We show that atomic spin motion can be controlled by circularly polarized
light without light absorption in the strong pumping limit. In this limit, the
pumping light, which drives the empty spin state, destroys the Zeeman coherence
effectively and freezes the coherent transition via the quantum Zeno effect. It
is verified experimentally that the amount of light absorption decreases
asymptotically to zero as the incident light intensity is increased.Comment: 4 pages with 4 figure

A. Hatakeyama

A. Luis

B. Misra

K. Mølhave

K. Yamane

M. Kitano

P. Kwiat

T. Nakanishi

T. P. Altenmüller

W. Happer

W. M. Itano

Physical Review A

English

arXiv

Crossref

Absorption-free optical control of spin systems: The quantum Zeno effect in optical pumping

Nakanishi, T

Yamane, K

Kitano, M

Kyoto University Research Information Repository

TitleAbsorption-free optical control of spin systems: The quantumZeno effect in optical pumpingAuthor(s)Nakanishi, T; Yamane, K; Kitano, MCitationPHYSICAL REVIEW A (2002), 65(1)Issue Date2002-01URL http://hdl.handle.net/2433/39821RightCopyright 2002 American Physical SocietyType Journal ArticleTextversionnone; publisherKyoto UniversityAbsorption-free optical control of spin systems: The quantum Zeno effect in optical pumpingT. Nakanishi, K. Yamane, and M. KitanoDepartment of Electronic Science and Engineering, Kyoto University, Kyoto 606-8501, Japan~Received 19 February 2001; published 13 December 2001!We show that atomic spin motion can be controlled by circularly polarized light without light absorption inthe strong pumping limit. In this limit, the pumping light, which drives the empty spin state, destroys theZeeman coherence effectively and freezes the coherent transition via the quantum Zeno effect. It is verifiedexperimentally that the amount of light absorption decreases asymptotically to zero as the incident lightintensity is increased.DOI: 10.1103/PhysRevA.65.013404 PACS number~s!: 32.80.Bx, 03.65.Xp, 42.50.2pThe quantum Zeno effect is known as the suppression ofunitary time evolution caused by decoherence in quantumsystems @1,2#. The decoherence is provided by measurement,interactions with the environment, stochastic fields, and soon. It is interesting in the sense that the coherent, unitaryevolution can be canceled by decoherent processes in a prob-ability conserving manner. If we look at the effect from theframe that moves so as to cancel the unitary evolution, thesystem, otherwise stationary, is guided by the decoherenceprocesses. Using this inverse Zeno effect, we can controlquantum systems with incoherent processes without the lossof probability @3#.In this paper, we will show that the quantum Zeno effectplays a crucial role in the optical pumping scheme. Thoughnot widely recognized, the light-induced decoherence has astrong influence on the spin dynamics. Optical pumping is auseful method to polarize atoms @4#. Let us consider a four-level atom with a J51/2 ground state and a J851/2 excitedstate. In order to polarize the atomic spin in the ground state,we apply a s1 pumping light beam that is propagated in thez direction and tuned to the transition between the groundstate and the excited state. The only spin-down atoms (mJ521/2) are excited by absorbing the pumping light, andrelax either to the spin-up state (mJ51/2) or to the spin-down state in the ground level. On the other hand, thespin-up atoms cannot absorb the pumping light. When thepumping light is strong enough, all the spin-down atoms arepumped out to the spin-up state. Once the spins are com-pletely polarized, the atomic ensemble does not absorb thepumping light anymore.However, in the presence of a magnetic field transverse tothe pumping light, the polarized spins are flipped back to thespin-down state. The magnetic field tends to equalize thepopulation of the spin-down state with that of the spin-upstate through the precession. Therefore, the absorption of thepumping light is needed to compensate the transition causedby the magnetic field.But it has been found that the spin polarization can beretained against the transverse magnetic field without anyabsorption of the pumping light @5#. At first sight, it mayseem contradictory, but the phenomenon can be understoodby considering the decoherence caused by the pumping light.The spin precession itself is suppressed by the light-induceddecoherence via the quantum Zeno effect, which accompa-nies no light absorption.In terms of the normal interpretation of the quantum Zenoeffect that the time evolution is suppressed by the frequentmeasurements, the transmission monitoring of the polarizedlight plays the role of measurements, from which we caninfer the spin direction. The absence of absorption is clearevidence that all the spin are in the up state. By performingthe null measurements frequently or continuously, one canfreeze the spin dynamics. This is a kind of interaction-freemeasurement @6#.When we apply a s1 pumping light beam in the z direc-tion under an external magnetic field B0 , the normalizedmagnetic moment m obeys the Bloch equation,dmdt 5m3V02Gm2P~m2ez!, ~1!where (ex ,ey ,ez) are the Cartesian unit vectors. The firstterm on the right-hand side represents the spin precessionaround B0 at the angular frequency uV0u5gguB0u with thegyromagnetic ratio gg . The second term represents the spinrelaxation by which the magnitude of the magnetic momentis decreased exponentially at the rate G. The relaxation is notan essential element for the quantum Zeno effect but wecannot ignore it in the actual experiment. The third termrepresents the optical pumping toward m5ez with the pump-ing rate P, which is proportional to the light intensity I.The steady-state solution to Eq. ~1! ism52PV0~P1G!21V02 ex1P~P1G!~P1G!21V02 ez , ~2!where we have assumed that the magnetic field is applied inthe y direction; V05V0ey .For the strong pumping limit, i.e., for P@V0 , P@G , wehave m;ez2O(V0 /P)ex . This means that in this limit allthe spin are polarized in the z direction even in the presenceof the transverse magnetic field.The key point of the optical pumping is the selectivepopulation transfer via excited states and a population distri-bution far from equilibrium in the ground states can beachieved. Therefore, one might think that in the above situ-ation the spin polarization is maintained by the repumping~population transfer! of the atoms flipped by the transversemagnetic field. However, as will be shown below, this is notthe case. The spin flip itself is suppressed by the quantumPHYSICAL REVIEW A, VOLUME 65, 0134041050-2947/2001/65~1!/013404~4!/$20.00 ©2001 The American Physical Society65 013404-1Zeno effect induced by the pumping light. By exciting theempty state ~the spin-down state in this case!, the pumpinglight destroys the Zeeman coherence and results in the Zenoeffect.One can distinguish the two scenarios by observing theabsorption of the pumping light. In the former case, weshould see some absorption corresponding to the repumpingof the spin flipped by the magnetic field. In the latter case,however, we will see no absorption, at least in principle,because the spin rotation is suppressed owing to the Zenoeffect. The Zeno effect can be realized without absorptionwhen the decoherence is provided by the excitation of theempty state.We will separate the pumping term in the Bloch equation~1! into the pumping ~population transfer! effect and the de-coherence effect. The pumping effect appears in the z com-ponent asdmzdt Upump5P~12mz!, ~3!which represents the population transfer from the spin-downstate to the spin-up state. The population transfer necessarilyaccompanies optical absorption ~and subsequent reemission!.For the completely polarized state, mz;1, this term has littleeffect on the spin dynamics.On the other hand, the decoherence effect appears in thex,y components asdmx ,ydt Upump52Pmx ,y . ~4!Note that both mx and my correspond to the coherence r12between the spin-up u1& and spin-down u2& states. The co-herence decays at the rate G1P in the presence of the pump-ing light. Therefore, Eq. ~4! represents the decoherence. Thisdecoherence causes the suppression of the spin precessionvia the quantum Zeno effect. It does not accompany opticalabsorption and works even when mz;1.The pumping rate P is connected with the pumping lightintensity I asP5hsI\v, ~5!where h, s, and \v are the pumping efficiency, the absorp-tion cross section, and the photon energy, respectively. Theabsorption coefficient a is defined asa5Ns 12 ~12mz!, ~6!where N is the atomic density. Substituting mz in Eq. ~6! byEq. ~2!, we obtaina5Ns2G~G1P !1V02~G1P !21V02 . ~7!For optically thin cases, i.e., aDz!1, the absorption of thepumping light DI is given by DI5IaDz , where Dz is thelength of the cell. With Eqs. ~5! and ~7!, we obtainDI5ePG~G1P !1V02~G1P !21V02 Dz , ~8!where we introduced e5N\v/2h for simplicity.Here we see that DI monotonically increases with P whenG.V0 , i.e., when the relaxation dominates the spin preces-sion. However, for G,V0 , DI increases up to a point P5(V021G2)/(V02G), then DI starts to decrease. In Fig. 1we plotted DI as a function of P in the case of G,V0 . Theabsorption approaches asymptotically a specific value:limP/V0→‘DI5eGDz . ~9!Thus, in the ideal condition where the intrinsic relaxationcan be neglected, one can suppress the spin evolution by thepumping light with no absorption. Notice that Eq. ~9! is in-dependent of the precession frequency V0 and is propor-tional to the relaxation rate G. The relaxation is an incoherentprocess and cannot be suppressed by the Zeno effect. On theother hand, the precession is a coherent process and can besuppressed.The dashed line in Fig. 1 represents the hypothetical curvefor which the decoherence presented by Eq. ~4! is omitted.The actual absorption ~the solid line! is much smaller thanthe dashed line. Moreover, the solid line is qualitatively dif-ferent from the dashed line in that it has a maximum pointand decreases with P thereafter. If the spin precession werenot suppressed by the pumping light, we would have a nor-mal saturated absorption profile like the dashed line in Fig. 1.This is because the polarized spins continue to precess at acertain rate and absorb the pumping light. The fact that theabsorption decreases with P is a clear evidence for the sup-pression of the precession by the pumping-induced decoher-FIG. 1. The solid line represents the theoretical absorption. Thedashed line is the absorption curve obtained by neglecting the termsrelated to the quantum Zeno effect. The optical pumping rate P andthe angular frequency of the precession V0 are normalized by therelaxation rate G, and these lines are calculated for V0 /G53. Theabsorption rate is also normalized to satisfy limP/V0→‘DI/I051.T. NAKANISHI, K. YAMANE, AND M. KITANO PHYSICAL REVIEW A 65 013404013404-2ence. The reduction of the absorption is a peculiar featureoriginating from the quantum Zeno effect.We use 85Rb atoms to verify the absorption-free featureexperimentally. The energy diagram for 85Rb is illustrated inFig. 2. A laser for the optical pumping is tuned to the tran-sition frequency between F53 and F853 in the D1 line(5S1/2→5P1/2). The circularly polarized pumping light(s1) induces the transitions satisfying DmF511, and even-tually populates all the atoms to the Zeeman sublevel mF53 in the absence of the transverse magnetic field.The pumping cycle is not closed within the transition be-tween F53 and F853; some of excited atoms in F853drop to the F52 level and are accumulated in that level. Inorder to prevent the hyperfine pumping we prepared anotherlaser which was tuned to the transition frequency from theF52 level in the ground state to the 5P3/2 state ~D2 line!.When the laser intensity is strong enough to repump theatoms in the F52 level, the pumping cycle is effectivelyclosed ~meshed region!. The intensity of the repumping lightmust be comparable to, or more than, that of the pumpinglaser.In our experimental condition, the absorption coefficientfor the pumping light is so small that we had to measure itwith some precision. We used a differential absorptionmethod. When the repumping light is turned on, Rb atomsshow the expected absorption of the pumping light. On theother hand, when the repumping light is turned off, due tothe hyperfine pumping, there remains few atoms in the F53 level, and the absorption of the pumping light becomesnegligibly small. The difference in the transmitted intensityof the pumping light between the two cases corresponds tothe absorption DI to be measured.Our experimental setup is illustrated in Fig. 3. We used anexternal-cavity diode laser with maximum output power 40mW for pumping ~D1 line!. A similar system was preparedfor repumping ~D2 line!. The power of the pumping laser canbe adjusted using a half-wave plate and a polarizing beamsplitter. The pumping and repumping beams were aligned soas to well overlap each other in the Rb cell. The cell ~2.2 cmin length and 2.0 cm in diameter! is kept at room tempera-ture. The cross section of the pumping beam, Ap , is about0.12 cm2, and that of the repumping beam, Ar , is about 0.36cm2.It is important to minimize the spin relaxation. The pri-mary factor of the relaxation is the diffusion of the atoms tothe cell wall. In order to suppress the atomic diffusion weused nitrogen as buffer gas at 8.0 kPa. A uniform magneticfield can be applied to the Rb cell by three pairs of Helm-holtz coils.As shown in Fig. 3, we measure the transmitted light in-tensity by using a photodiode ~PD! while chopping the re-pumping laser by a mechanical chopper. We have a rectan-gular wave form whose amplitude corresponds to theabsorption of the pumping light ~see the inset!. The choppingfrequency ~91 Hz! is smaller than the characteristic frequen-cies of the system, P, V0 , and G ~. several kilohertz!.In order to increase the pumping rate effectively, thetransmitted light through the Rb cell is reflected back by amirror so that the reflected light takes almost the same path.It should be noted that this does not mean that only the lightpath Dz interacting with Rb atoms is doubled. By overlap-ping the beams we can also double the pumping rate P ef-fectively. Then Eq. ~5! is modified asP52hs\vI , ~10!and the absorption ~8! is replaced byDI5Ia~2Dz !5ePG~G1P !V02~G1P !21V02 Dz . ~11!Figure 4 shows the experimentally obtained absorptioncurve. The power of the pumping laser incident to the Rb cellwas varied from 0 to 28 mW, and the power of the repump-ing laser was fixed at 32.8 mW. The strength of appliedmagnetic field was 2 mT (V0;9 kHz). Fitting the results tothe theoretical curve ~solid line!, we estimated the relaxationrate to be about 3 kHz. Owing to the differential absorptiontechnique, we were able to measure small variation in theabsorption constant (DI/I,2%) with high accuracy~,0.1%!.The result shows that the absorption decreases when thepumping power is over about 10 mW. The decrease in theFIG. 2. 85Rb energy diagram. The arrows represent opticalpumping ~thick lines!, repumping ~dashed line!, and the spontane-ous emission ~solid lines!. FIG. 3. Experimental setup. The inset shows the output signal ofthe photodetector ~PD!. Chopping of the repumping laser results inthe rectangular wave whose amplitude corresponds to the absorp-tion of the pumping light.ABSORPTION-FREE OPTICAL CONTROL OF SPIN . . . PHYSICAL REVIEW A 65 013404013404-3absorption was more than fluctuations ~a few mW!. We em-phasize repeatedly that the decrease in the absorption isqualitatively different either from linear absorption or fromsaturated absorption. This phenomenon is induced by theZeno suppression of the spin precession. The theoreticalcurve shows good agreement with the experimental result.As mentioned before, in the strong pumping limit the spinprecession can be suppressed completely by the quantumZeno effect, but the spin relaxation still persists. The dashedline in Fig. 4 shows the absorption curve for which the ab-sorption related to the relaxation is subtracted. This line de-clines more rapidly with the increase of pumping power, andis supposed to tend to zero. If we were to eliminate theintrinsic relaxation, we would have the pronounced decreasein the absorption.We can increase buffer gas pressure to reduce the relax-ation due to the diffusion. However, the spin relaxation bythe collision increases instead, and we cannot expect drasticimprovement. A considerable improvement will be expectedby cooling the atoms. But the laser cooling is usually per-formed under inhomogeneous magnetic fields, so we have toturn off the magnetic fields as well as the cooling laserbeams. Another possible method is the use of a glass cellcontaining dense 4He buffer gas. At the temperature blow 2.1K, the inner wall is coated with liquid 4He films and the spinrelaxation time is significantly reduced @7#. This method hasthe advantage that it is free from magnetic fields and gravity.It is reported that the spin polarization time can be extendedto as long as ;60 s.The suppression of the coherent transition by the opticalpumping is applicable to the quantum-state control of highlydegenerate multilevel systems such as in quantum logicgates. In order to prevent the population diffusion to unde-sired levels, we can optically pump these empty levels selec-tively. Moreover, we can attain active control of spin statesby using the inverse Zeno effect. By changing the pumpingdirection or the polarization continuously, we can change thespin direction arbitrarily. This is similar to the coherentpopulation trapping or the adiabatic passage with the darkstate @8#. A recent paper @9# presents the application to thepreparation of quantum state in superposition.Note added. A related paper by Molhave and Drewsen@10# was previously published.We wish to thank T. Ikushima for helpful discussions.This research was supported by the Ministry of Education,Culture, Sports, Science and Technology in Japan under aGrant-in-Aid for Scientific Research No. 11216203 and No.11650043.@1# B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18, 756~1977!.@2# W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland,Phys. Rev. A 41, 2295 ~1990!.@3# T. P. Altenmu¨ller and A. Schenzle, Phys. Rev. A 48, 70 ~1993!.@4# W. Happer, Rev. Mod. Phys. 44, 169 ~1972!.@5# M. Kitano, K. Yamane, and T. Ikushima, Phys. Rev. A 59, 3710~1999!.@6# P. Kwiat, H. Weinfurter, T. Herzog, and A. Zeilinger, Phys.Rev. Lett. 74, 4763 ~1995!.@7# A. Hatakeyama, K. Oe, K. Ota, S. Hara, J. Arai, and T.Yabuzaki, Phys. Rev. Lett. 84, 1407 ~2000!.@8# M. Kitano, Phys. Rev. A 56, 1138 ~1997!.@9# A. Luis, Phys. Rev. A 63, 052112 ~2001!.@10# K. Molhave and M. Drewsen, Phys. Lett. A 268, 45~2000!.FIG. 4. Experimental results ~(!, theoretical line fitted with theresults ~solid line!, and theoretical line without relaxation ~dashedline!. Applied magnetic field was 2 mT.T. NAKANISHI, K. YAMANE, AND M. KITANO PHYSICAL REVIEW A 65 013404013404-4

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Absorption-free optical control of spin systems:the quantum Zeno effect
  in optical pumping

Absorption-free optical control of spin systems:the quantum Zeno effect in optical pumping

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Kyoto University Research Information Repository

Kyoto University Research Information Repository