. The laser beam froman external-cavity diode laser (ECDL), whose wave-length is tuned to the Rb D1 line at 794 nm (naturallinewidth: 6 MHz), passes though an optical isolatorand is split into three beams: a pump beam, a probebeam, and a beam for saturated absorption spectros-copy using a conventional Rb cell. The pump beampasses through an optical chopper, cylindrical lenses,and the upper portion of the thin Rb cell. The probebeam is sent through cylindrical lenses, a ��2 platethat rotates the polarization perpendicular to that ofthe pump beam, and it then passes through the lowerportion of the thin cell. The pump and probe beamsare introduced to the upper and lower region of thecell as shown in Fig. 2, respectively. Both beams areexpanded in one direction by cylindrical lenses inorder that the beams irradiate as large a cross sectionas possible. The distance between the beams can bevaried. The dimensions of both beams are set to be�16 mm � 3.3 mm. Intensities of the pump and

Fig. 1. Velocity distribution of the three-level model with a pump-ing beam. Inset: Schematic showing the thin-cell orientation andthe propagating direction of the laser beam.

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probe beams are �90 and 20 �W�cm2 at the cell,respectively. The probe beam is focused onto a pho-todetector by a lens. The signal-to-noise ratio isgreatly reduced if leakage from the pump beam isdetected. The pump beam is thus masked before thelens, and it is also blocked by using a polarizing beamsplitter and a linear polarizer. The pump beam ischopped at 1 kHz so that the difference from the ther-mal equilibrium state can be detected using a lock-inamplifier. The time constant of the lock-in amplifieris set to be 100 ms. The thin cell is heated to T� 40 °C, at which the full width at half maximum(FWHM) of the Doppler-broadened spectral line isapproximately 520 MHz.

Figure 3 shows the dependence of the FWHM of the85Rb S1�2 �F � 3� → P1�2 �F� � 2, 3� transitions on thedistance between the two beams. The inset of thisfigure shows the observed spectrum for a beam sep-aration of 18 mm and the saturated absorption spec-trum obtained using a conventional Rb cell. Thecrossover resonance observed in the saturated ab-

sorption spectrum does not appear in the thin-cellspectrum. As expected, a reduction in linewidth isobserved as the distance between the two beamsis increased. The minimum sub-Doppler FWHM of40 MHz was observed at a beam separation of18 mm, which is approximately one-third of that ob-served in a previous study by us [16].

B. Pump–Probe Method

In the pump–probe method, the time sequence andintensities of the pump beam and the probe beamneed to be accurately controlled. We used the first-order beam diffracted by an acousto-optic modulator(AOM) to modulate the beam intensity. The opticalsetup and time sequence for the pump and probebeams are shown in Fig. 4. The laser beam from theECDL passes through the optical isolator and theAOM, and it is then expanded using lenses so that itirradiates the entire cross section of the thin cell. Thebeam intensity is controlled by employing the follow-ing steps. First, we irradiate the relatively intensebeam for 10 �s. Next, we turn off the beam for a timeof T1 to allow atoms having high velocities to collidewith the walls. We then irradiate the first probe beamfor 10 �s to observe the velocity distribution that hasa sub-Doppler dip. We wait for T2 �120 �s� and irra-diate the second probe beam for 10 �s to measure thethermal equilibrium distribution. We set the intensi-ties of the probe pulses to be 1�18 that of the pumpbeam. The sub-Doppler spectrum is obtained by de-tecting the intensity difference between the two probepulses. We measured the FWHM of the 85Rb S1�2 �F� 3� → P1�2 �F� � 2, 3� transitions using different T1in the range of 10–45 �s. The maximum value of T1was practically determined by the signal-to-noiseratio of the circuit that was used for subtracting thetransmitted light intensities of the two probepulses. The circuit consisted of an I–V converter forthe photodetector, amplifiers, switches, and a low-pass filter. The switches controlled the output of theI–V converter so that it worked only for the periodswhen the probe pulses were being irradiated. Theoutput of the I–V converter was also switched sothat the signal of the first probe pulse was sentthrough an inverting amplifier to the low-pass fil-ter, whereas that of the second pulse was directly

Fig. 4. Setup for the pump–probe method and time sequence.ECDL, external cavity diode laser; AOM, acousto-optic modulator;BS, beam splitter; L, lens; PD, photodetector. The time chart is notdrawn to scale for both time and intensity.

Fig. 2. Setup for the spatially separated beam method. ECDL,external cavity diode laser; M, mirror; BS, beam splitter; CL, cy-lindrical lens; PD, photodetector; PBS, polarizing beam splitter.The height of the probe beam is set lower than that of the pumpbeam. The mirror in front of the thin cell reflects only the probebeam, as shown in the right inset.

Fig. 3. FWHM of the spectrum versus distance between the pumpand probe beams. Inset: observed spectrum for the beam separa-tion of 18 mm (lower profile). The upper profile shows the satu-rated absorption spectrum that was observed simultaneously forfrequency reference.

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connected to the low-pass filter. The resultant out-put is the difference between the signals of the twoprobe pulses. The cutoff frequency of the low-passfilter was approximately 10 Hz, which determinedthe detection response.

The dependence of the linewidth on T1 is shown inFig. 5. The thin cell was heated up to T � 70 °C, atwhich the corresponding Doppler width (FWHM)was approximately 540 MHz. The observed spectrumwidth became narrower as T1 was increased. Sub-Doppler profile with a linewidth of 51 MHz was ob-tained at T1 � 45 �s (inset of Fig. 5). In this case thenumber of atoms contributing to the signal was ob-served to decrease. This behavior was confirmed bysolving the rate equations given in [13]. We solved thetime evolution of the velocity distribution by consid-ering spontaneous emission and relaxation by colli-sion with the walls.

This method can be used for long-term stabilizationof the laser frequency. If the frequency of the laser isalternately stepped to the approximate half maxi-mum on either side of the sub-Doppler profile, theasymmetry between the signal height on the high-and low-frequency sides of the profile can be used forcompensating a drift in the laser frequency.

4. Conclusion

By using both the spatially separated beam and thepump–probe methods, we observed spectra havingmuch narrower resolutions than the Doppler widthwithout crossover resonance, which appears in con-ventional saturated absorption spectra. By furtherincreasing the signal-to-noise ratio in the accumu-lation of the signal of the probe beams, the pump–probe method can theoretically achieve a narrowerspectrum than the spatially separated beammethod using a cell having the same dimensions. Inthe pump–probe method, the components (i.e., thediode laser, isolator, modulator, lenses, thin cell,and photodetector) can be installed in a straightline, which does not require delicate alignment. Re-cently, a saturated absorption laser spectrometerthat used a microfabricated Rb cell and micro-

optical components was reported [22]. It may bepossible to reduce the size of our setup by utilizingthe small optical components as reported in [22]and thus use it to construct a simple and robustlaser-frequency stabilization system.

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