High-contrast dark resonances with linearlypolarized light on the D1 line of alkali atoms

with large nuclear spin

Ken-ichi Watabe,1,* Takeshi Ikegami,1 Akifumi Takamizawa,1 Shinya Yanagimachi,1

Shin-ichi Ohshima,1 and Svenja Knappe2

1National Metrology Institute of Japan (NMIJ), Advanced Industrial Science and Technology,1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan

2National Institute of Standards and Technology, 325 South Broadway, Boulder, Colorado 80305-3322, USA

*Corresponding author: k.watabe@aist.go.jp

Received 19 June 2008; revised 14 November 2008; accepted 15 January 2009;posted 16 January 2009 (Doc. ID 97660); published 13 February 2009

High-contrast coherent population trapping signals were observed on the Cs D1 line by use of a bichro-matic linear polarized light (lin‖lin field). A maximum absorption contrast of about 10% was obtained.This was nearly twice as high as that measured with the standard configuration of bichromatic circularlypolarized light (σ − σ field). The results are compared with density matrix calculations of 4 and 5 levelsystems. © 2009 Optical Society of America

OCIS codes: 120.4820, 020.1670, 300.6360.

1. Introduction

Coherent population trapping (CPT) [1,2] resonanceshave recently gained renewed interest, partlythrough the development of chip-scale atomic clocks,such as microfabricated atomic clocks [3,4]. Highcontrasts and narrow resonance linewidths are im-portant factors for the applications of CPT-basedatomic frequency references [5,6]. For conventionalCPT interrogation with bichromatic circularlypolarized light (σ − σ field), the signal amplitudescan be limited by the loss of atoms toward the ex-treme Zeeman sublevels jF;mF ¼ �Fi through opti-cal pumping. The atoms that accumulate in thesestates contribute to neither the CPT signal nor thebackground absorption. To reach the same net ab-sorption, the vapor temperature could be increased.Inmany cases, however, this is not desirable, becauseof increased resonance broadening through spin-exchange collisions and higher power consumption.

Much effort has been dedicated to maximizingthe resonance contrast without significant linebroadening. It has been shown that excitation ofthe D1 transition instead of the D2 transition resultsin both a higher resonance contrast and a narrowerresonance width [7,8]. Other approaches to increasethe contrast include push–pull optical pumping withalternating circular polarizations [9], counterpropa-gating waves with orthogonal circular polarizations[10], interrogation with crossed linear polarizations[11], and four-wave mixing [12]. These methods ex-cite a two-photon Λ resonance on the ground-statehyperfine sublevels with jF;mF ¼ 0i, jF þ 1;mF ¼0i to minimize the frequency shift due to the mag-netic field. However, most of these configurationsare complex to implement.

Recently, the observation of high-contrast dark re-sonances was reported in the most simple setup pos-sible: Taichenachev et al. [13] and Kazakov et al. [14]proposed to measure CPT resonances with a bichro-matic linearly polarized light (lin‖lin field) on theD1 line of 87Rb (with nuclear spin I ¼ 3=2). Theydemonstrated that two Λ schemes can be formed

0003-6935/09/061098-06$15.00/0© 2009 Optical Society of America

1098 APPLIED OPTICS / Vol. 48, No. 6 / 20 February 2009

with two pairs of ground-state hyperfine sublevels si-multaneously: jF ¼ 1;mF ¼ −1i, jF ¼ 2;mF ¼ 1i andjF ¼ 1;mF ¼ 1i, jF ¼ 2;mF ¼ −1i coupled with thecommon excited states jF0 ¼ 1;mF ¼ 0i [seeFig. 1(a)]. Very high CPT resonance contrasts weremeasured in this case, because the ground-stateZeeman components involved in theΛ system cannotcouple to any other excited states by single-photontransitions. If the contribution of the nuclear spinto the Zeeman splitting is neglected, the two-photon

resonance frequencies (both jF ¼ 1;mF ¼ −1i,jF ¼ 2;mF ¼ 1i and jF ¼ 1;mF ¼ 1i, jF ¼ 2;mF ¼ −1i) are equal to the frequency of the 0–0 reso-nance formed on jF ¼ 1;mF ¼ 0i, jF ¼ 2;mF ¼ 0i.This means that at least two superposition darkstates exist in the case of exact two-photon resonancefor fields with linear polarizations. A CPT resonanceon the ground-state hyperfine sublevels withjF;mF ¼ 0i, jF þ 1;mF ¼ 0i is not excited in the caseof the lin‖lin configuration, because the differentcomponents of the circularly polarized light interferedestructively [15].

Unfortunately as pointed out in [13], this is possi-ble only for atoms with nuclear spin I ¼ 3=2 on theF0 ¼ 1 excited state. For higher angular momenta(i.e., F0 > 1) the ground-state levels jF;mF ¼ −1i,jF þ 1;mF ¼ −1i and jF;mF ¼ 1i, jF þ 1;mF ¼ 1ican also couple to the excited states jF0;mF ¼ −2iand jF0;mF ¼ 2i and form W and M systems [seeFig. 1(b)]. This usually reduces the contrast of theCPT resonances. It was therefore expected that theCPT resonance contrast on the Cs D1 line (I ¼ 7=2)is very small, due to the high nuclear spin of theCs. Nevertheless, the CPT signal with absorptioncontrasts around 10% could be observed on the D1line of Cs atoms by use of the lin‖lin configuration,even higher than the ones measured for the classiccase with circularly polarized light fields. InSections 2 and 3 the details of these CPT signalsusing lin‖lin field excitation are described.

2. Experiments

The excitation scheme is shown in Fig. 1(b). A laserbeam with a linear polarization was transmittedthrough a vapor of cesium atoms in a magneticfield parallel to the beam direction. Therefore, σþand σ− transitions could be excited. Two two-photonresonances of a Λ type are formed involving twopairs of ground-state hyperfine sublevels: jF ¼ 3;mF ¼ −1i, jF ¼ 4;mF ¼ 1i and jF ¼ 3;mF ¼ 1i,jF ¼ 4;mF ¼ −1i. Both Λ schemes are excitedthrough the common excited state jF0 ¼ 3;mF ¼ 0i.

Figure 2 shows the experimental setup. The twooptical fields needed for the CPT signals were de-rived by phase modulating the output of a singleextended cavity diode laser (ECDL) in the vicinityof the D1 line of Cs (62S1=2 → 62P1=2, λ ≈ 894:6nm).A waveguide-type electro-optic modulator (EOM)modulated the phase of the optical field with afrequency around 4:6GHz, half of the ground-statehyperfine splitting frequency of Cs. The laser fre-quency was tuned such that the two first-ordersidebands were resonant with the transitions tothe F0 ¼ 3 excited state. The phase modulated laserbeam passed a linear polarizer with an extinctionratio of 50dB. A vapor cell 25mm in diameterand 25mm long was used in the measurementsat room temperature containing Cs and 10Torrof N2 buffer gas. The cell was surrounded by a mag-netic shield and placed inside a solenoid thatapplied a longitudinal magnetic field of the order

Fig. 1. (Color online) Excitation schemewith a lin‖lin field on theD1 line of (a) 87Rb and (b) Cs. (a) CPT resonances in 87Rb involvetwo pairs of ground-state hyperfine sublevels withjF ¼ 1;mF ¼ −1i, jF ¼ 2;mF ¼ 1i (solid lines) andjF ¼ 1;mF ¼ 1i, jF ¼ 2;mF ¼ −1i (dashed lines) coupled withthe common excited states jF0 ¼ 1;mF ¼ 0i. (b) CPT resonancesin Cs involve two pairs of ground-state hyperfine sublevels withjF ¼ 3;mF ¼ −1i, jF ¼ 4;mF ¼ 1i (solid lines) andjF ¼ 3;mF ¼ 1i, jF ¼ 4;mF ¼ −1i (dashed lines) coupled withthe common excited states jF0 ¼ 3;mF ¼ 0i. Additional single-photon resonances are possible in the case of Cs,indicated by the alternate long and short dashed lines.

20 February 2009 / Vol. 48, No. 6 / APPLIED OPTICS 1099

of 10 μT to lift the Zeeman energy levels’ degener-acy and to separate the “clock” resonance, whichhas no first-order magnetic field dependence, fromthe field-dependent resonances. To measure theCPT resonances, the EOM frequency was scannedover a range of 10kHz around 4:596315885GHz.The measured beam diameter was 19mm. The op-tical power transmitted through the gas cell wasthen detected with a Si photodiode. We performeda comparative study of four different excitationschemes of CPT resonance: (i) jF ¼ 3i →jF0 ¼ 3i, jF ¼ 4i → jF0 ¼ 3i with lin‖lin field;(ii) jF ¼ 3i → jF0 ¼ 4i, jF ¼ 4i → jF0 ¼ 4i withlin‖lin field; (iii) jF ¼ 3i → jF0 ¼ 3i, jF ¼ 4i →jF0 ¼ 3i with σ − σ field; (iv) jF ¼ 3i →jF0 ¼ 4i, jF ¼ 4i → jF0 ¼ 4i with σ − σ field. Aquarter-wave plate was used in front of the Cs cellwhen the laser radiation was circularly polarized.

3. Results and Discussion

The CPT amplitude, the absorption contrast of theresonance, and the full width at half-maximum(FWHM) linewidth of the four different excitationschemes are shown in Fig. 3. The absorption con-trast is defined as the ratio of the change in lightabsorption due to the CPT resonance to the absorp-tion off CPT resonance and gives us an idea of the“darkness” of the coherent dark state, i.e., the frac-tion of atoms that become “dark” when the two-photon resonance condition is fulfilled. It can be seenthat the CPT absorption contrast for lin‖lin excita-tion keeps increasing with higher laser intensities,while it reaches a maximum much earlier in the σ −

σ schemes [16]. The highest absorption contrast forlarger laser intensities was reached in the lin‖lincase with the common excited state jF0 ¼ 3i. Atnearly 10%, it was almost twice as high as the

Fig. 2. (Color online) (a) Experimental arrangement used to ob-serve the CPT phenomenon on the D1 line of Cs atoms. ECDL, ex-tended cavity diode laser; EOM, electro-optic modulator; PD,photo-detector. (b) CPT resonance absorption contrast with a totallaser power of 2:1mW: (i) lin‖lin excitation through a common ex-cited state jF0 ¼ 3i, (ii) lin‖lin excitation through a common ex-cited state jF0 ¼ 4i, (iii) σ − σ excitation through a commonexcited state jF0 ¼ 3i, (iv) σ − σ excitation through a commonexcited state jF0 ¼ 4i.

Fig. 3. (Color online) CPT (a) resonance amplitude, (b) absorptioncontrast, and (c) full width at half-maximum (FWHM): (i) lin‖linexcitation through a common excited state jF0 ¼ 3i (solid trian-gles), (ii) lin‖lin excitation through a common excited state jF0 ¼4i (open triangles), (iii) σ − σ excitation through a common excitedstate jF0 ¼ 3i (solid circles), (iv) σ − σ excitation through a commonexcited state jF0 ¼ 4i (open circles).

1100 APPLIED OPTICS / Vol. 48, No. 6 / 20 February 2009

maximum contrast measured in the σ − σ case. Con-sidering the fact that Cs has 16 ground-state Zeemanlevels, an absorption contrast of 10% means that alarge fraction of atoms accumulates in the darkstates and the destruction of the dark states dueto coupling to the other excited states is not as sig-nificant, as we expected. A slight degradation ofthe CPT contrast and linewidth could be caused byoff-resonant excitations to the excited F0 ¼ 4 state,which is separated from the F0 ¼ 3 state by1:1GHz. This splitting is considerably larger thanboth the Doppler width (∼400MHz) and the homoge-nous linewidth broadened by collisions with thebuffer gas (∼200MHz), but could nevertheless con-tribute to some destructive interference. Further-more, we want to note that in both excitationschemes, magnetically sensitive resonances can beobserved, for example, those involving the groundstates jF ¼ 3;mF ¼ −1i and jF ¼ 4;mF ¼ −1i. Thecontrast of these resonances was almost the sameas those of the clock resonances.It can be seen from Fig. 3 that the linewidth of CPT

resonance in the lin‖lin case broadens roughly line-arly with increased laser intensity. As expected, theyare slightly broader than the widths in the σ − σ case[17]. The broadening for the lin‖lin fields caused bythe splitting of the two CPT resonances in the mag-netic field can be neglected for higher laser intensi-ties. Through the nuclear contribution to the gfactors of the hyperfine components, the two Λ reso-nances shift apart at a rate of 22Hz=μT. In a 10 μTfield this splitting is therefore roughly 220Hz.Although the frequency splittings of jF ¼ 3;mF ¼ −1i, jF ¼ 4;mF ¼ 1i and jF ¼ 3;mF ¼ 1i, jF ¼4;mF ¼ −1i are slightly different, their position isto first order symmetrical relative to the hyperfinesplitting frequency. Thus, in the case of the lin‖linexcitation scheme, the presence of a small magneticfield leads only to broadening of the resonance andnot to a shift [13]. Also, the neighboring CPT reso-nances did not overlap because the resonances splitabout 70kHz in the magnetic field of 10 μT. It can beseen that in the lin‖lin case, the resonance ampli-tude and width both increase roughly linearly for alarge range of laser intensities, while the amplitudein the circular case reaches a maximum at muchlower intensities. This can allow for nearly constantresonance slopes for a wide range of intensities in thelin‖lin case with increased bandwidths, which couldbe of interest for applications such as atomicclocks less sensitive to accelerations and atomicmagnetometers.Finally, we would like to point out that the con-

trasts measured for the lin‖lin case, when coupledto the excited F0 ¼ 4 state, are much lower thanall the other cases investigated for Cs. Taichenachevet al. found similar behavior in 87Rb [13]. While thiscan be intuitively understood in the 87Rb case, itis not necessarily obvious in the case of Cs. In87Rb, there is a fundamental difference betweenthe schemes for the two excited states, because

single-photon transitions couple the Λ systems tothe F0 ¼ 2 state, but not the F0 ¼ 1 state [see Fig. 1(a)]. For Cs however, for both excited states F0 ¼ 3and 4, these single-photon transitions are possible,and it is more surprising that such different con-trasts are measured for the two excited states.

To gain some insight into these surprising results,density matrix calculations were performed for twosimplified systems. For the conventional σ − σ case,a 4-level model was used similar to the one of Vanieret al. [16]. Two ground states jF ¼ 3;mF ¼ 0i, jF ¼4;mF ¼ 0i couple to a common excited state jF0 ¼3; 4;mF ¼ 1i and a fourth ground state jF ¼ 4;mF ¼ 4i acts as a “trap”, as shown in Fig. 4(a).The parameters were chosen to resemble the experi-mental conditions: the population and coherencedecay rates are γ ¼ 5MHz and Γ ¼ 200MHz, respec-tively, for the excited state and γ12 ¼ 5MHz andΓ12 ¼ 200MHz for the ground states. The vapor is as-sumed to be optically thin and the atom at rest. Onelaser is tuned on resonance with the transition statejF ¼ 3i → jF0i, while the second laser frequency isscanned through the Raman resonance. The ratiosof Rabi frequencies are kept constant proportionalto the dipole matrix elements. The density matrixwas solved numerically as a function of two-photonRaman detuning to produce a spectrum of the CPTresonance. These resonances have been fitted withLorentzian line shapes similar to the fits performedon the experimental data.

Even though this is a very simplified model of thecomplicated Cs atom, it has been shown to predict

Fig. 4. Energy level diagrams used for modeling: (a) the 4-levelsystem was used for the σ − σ excitation scheme, where the jF ¼4;mF ¼ 4i serves as a “trap” state; (b) the 5-level system was usedfor the lin‖lin excitation scheme.

20 February 2009 / Vol. 48, No. 6 / APPLIED OPTICS 1101

the dependence of the dark line amplitude and widthwell [16]. The results shown in Figs. 5(a) and 5(b)(filled circles for the jF0 ¼ 3i excited state and opencircles for jF0 ¼ 4i). Both excited states give very si-milar results although the F0 ¼ 4 state gives slightlyhigher resonance amplitudes and linewidths. Forboth cases, the amplitudes saturate, as more atomsare pumped into the “trap” state.The lin‖lin case wasmodeled as a 5-levelM system

as shown in Fig. 4(b). The decay rates were identicalto the ones in the case with circularly polarized light.Figure 5 shows the results of the numerical solutions(filled triangles for jF0 ¼ 3i and open triangles forjF0 ¼ 4i). It can be seen, that the model predicts nosaturation of the amplitudes in this case. Further-more, the results for both excited states in this caseare not equal, but the F0 ¼ 3 states yields muchhigher amplitudes and narrower linewidths thanthe F0 ¼ 4 case. This is in agreement with the experi-mental results. Since two different very simplifiedmodels were used for the two systems, the absolute

amplitudes are not necessarily comparable and themodels can only give qualitative results. To makemore quantitative predictions, a calculation of thefull 32-level system would be useful, which is beyondthe scope of this paper. Nevertheless, we can getsome hints why the lin‖lin case results in high reso-nance amplitudes by varying the coupling strengthsΩ3 → Rp × Ω3 and Ω4 → Rp × Ω4 of the transitions tothe additional excited state jF0 ¼ 3; 4;mF ¼ 2ithrough a common scaling factor Rp. In the limitRp → 0, the system collapses to a 4-level system witha trap and an extra uncoupled excited state. ForRp → 1, it is the 5-level system used previously.For very low Rabi frequencies Ω1 and Ω2, the reso-nance amplitudes stay constant for low Rp and drop,as Rp increases, since more atoms are pumped out ofthe dark state into the additional states. For highRabi frequencies Ω1 and Ω2 however, the resonanceamplitudes can dramatically increase with increas-ing Rp. They reach a maximum around Rp ¼ 0:8and decrease afterward. This suggests that, in thecase of strong pumping, a large fraction of atomscan get trapped in the noncoupled “trap” state andthe additional light fields can repump these atomsback into the states that can contribute to a CPTresonance. This repumping could outweigh theadditional decoherence caused by the fields for mod-erate rates of Rp. This could be one possible explana-tion for the higher resonance amplitudes in thelin‖lin configuration compared to the conventionalsigma one.

4. Conclusion

We have experimentally realized a high-contrastdark resonance using a scheme of excitation of theD1 line of Cs with nuclear spin I ¼ 7=2 for lin‖linlight fields. A maximum absorption contrast of10% was obtained, which was higher than thatobserved in the conventional σ − σ case.

This work was partially supported by the StrategicInformation and Communications R&D PromotionProgramme (SCOPE) from the Ministry of InternalAffairs and Communications of Japan.

References1. G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimen-

tal method for the observation of r.f. transitions and laser beatresonances in oriented Na vapors,” Nuovo Cimento Soc. Ital.Fis. B 36, 5–20 (1976).

2. E. Arimondo, “Coherent population trapping in laser spec-troscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1996),Vol. 35, pp. 257–354.

3. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching,L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,”Appl. Phys. Lett. 85, 1460–1462 (2004).

4. S. Knappe, “MEMS atomic clocks,” in Comprehensive Micro-systems 3-Volume Set, Y. Gianchandani, O. Tabata, andH. Zappe, eds. (Elsevier, 2007), pp. 571–612.

5. N. Cyr, M. Tetu, and M. Breton, “All-optical microwavefrequency standard: a proposal,” IEEE Trans. Instrum. Meas.42, 640–649 (1993).

6. J. Vanier, “Atomic clocks based on coherent population trap-ping: a review,” Appl. Phys. B 81, 421–442 (2005).

Fig. 5. (Color online) Theoretical results from the numerical den-sitymatrix calculations: (a) resonance amplitude and (b) resonancelinewidth as a function of laser intensity: lin‖lin excitationthrough a common excited states jF0 ¼ 3i (solid triangles) andjF0 ¼ 4i (open triangles). The amplitudes for the σ − σ excitationthrough a common excited states jF0 ¼ 3i (solid circles) and jF0 ¼4i (open circles) are scaled by a factor of 10 for better visibility.

1102 APPLIED OPTICS / Vol. 48, No. 6 / 20 February 2009

7. M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg,A. Taichenachev, and V. Yudin, “Coherent population trappingresonances in thermal 85Rb vapor: D1 versus D2 line excita-tion,” Opt. Lett. 27, 1472–1474 (2002).

8. R. Lutwak, D. Emmons, T. English, and W. Riley, “The chip-scale atomic clock—recent development progress,” in Proceed-ings of the 35th Annual Precise Time and Time Interval (PTTI)Systems and Applications Meeting (U.S. Naval Observatory,2004), pp. 467–478.

9. Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer,“Push-pull optical pumping of pure superposition states,”Phys. Rev. Lett. 93, 160802 (2004).

10. S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichena-chev, V. L. Velichansky, and V. I. Yudin, “High-contrast darkresonance in σþ − σ

−optical field,” Laser Phys. Lett. 1, 495–

499 (2004).11. T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N.

Dimarcq, and A. Clairon, “High contrast Ramsey fringes withcoherent-population-trapping pulses in a double lambdaatomic system,” Phys. Rev. Lett. 94, 193002 (2005).

12. V. Shah, S. Knappe, L. Hollberg, and J. Kitching, “High-contrast coherent population trapping resonances usingfour-wave mixing in 87Rb,” Opt. Lett. 32, 1244–1246 (2007).

13. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, andS. A. Zibrov, “On the unique possibility of significantly increas-ing the contrast of dark resonances on the D1 line of 87Rb,”JETP Lett. 82, 398–403 (2005).

14. G. Kazakov, B. Matisov, I. Mazets, G. Mileti, and J. Delporte,“Pseudoresonance mechanism of all-optical frequency-standard operation,” Phys. Rev. A 72, 063408 (2005).

15. F. Levi, A. Godone, J. Vanier, S. Micalizio, and G. Modugno,“Line-shape of dark line and maser emission profile inCPT,” Eur. Phys. J. D 12, 53–59 (2000).

16. J. Vanier, M.W. Levine, D. Janssen, andM. Delaney, “Contrastand linewidth of the coherent population trapping transmis-sion hyperfine resonance line in 87Rb: effect of optical pump-ing,” Phys. Rev. A 67, 065801 (2003).

17. F. Renzoni and E. Arimondo, “Population-loss-induced nar-rowing of dark resonances,” Phys. Rev. A 58, 4717–4722(1998).

20 February 2009 / Vol. 48, No. 6 / APPLIED OPTICS 1103