1280 OPTICS LETTERS / Vol. 21, No. 16 / August 15, 1996

Hyperfine structure and absolute frequencyof the 87Rb 5P3y2 state

Jun Ye, Steve Swartz, Peter Jungner,* and John L. Hall

Joint Institute for Laboratory Astrophysics, University of Colorado, and National Institute of Standards and Technology,Boulder, Colorado 80309-0440

Received February 5, 1996

We have constructed two highly stable and reproducible 87Rb D2-saturated-absorption spectrometers at780 nm, using dither/third-harmonic lock-in detection and radio-frequency sideband techniques, respectively.We achieved 63-kHz reproducibility and agreement between these two independent systems. Heterodynemeasurements of the hyperfine splittings of the 5P3/2 state give its magnetic dipole sAd and electric quadrupolesBd hyperfine constants with a 10-fold reduction in uncertainty. 1996 Optical Society of America

In the pursuit of simple, low-cost, yet high-quality vis-ible optical frequency sources, we recently constructedan optical chain to measure the absolute frequencyof molecular I2 hyperfine resonances in the 532-nmregion1 (doubled YAG). A saturated-absorption spec-trometer of the 87Rb D2 line at 780 nm was used asa reference transfer standard.2 The accuracy of ourinitial chain result was limited by the 660-kHz un-certainty of the 87Rb D2 line, which was in part as-sociated with its broad natural resonance line width of6-MHz FWHM. To improve the utility of this refer-ence standard we studied its systematics and madecorresponding corrections. A dramatic improvementon the available frequency stability and reproducibil-ity has been achieved, and we are now able to lock ontothe line centers with an accuracy of ,1y2000 of thelinewidth.

Degradation of the 87Rb D2 profiles occurs for thehyperfine-structure components with strong cyclingcharacter (e.g., F 00 2 ! F 0 3, F 00 1 ! F 0 0).With optical intensities below 0.2 mWycm2 we ob-served sign reversals on the saturated-absorptionpeaks owing to velocity-selective optical pumpingprocess.3 With careful experimentation on the spec-trometer, we were able to find a comfortable opticalintensity range in which the observed line shapes canbe well accounted for by a simple FM or third-harmonicformula. We stress here that the optimal intensitydepends on the choice of the beam size. We also min-imized optical power shift on the lines by dividing thepower into pump and probe beams in an appropriateratio, balancing various effects of light pressure4 andoptical pumping.

Heterodyne experiments between two 87Rb D2spectrometers offer a powerful check on their sys-tematics as well as a natural determination of allpossible hyperfine component intervals. We builttwo such systems based on two different signal-recovery modulation schemes. JILA-built Ti:sapphirelasers were used for the sole reason of participatingin the power-demanding optical frequency chain.Figure 1(a) shows the dither/third-harmonic lock-indetection system. The 6-MHz peak-to-peak opticalfrequency dither at 5 kHz was provided by a double-passed acousto-optic modulator (AOM) fed from an

0146-9592/96/161280-03$10.00/0

FM-dithered 80-MHz voltage-controlled oscillator. Toensure a stable center frequency, we tightly phaselocked this oscillator (after a digital phase division by10) to an 8-MHz precision FM waveform generated bya direct-digital-synthesis (DDS) frequency synthesizer.To achieve a better rejection of offsets by neighboringlines and Doppler background we recovered the signalat the third harmonic, using a lock-in synchronizedto three times the 5-kHz dither. The residual AM at15 kHz was carefully monitored on our probe detector.(The 5- and 10-kHz signals were heavily notched out,to near the shot-noise level.) By adjusting the Braggangle of the AOM, we reduced the 15-kHz AM to bebelow 260 dB relative to our signal. A broadbandintensity stabilizer following the spatial mode filterprovided another .10-dB suppression. We choppedthe saturating beam at 610 Hz and demodulated the15-kHz lock-in output additionally by a 610-Hz lock-into capture the part of the Rb signal that was changedby the chopped saturating beam.

Figure 1(b) shows our FM system. The pump beamis chopped and frequency offset by an 80-MHz AOM,and 4-MHz FM sidebands with modulation index of 0.8are imposed on the probe beam. A resonant 4-MHzphotodetector detects the AM signal converted fromFM by the Rb atoms, and its signal is subsequentlydemodulated by a double-balanced mixer (DBM). Inboth spectrometers the pump and probe beams propa-gate accurately antiparallel and are spatially over-lapped to avoid residual Doppler shifts and broadening.Polarizers guarantee parallel linear polarizations inthe Rb cells. Magnetic f ields in the cells are reducedto be ,2 mT by two layers of magnetic shields. Theratios of pump to probe powers were kept near 4. Inthe 3-f system the beam diameter was ,3.5 mm, andwe typically used 35-mW pump power (0.37 mWycm2);in the FM system they were 1 mm and 7 mW , respec-tively (0.89 mWycm2). The 3-f spectrometer showedsmall power shifts (see Fig. 2, 620%): e compo-nent, 150 HzymW ; d component, 11 HzymW ; dyfcrossover, 170 HzymW . High-quality Rb cells weremade at JILA with the standard cleaning and bakingprocedure.5 The Rb was purified several times bydistillation before being transferred into the cells.The pressure at tip-off was ,130 mPa. The resid-

1996 Optical Society of America

8626(DMW)

August 15, 1996 / Vol. 21, No. 16 / OPTICS LETTERS 1281

Fig. 1. Experimental setup for our Rb D2 spectrometers.Both use an AOM to chop and frequency offset the satu-rating beam. The third-harmonic dither lock-in detectionapproach is shown in (a), and the FM technique is shown in(b). PLLs, phase-locked loops.

ual background contamination can be estimated bymeasurement of the linewidths of the Rb transitions.Extrapolating to zero power results in a measuredlinewidth in both spectrometers of ,7 MHz, comparedwith ,6-MHz natural linewidth. This extra 1 MHzincludes all experimental parameters and in part isdue to vibration of the laser prestabilizing referencecavities as well as to any possible gas contaminationin the cell. Various cells placed in one spectrometerproduced frequency shifts of less than a few kilohertz.It is satisfying that the lasers are locked with anoffset of ,3 kHz from the unperturbed line center of afree atom.

Figure 2 shows a typical scan for the 87Rb 5S1/2sF 00 2d ! 5P3/2sF 0 1, 2, 3d saturated-absorptionprofiles in both spectrometers. Assignment of thehyperfine components is indicated. Excellent SyNresults (normalized for 1-Hz bandwidth) of 7200:1 inthe FM and 2600:1 in the 3-f systems were achieved.Increased laser noise at the relatively low modulationfrequency of 5 kHz in the 3-f system is mainly re-sponsible for the reduced SyN. FM6 and Wahlquistthird-derivative line-shape formulas were used tofit the correspondingly scanned data. The latterthird-derivative line shape7 is derived from

Signals3vd SignsHdd

2

Hv

!2" p2g 2 m

2p

m 2 2 sm 2 gd

2 2p

2g 2 m

m 2 1pm 2 2

2p

m

!#, (1)

where Hd is the frequency detuning from the linecenter and Hv is the modulation amplitude. The

dimensionless parameters are defined as follows:

g 1 1 b2 1 a2, m g 1q

g2 2 4a2 , (2)

with a sHdyHvd and b 1/2H1/2yHv, H1/2 beingthe FWHM of the resonance line. The fit residuals,displayed in Fig. 2 with 10-fold magnification, showbasically structureless noise, indicating that the lineshape of our spectrometers is well understood.

Figure 3 shows the recorded long-time beatbetween the FM and the third-harmonic-detectionstabilized lasers, both locked on the df -crossovercomponent. The corresponding Allan variance ofsy 3.8 3 10212y

pt matches that calculated from the

SyN data of the 3-f spectrometer, and it has the whitefrequency noise characteristics. This noise is roughlyhalf that of the 633-nm HeNeyI2 system. At 1-saveraging we obtained a frequency noise of 61.4 kHz.More significantly, the Allan variance continues to

Fig. 2. Frequency scan over the hyperfine components in87Rb in both spectrometers. Theoretical f its for the dfcrossover and their residuals s103d are shown. Assign-ment of the components is indicated.

Fig. 3. Time record of the beat frequency between the twospectrometer-stabilized laser systems. Allan variance iscalculated from these data. The offset of 5 kHz betweenthe two systems has been suppressed.

1282 OPTICS LETTERS / Vol. 21, No. 16 / August 15, 1996

Fig. 4. (a) Measured values of the hyperf ine splittingsof the 87Rb 5P3/2 state; (b) comparison between A and Bvalues determined here and some previous results. Thekey to references is as follows: a, Ref. 10; b, Ref. 11; c,Ref. 12; d, Ref. 8; e, Ref. 2. The Schussler measurementof the constant A is also the recommended value given inRef. 8.

decrease below 2 3 10213 with increasing averagingtime to .2500 s, indicating the relative absence ofchanging systematic offsets. This is clearly verifiedby the beat frequencys slow drift of 90 Hzyh. Byf lipping the lasers back and forth between severalpairs of transitions one can determine the offsetsbetween the two systems. In the FM spectrometer,frequency pulling effects by neighboring lines areexacerbated by their broader features, so appropriatecorrections were subsequently calculated and applied.Transitions originating from both F 00 1 and F 00 2components of the ground state 5S1/2 were used, anddata for hyperfine splittings were accumulated overseveral months with a reproducibility of approxi-mately 63 kHz. The scale of this frequency noise andreproducibility is set by the linewidth of 6 MHz.

Figure 4(a) summarizes our result for the hyper-fine splittings of 5P3/2 state. Using least squareswith the hyperfine Hamil