Transverse Optical Pumping of Spin States

ARTICLE

https://doi.org/10.1038/s42005-019-0170-4 OPEN Transverse optical pumping of spin states

Or Katz1,2 & Ofer Firstenberg 1

Optical pumping is an efﬁcient method for initializing and maintaining atomic spin ensembles

1234567890():,; in a well-defined quantum spin state. Standard optical pumping methods orient the spins by transferring photonic angular momentum to spin polarization. Generally the spins are oriented along the propagation direction of the light due to selection rules of the dipole interaction. Here we present and experimentally demonstrate that by modulating the light polarization, angular momentum perpendicular to the optical axis can be transferred efficiently to cesium vapor. The transverse pumping scheme employs transversely oriented dark states, allowing for control of the trajectory of the spins on the Bloch sphere. This new mechanism is suitable and potentially beneficial for diverse applications, particularly in quantum metrology.

1 Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel. 2 Rafael Ltd, IL-31021 Haifa, Israel. Correspondence and requests for materials should be addressed to O.K. (email: [email protected])

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= 〉 ^ ^; ^ ptical pumping is the prevailing technique for orienting polarized state |mg ±Fg is dark. Linearly polarized light e ¼ y z atomic spins, conveying order from polarized light onto generates spin alignment along ^x ´ê and zero net orientation with O 1–3 = → the state of spins . Many applications in precision the selection rules me mg when tuned to the transition Fg Fe 4–7 8–10 = − 1 metrology , quantum information , noble gas hyper- Fg 1. This generates a quadrupole magnetic moment , leav- 11–13 polarization , and searches for new physics beyond the ing both |mg = Fg〉 and |mg = −Fg〉 dark. It thus seems that no standard model14,15 employ optical pumping for initializing the orientation is built perpendicularly to the optical axis ^x for any orientation moment of the spins, that is, for pointing the spins light polarization. In the presence of a constant magnetic field, towards a preferred direction. The required degree of polarization precession around it may orient the spins along the transverse depends on the specific application, where optimized perfor- direction, but this is never achieved with considerable orientation. mance in quantum metrology is often practically achieved around Our scheme overcomes this limitation and allows for transverse 50% polarization16–18. Standard optical pumping schemes gen- optical pumping of the spins by temporally modulating the light erate polarization along the propagation direction of the laser polarization. beam. These schemes include depopulation pumping1, synchro- Here we propose and demonstrate an optical pumping scheme nous pumping19–21, spin-exchange indirect pumping22,23, for efficient spin polarization transversely to the propagation alignment-to-orientation conversion24,25, and hybrid spin- direction of the laser beam. The scheme incorporates a exchange pumping16. However, in various applications, it is polarization-modulated light beam, which steers the spins in often desired to polarize the spins along an applied magnetic field, helical-like trajectories on the Bloch sphere around and along a perpendicular to the optical axis18,26–30. While at extreme mag- transverse magnetic field, while gradually increasing their polar- netic fields, it is possible to polarize the spins transversely31,at ization. The scheme exhibits sharp resonances, reaching max- moderate magnetic fields, typical to alkali-metal spin experiments imum efficiency when the optical modulation is resonant with the for example, the pumping efficiency is rather low. Larmor precession of the spins. We develop a simple analytical In standard optical pumping schemes, the atomic ground state model for analyzing the experimental results and discuss the is polarized via repeated cycles of absorption and spontaneous applicability of the scheme for various applications. emission. Ideally, the atoms cease to absorb the pump photons when they reach a ‘dark state’, which is determined by the excited Results transitions during pumping1. For a light field with an electric field Experimental pumping of cesium spins. We employ the ω EðÞ¼t E eið LtÀkxÞê, the relevant transitions depend on the rela- experimental setup shown schematically in Fig. 1a, containing 0 ω tive detuning of the light frequency L from the atomic transition cesium vapor at room temperature. The energy level for a I = 1/2 ω fi frequency 0, on the external electric and magnetic elds, and on model is shown in 1b. Setting a constant magnetic field the selection rules of the dipole interaction for polarization ê. For B^z determines the quantization axis ^z and the Larmor frequency ω = = π alkali-metal vapors, the latter enables the pumping process of B gB, where g 0.35(2 ) MHz/G is the gyro-magnetic ratio spin orientation at moderate magnetic fields, when the ground for cesium. For the transverse pumping, we use a pump beam, ; fi = → = and excited magnetic sublevels jmg i jmei within each hyper ne whose frequency is tuned to the D1 transition Fg 4 Fe 3 manifold Fg, Fe are optically unresolved. and whose polarization is modulated according to In the absence of magnetic field and for constant polarization ê, ^ θ ^ iωt θ ^: one-photon absorption of light does not produce spin orientation etðÞ¼cosðÞz þ ie sinðÞy ð1Þ ^ transverselypffiffiffi to the optical axis. Circular light polarization e ± ¼ θ ω ^ ^ = ^ Here, sin( ) is the modulation depth and is the modulation ðy ± izÞ 2 orients the spins along the optical axis ± x via the angular frequency. For the sake of analysis and presentation, we allowed transitions m = m ± 1; For F ≤ F , the maximally e g e g introduce two far-detuned monitor beams propagating along x^ and ^y, measuring the three-dimensional orientation state of the spins (2Sx,2Sy,2Sz) on the Bloch sphere during the pumping a b ⏐e〉 zˆ F = 0 process. See Methods for additional experimental details. e In Fig. 2a–d, we present measurement and theoretical yˆ xˆ i t Ωe i t Ωe calculation of the spin dynamics on the Bloch sphere. Figure 2a sin sin 2 2 shows a typical measurement of the pumping process during Bzˆ continuous pumping operation. We observe that the spin Ω cos orientation follows a helical trajectory transversely to the optical ^ axis x. In this experiment, the pump power is P0 = 250 μW and 2 B ⏐1〉 the modulation frequency is tuned to resonate with the Larmor ⏐ 〉 F = 1 0 g frequency ωB ≈ ω = 1.5 (2π) kHz. The final value of 2Sz quantifies ⏐–1〉 fi Monitor the pumping ef ciency. Its dependence on the modulation ω θ Pump parameters and is shown in Fig. 3. We identify two resonant Fg = 0 ω ω ≈ ω θ = features of 2Sz( )at ± B as shown in Fig. 3a for 0.24 and two laser powers. The laser power governs the width of the Fig. 1 Experimental system and toy model. a Schematics of the resonance, as well as, the shift of the peak from the actual Larmor frequency. Figure 3b presents 2Sz(θ) on one of the resonances [ω experimental setup and the spiral motion of the atomic spins (green) = π ^ 10.3 (2 ) kHz]. We achieved an overall maximal polarization of towards þz. The polarization of the pump beam (red) alternates between = linear and circular (blue arrows). The spin orientation is monitored using 2Sqz ffiffiffiffiffiffiffiffiffiffiffiffiffiffi65% (with small residual transverse polarization 2 2 = balanced polarimetry of a far-detuned monitor beam (yellow). Not shown 2 Sx þ Sy 3.5%) as shown in Fig. 3c. are the repump beam and a second monitor beam, which co-propagate with the pump. b Toy model for alkali atoms with nuclear spin I = 1/2. The Dynamics of pumped spins. To explain the transverse pumping repump laser (blue arrow) empties the lower hyperfine state (with mechanism we utilize a simple model of an alkali-like level quantum number Fg = 0), while the pump laser (red and green arrows) structure with nuclear spin I = 1/2, as shown in Fig. 1b. The ω drives the atoms into the dark state d θ 1 p1ffiffiei t θ 0 (gray fi ^ j þi/cos jiÀ 2 sin ji magnetic eld B ¼ Bz (henceforth, assume B > 0) breaks the shading), eventually oriented perpendicular to the beam direction isotropy in the transverse yz plane, setting our quantization axis ^z

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a Experiment (I = 7/2)b Model (I = 1/2)

0.4 0.4 0.3 0.3 z z S 0.2 S 0.2 2 2 0.1 0.1 0 –0.2 0 –0.2 0.2 0 0.2 0 0 0 2S 0.2 0.2 2Sx –0.2 –0.2 2S y 2Sy x

c Experiment (I = 7/2)d Model (I = 1/2)

0.3 0.3 0.2 z 0.2 z S S 2 0.1 2 0.1 0 0 0.2 –0.2 0.2 –0.2 0 0 0 0 0.2 –0.2 2Sx 2S 0.2 –0.2 2Sx 2Sy y

Fig. 2 Spin trajectories on the Bloch sphere. The optical axis is ^x, within the equatorial plane. a, c Measurements of the pumping process from t = 0tot = 100 ms. b, d Theoretical toy model with nuclear spins I = 1/2. Red (green) circles mark the initial (final) states of the spin. a When pumping with a constant modulationpffiffiffiffiffiffiffi depth θ = 0.2 rad, the measured cesium spins follow a spiral-helical trajectory around the þ^z direction. c Adiabatically varying θðÞ¼t arccos t=T over T = 100 ms allows for driving the spins in a spherical-helical trajectory that ends along the ^z axis

a c

0.5 0.6 z

S 0 2

μ P0 = 120 W –0.5 μ P0 = 40 W 0.4

–12 –10 –8 81012 z

[2 KHz] S 2 b 0.6 0.2

z 0.4 S 2 0.2 0 0 0 /6 /3 /2 0.1 0 –0.1 [rad] 2Sx

Fig. 3 Dependence of the pumping degree on the modulation parameters. a Measured spin Sz(ω)att = 200 ms for cesium atoms with a modulation depth θ = 0.24 rad and Larmor precession rate ωB = 10.2 (2π) kHz. The resonance peaks at modulation frequency ω ≈ ± ωB are associated with the two coherent population trapping (CPT) dark states |d±〉. b Dependence on the modulation depth θ: measured Sz(θ)att = 200 ms with ω = ±10.3 (2π) kHz and pump 2 power P0 = 120 μW. Pumping is optimal at moderate modulation depths, such that |d+〉 is oriented towards þ^z, but the dark state pumping Γ sin ðÞθ competes the relaxation rate γ. Vertical error bars indicate standard deviation of the measured value. c Measured spin trajectory, corresponding to the point marked by an arrow in b. The ﬁnal polarization (green circle) is along ^z, i.e. perpendicular to the optical axis, with a small residual polarization along ^x and ^y

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; ħω = and splitting the Zeeman sublevelsji 0 ji±1 by B. The Fg 0 system via destructive interference of two excitation pathways. level is emptied by a repump field or by spin–exchange collisions. Considering the level structure in Fig. 1b and decomposing the fi = → = ^ The pump eld, resonant with the Fg 1 Fe 0 transition, is modulated pump into its two polarization components Ez and ^ Λ Λ ; ; polarization-modulated according to Eq. (1). We describe the Ey, we identify two systems: þ ¼fji1 jie jig0 and Λ ; ; Λ effect of the polarization modulation on the spin dynamics by À ¼fÀji1 jie jig0 . System + has the dark state jdþi/ decomposing the polarization vector êtðÞinto its Stokes compo- 1ffiffi iωt cosðÞθ ji1 À p e sinðÞθ ji0 at ω ≈ ω , while system Λ− has the bs ; ; 32,33 ^ 2 B nents ¼ðs1 s2 s3Þ . The unmodulated linear polarization z, ω ^ dark state jd i/cosðÞÀθ ji1 À p1ffiffiei t sinðÞθ ji0 at ω ≈ −ω . For represented by s1, aligns the atoms along z at a rate À 2 B Γ 2 θ θ Ra cos ðÞ, creating spin alignment (see Supplementary 1, the dark states jd ± iji±1 represent the polarized states Γ = Ω2 γ Note 1). Here / e is the characteristic pumping rate, with perpendicular to the optical axis. The application of magnetic γ Ω fi ^ Λ Λ ω e the spontaneous emission rate and the Rabipffiffiffi frequency of the eld Bz separates the CPT resonances of + and − by 2 B,so pump beam. The linear polarization ð^y ± ^zÞ= 2, represented by that the states |d+〉 and |d−〉 cannot be simultaneously dark when ^ ω Γ ω = ω Λ− s2, induces a tensor light shift of Γ sin(2θ) sin(ωt) along ± x, B . Consequently, setting B depopulates the system which acts like a magnetic field. This light shift appears when the while pumping the Λ+ system towards the transversely oriented linearly polarized light is neither parallel nor perpendicular to the dark state |d+〉. We conclude that destructive interference of two spin alignment34. The circular polarization ê , represented by s , excitation pathways effectively modifies the absorption selection ± 3 ω pumps the spins longitudinally along ± ^x at a rate Γ sin(2θ) cos rules, such that one polarized state (e.g. jiÀ1 for B > 0) absorbs ω (ωt), while vector light shift is absent for the resonant optical photons, while the opposite state (ji 1 for B > 0) is transparent. transition. Therefore, the modulated polarization alternates We associate the two resonances in Fig. 3a with the CPT dark between pumping (s ) and light shifting (s ) the atomic spins states of Λ+ at ω > 0 and Λ− at ω < 0. In the absence of the upper 3 2 fi = fi along ^x at a rate ω. For ω = ω , the pumping and light shifts are hyper ne level Fe 4, we expect to nd distinct resonance peaks B ω = synchronous, efficiently driving the precessing spins away from at ± B; it is the presence of Fe 4 that breaks the symmetry ω ω ≠ − −ω the xy plane, transversely to the optical axis. The resulting evo- between positive and negative [Sz( ) Sz( )], generates the ω = ω lution of the Bloch vector (2Sx,2Sy,2Sz) is shown graphically in small Fano-like features, and shifts the peak from B. As seen Fig. 4 and further detailed in Methods. in Fig. 3b, the pumping is most efficient at moderate modulation θ → π The toy model enables one to reconstruct the main features of depths: For /2 the dark state is jdþi!ji0 , with zero net θ → the measured trajectories as shown in Fig. 2b, by solving the I = orientation. For 0, the dark state is jdþiji1 , but the 2 1/2 model numerically and tuning its parameters (see Supple- depopulating rate of |d−〉, proportional to Γ sin ðÞθ , is too small mentary Note 1). We note however that this model only aims at compared to the overall depolarization rate γ. explaining the qualitative features of the process, while disregard- A benefit of the CPT resonant operation is the ability to ing effects arising from the multilevel structure of cesium and temporally vary the system state in a controlled, adiabatic from level mixing due to line broadening, which would reduce the manner. To demonstrate this, we monitor the pumping process fi ω = ω = π pumping ef ciency. We attribute these effects to the observed on resonance [ B 1.5 (2 ) kHz], while temporally varyingpffiffiffiffiffiffiffiffi maximum of 65% polarization, rather than the 100% polarization θ over a duration T = 100 ms according to θðÞ¼t arccos t=T. expected for an I = 1/2 system (see Methods). The spin state, initially pumped to jdþiθðÞt¼0 ji0 , adiabatically 〉 fi follows the varying dark state |d+ θ(t) to its nal value Coherent population trapping. The resonant nature of the jdþiθðÞt¼T ji1 , tracing a spherical-like trajectory as shown in pumping process can also be understood using the following Fig. 2c (experiment) and Fig. 2d (theory). This process is similar supplementary picture, as originating from coherent population to stimulated Raman adiabatic passage36 and can therefore be trapping (CPT)35. In CPT, a dark state is formed within a Λ level- used to tailor desired trajectories and final states. Notably, it enables the zeroing of the transverse spin components Sx and Sy at zˆ a the end of the process, as shown in Fig. 2c, d. Bzˆ yˆ xˆ b c Discussion −S 3 d It is relatively simple to implement the presented scheme in −S2 applications. Polarization modulation can be done using a single

S3 photo-elastic modulator (Photoelastic Modulators, www.hind- sinstruments.com/products/photoelastic-modulators) or with S Pumping 2 readily available, on-chip, integrated photonics37. Various appli- t = 0 Light shift cations that rely on optical spin manipulation and feature fi fi t = /2 Pumping resolved hyper ne spectra could potentially bene t from utilizing fl t = Light shift the scheme. Here we brie y consider some directions with spin t = 3/2 vapors. First, devices currently employing perpendicular beams in a – Fig. 4 Transverse pumping mechanism. One period of the transverse pump-probe configuration26 28 could be realized with a simpler, pumping mechanism for ω = ωB, where the modulation frequency ω is co-propagating arrangement, with the spins oriented transversely fi synchronous with the Larmor precession rate ωB. The spins (green arrows) to the optical axis. Such arrangement is most bene cial for precess ωBt = π/2 radians between each subplot due to the magnetic field miniaturized sensors, such as nuclear magnetic resonance (NMR) 28,29 B^z. a The spins are optically pumped towards À^x. b The spins are tilted oscillators , where the size and complexity depend crucially on towards þ^z due to tensor light shift. c The spins are optically pumped the beam's configuration, especially if the light source, manip- towards þ^x. d The spins are again tilted towards þ^z due to tensor light ulation, and detection can be implemented on a single stack over shift. Black arrows indicate the pumping/tilting directions. The eventual a chip27. These sensors are used in various applications as well as 29,38 spin orientation is along þ^z, perpendicular to the propagation direction of in fundamental research, such as search for new physics . the pumping beam Particularly for NMR oscillators, the projection of the alkali spin

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fi = along the magnetic eld will be unmodulated, thus sustaining the higher magnetic moments. At low atomic densities and depopulated Fg 3 spin-exchange optical pumping of the noble gas spins. hyperfine manifold, the detected Faraday-rotation angles are proportional to the 2,49 Second, any application that is restricted to a single laser spin orientation along the direction of the beam . We calibrate the pro- portionality constants of each monitor beam by measuring its maximal polariza- direction and requires moderate alkali polarization (tens of per- tion rotation when the ground state is fully pumped using two circularly polarized cents) can now use our scheme to control and fine-tune the final beams resonant with the two ground-state hyperfine manifolds. We reconstruct the direction of the pumped spins (longitudinal, transversal, or three spin components by making two consecutive measurements: First, Sx and Sy are measured when B ¼ B^z. Second, a measurement is conducted with B ¼ B^y and combination thereof). One example includes remote magneto- θ θ → π − θ 26,39 changed by /2 , keeping the other experimental parameters unchanged. metry of mesospheric sodium spins . Third, transverse As a result, spin is built along ^y and measured by the ^y monitor. This provides the fi fi pumping may form the basis for an all-optical magnetometer Sz component of the rst con guration. We verify that Sx is unaffected by the using either alkali-metal atoms or metastable 4He atoms designed change of θ, B, by confirming that the parameter change is appropriate. for space applications26,38. This magnetometer would rely on measuring the resonant response to the modulated light, pro- Spin dynamics with polarization-modulated light. For small modulation depths θ 〈 〉 = viding a dead-zone-free operation32, or on measuring the Faraday 1, the dynamics is governed by Bloch-like equations of the vector F (Fx, Fy, Fz) (see Supplementary Note 1 for the general treatment). This dynamics is rotation of off-resonant probe light, thus reducing the photon qualitatively shown in Fig. 4 at four parts of the pumping period: at ωt = 0 shot-noise commonly limiting magnetometers based on electro- [Fig. 4a], at ωt = π/2 [Fig. 4b], at ωt = π [Fig. 4c] and at ωt = 3π/2 [Fig. 4d]. The 40 magnetically induced transparency . Moreover, the polarization- spin orientations Fx (along the optical axis) and Fy are subject to modulated pump generates the m = 1 Zeeman coherence30, _ γ ω Γ θ ω ; Fx ¼À ?Fx À BFy À sinðÞ 2 cosðÞt ð2Þ implying that these magnetometers could operate in the spin- 41 _ γ ω Γ θ ω ; exchange relaxation-free (SERF) regime , where spin-exchange Fy ¼À ?Fy þ BFx þ sinðÞ 2 sinðÞt Fz ð3Þ fi collisions may also assist in repumping the lower hyper ne γ γ 2 θ Γ which include a transverse decay rate ? ¼ þð1 þ cos Þ and Larmor pre- 42 ω γ manifold . cession at the rate B. Here denotes a slow ground-state depolarization rate (e.g., Finally, our scheme does not rely on any process particular due to wall collisions). The third term in Eq. (2) is due to s3. It describes a to vapor physics. It is thus readily applicable to any spin temporally modulated optical pumping, which is maximal at ωt = 0 (and at all ωt Λ = 2πn for any integer n) towards À^x (Fig. 4a) and at ωt = π towards þ^x (Fig. 4c). system having a non-degenerate -system with a meta-stable fi The pumping of Fx is thus most ef cient when the optical modulation is syn- ground manifold, such as those employed in diamond color chronous with the Larmor precession ω = ω . The third term in Eq. (3) is due to 43,44 45 B centers , rare-earth doped crystals , and semiconductor the modulated linear polarization component s2. It describes a tensor light shift, quantum dots46–48. which acts as a magnetic field along ^x that rotates the spins in the yz plane at a Γ θ ω fi In conclusion, we have demonstrated a new optical pumping modulated rate sin (2 ) sin ( t). The orientation Fz along the magnetic eld, which we aim to generate, is subject to technique, generating significant spin orientation transversely to hi _ γ Γ θ ω ω ; ; the propagation direction of the pump beam. The spins are Fz ¼À kFz À sinðÞ 2 sinðÞt Fy À cosðÞt fgFz Fx ð4Þ oriented along the external transverse magnetic field via alter- where the first term is a longitudinal decay at a rate γ ¼ γ þ 2Γ sin2 θ, the second nating actions of pumping and tensor light shifts, which are k term is again light shift due to s2, and the third term is an alignment-induced shift. resonant with the Larmor precession. The resonance features, The temporal modulation sin(ωt) of the light shift is a key ingredient in pumping F associated with transversely orientated dark states, allow one to towards þ^z, as it breaks the symmetry between the ± ^z directions: The sign of the control the spin trajectory on the Bloch sphere by varying the light shift changes together with the sign of Fy, thus acting as an alternating fi ^ modulation parameters. This scheme could be highly suitable for magnetic eld that always tilts the spins -towards þz, with maximal tilting rate obtained at ωt = π/2 (Fig. 4b) and ωt = 3π/2 (Fig. 4d). The tensor term quantum-metrology applications. ; ^; ^ ω fFz FxghfgiFz Fx , resonant at B, contributes similar spin buildup in ampli- tude, but with a π/2 delay (see Supplementary Note 1). Contribution of other ω ω ω Γ ω = ω tensor terms resonant at 2 B is negligible for B . For B, both the Methods synchronous pumping and the light shift are most efficient, driving the precessing Additional experimental details. We use a 10-mm-diameter, 30-mm-long spins away from the xy plane, transversely to the optical axis. For large magnetic cylindrical glass cell containing cesium vapor (I = 7/2, S = 1/2) at room tem- fi ω Γ Γ 2 θ; γ fi elds and strong control beam B sin , the steady-state polarization perature. The cell is paraf n coated and free of buffer gas, exhibiting spin coher- on resonance (ω = ω ) is given by ence time of 150 ms30. We set a constant magnetic field B^z in the cell using B Helmholtz coils and four layers of magnetic shields. For the transverse pumping, Γ sin2 θ F ¼ ; we use an 895-nm single-mode pump beam using a free-running distributed Bragg z Γ sin2 θ þ γ fl re ector (DBR) diode laser (see optical schematics in Supplementary Fig. 1). We Γ 2 θ modulate the pump polarization by splitting it with a polarizing beam splitter where sin can be interpreted as the effective optical pumping rate for depopulating the bright state |−1〉 (see derivation in Supplementary Note 2). The (PBS) and sending each output arm to an acousto-optic modulator (AOM), = θ Δ + π + fl transverse spin components are then given by Fx tan cos ( t )(1 Fz)/2, operating at 200 MHz. The two beams de ected by the modulators are recombined = θ Δ + Δ = ω − ω and mode-matched using a second PBS, resulting with the polarization given in Eq. and Fy tan sin( t)(1 Fz)/2, where B denotes the frequency mis- (1). The pump frequency after passing the modulators is tuned to resonance with match from resonance. We thus conclude that high polarization along the mag- = → = netic field and transverse to the optical axis is achievable for I = 1/2 spins. the D1 transition Fg 4 Fe 3, within the Doppler width. We control the modulation angular frequency ω by setting the relative radio frequencies of the two modulators. We control the modulation depth sin(θ) either by rotating the linear Data availability fi θ polarization using a half-wavelength wave-plate before the rst PBS for constant The data that support the findings of this study are available from the corresponding (e.g., Figs. 2a, 3c), or by varying the relative RF amplitudes of the two AOMs for a author on reasonable request. time-varying θ(t) (e.g., Fig. 2d). We sample the pumping beam before the entrance to the cell and measure the Stokes component S2 to determine the polarization state fi = of the light. To keep the lower hyper ne manifold Fg 3 empty, we use 1 mW of Received: 6 January 2019 Accepted: 17 May 2019 auxiliary repump beam at 895 nm, using a second free-running DBR laser. The = → = repump is resonant with the Fg 3 Fe 4 transition, within the Doppler width, and linearly polarized along ^y. The pump and repump, both with a diameter of 8 mm, counter-propagate along the ^x axis.

Reconstruction of the spin state on the Bloch sphere. The spin state is References = 〈 〉 1. Happer, W. Optical pumping. Rev. Mod. Phys. 44, 169 (1972). reconstructed by evaluating the electronic spin orientations (2Sx,2Sy,2Sz) F /4, where 〈F〉 is the orientation moment of the total spin operator F = I + S. The spin 2. Happer, W., Jau, Y.-Y. & Walker, T. G. Optically Pumped Atoms (Wiley, New orientations are measured by using balanced polarimetry of two linearly polarized York, 2009). monitor light beams propagating along x^ and ^y. The monitor light is 30 GHz blue- 3. Auzinsh, M., Budker, D. & Rochester, S. M. Optically Polarized Atoms: = → = detuned from the optical transition Fg 4 Fe 3. Polarization rotation of far- Understanding Light-Atom Interactions. 1st edn (Oxford University Press, detuned light is sensitive to spin orientation along the optical axis and insensitive to Oxford, 2010).

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4. Budker, D. & Romalis, M. V. Optical magnetometry. Nat. Phys. 3, 227 (2007). 36. Vitanov, N. V., Rangelov, A. A., Shore, B. W. & Bergmann, K. Stimulated 5. Kominis, I. K., Kornack, T. W., Allred, J. C. & Romalis, M. V. Nature 422, Raman adiabatic passage in physics, chemistry, and beyond. Rev. Mod. Phys. 596–599 (2003). 89, 015006 (2017). 6. Kitching, J., Knappe, S. & Donley, E. A. Atomic sensors – a review. IEEE Sens. 37. Sarmiento-Merenguel, J. D. et al. Demonstration of integrated polarization J. 11, 1749 (2011). control with a 40 dB range in extinction ratio. Optica 2, 1019–1023 (2015). 7. Horsley, A., Du, G. X. & Treutlein, P. Widefield microwave imaging in alkali 38. Patton, B., Zhivun, E., Hovde, D. C. & Budker, D. All-optical vector atomic vapor cells with sub-100 mm resolution. New J. Phys. 17, 112002 (2015). magnetometer. Phys. Rev. Lett. 113, 013001 (2014). 8. Hammerer, K., Sørensen, A. S. & Polzik, E. S. Quantum interface between light 39. Higbie, J. M. et al. Magnetometry with mesospheric sodium. Proc. Natl Acad. and atomic ensembles. Rev. Mod. Phys. 82, 1041–1093 (2010). Sci. USA 108, 3522 (2011). 9. Møller, C. B. et al. Quantum back-action-evading measurement of motion in a 40. Fleischhauer, M., Matsko, A. B. & Scully, M. O. Quantum limit of optical negative mass reference frame. Nature 547, 191 (2017). magnetometry in the presence of ac Stark shifts. Phys. Rev. A 62, 013808 10. Novikova, I., Walsworth, R. & Xiao, Y. Electromagnetically induced (2000). transparency-based slow and stored light in warm atoms. Laser Photon. Rev. 6, 41. Katz, O. et al. Nonlinear elimination of spin-exchange relaxation of high 333–353 (2012). magnetic moments. Phys. Rev. Lett. 110, 263004 (2013). 11. Walker, T. G. & Happer, W. Spin-exchange optical pumping of noble-gas 42. Chalupczak, W., Josephs-Franks, P., Patton, B. & Pustelny, S. Spin-exchange nuclei. Rev. Mod. Phys. 69, 629 (1997). narrowing of the atomic ground-state resonances. Phys. Rev. A 90, 042509 12. Appelt, S. et al. Theory of spin-exchange optical pumping of 3He and 129Xe. (2014). Phys. Rev. A 58, 1412 (1998). 43. Yale, C. G. et al. All-optical control of a solid-state spin using coherent dark 13. Chupp, T. & Swanson, S. Medical imaging with laser-polarized noble gases. states. Proc. Natl Acad. Sci. USA 110, 7595 (2013). Adv. Mol. Opt. Phys. 45, 41 (2001). 44. Zhou, B. B. et al. Holonomic quantum control by coherent optical excitation 14. Kuchler, F. et al. A new search for the atomic EDM of 129Xe at FRM-II. in diamond. Phys. Rev. Lett. 119, 140503 (2017). Hyperfine Interact. 237, 95 (2016). 45. Schraft, D., Hain, M., Lorenz, N. & Halfmann, T. Stopped light at high storage fi 3+ 15. Vasilakis, G., Brown, J. M., Kornack, T. W. & Romalis, M. V. Limits on new ef ciency in a Pr :Y2SiO5 crystal. Phys. Rev. Lett. 116, 073602 (2016). long range nuclear spin-dependent forces set with a K−3He comagnetometer. 46. Weiss, K. M. et al. Coherent two-electron spin qubits in an optically active pair Phys. Rev. Lett. 103, 261801 (2009). of coupled InGaAs quantum dots. Phys. Rev. Lett. 109, 107401 (2012). 16. Romalis, M. V. Hybrid optical pumping of optically dense alkali-metal vapor 47. Houel, J. et al. High resolution coherent population trapping on a single without quenching gas. Phys. Rev. Lett. 105, 243001 (2010). hole spin in a semiconductor quantum dot. Phys. Rev. Lett. 112, 107401 17. Kornack, T. W. A Test of CPT and Lorentz Symmetry Using a K-3He Co- (2014). magnetometer. Ph.D. thesis (Princeton University, Princeton, 2005). 48. Weinzetl, C. et al. Coherent control and wave mixing in an ensemble of 18. Muschik, C. A., Polzik, E. S. & Cirac, J. I. Dissipatively driven entanglement of silicon-vacancy centers in diamond. Phys. Rev. Lett. 122, 063601 (2019). two macroscopic atomic ensembles. Phys. Rev. A 83, 052312 (2011). 49. Katz, O., Peleg, O. & Firstenberg, O. Coherent coupling of alkali atoms by 19. Fescenko, I., Knowles, P., Weis, A. & Breschi, E. A Bell-Bloom experiment random collisions. Phys. Rev. Lett. 115, 113003 (2015). with polarization-modulated light of arbitrary duty cycle. Opt. Express 21, 15121 (2013). 20. Seltzer, S. J., Meares, P. J. & Romalis, M. V. Synchronous optical pumping of Acknowledgements quantum revival beats for atomic magnetometry. Phys. Rev. A 75, 051407(R) We thank O. Peleg, R. Shaham, and C. Avinadav for helpful discussion. We acknowledge (2007). financial support by the Israel Science Foundation and ICORE, the European Research 21. Klepel, H. & Suter, D. Transverse optical pumping with polarization- Council starting investigator grant Q-PHOTONICS 678674, the Pazy Foundation, the modulated light. Opt. Commun. 90, 46 (1992). Minerva Foundation with funding from the Federal German Ministry for Education and 22. Chalupczak, W. et al. Enhancement of optically pumped spin orientation via Research, and the Laboratory in Memory of Leon and Blacky Broder. spin-exchange collisions at low vapor density. Phys. Rev. A 85, 043402 (2012). 23. Chalupczak, W. & Josephs-Franks, P. Alkali-metal spin maser. Phys. Rev. Lett. Author contributions 115, 033004 (2015). O.K. conducted the experiment and analyzed the data. O.F. and O.K. designed the 24. Budker, D., Kimball, D. F., Rochester, S. M. & Yashchuk, V. V. Nonlinear experiment, performed the theoretical analyses, and wrote the paper. magneto-optical rotation via alignment-to-orientation conversion. Phys. Rev. Lett. 85, 2088 (2000). 25. Budker, D. et al. Resonant nonlinear magneto-optical effects in atoms. Rev. Additional information Mod. Phys. 74, 1153 (2002). Supplementary information accompanies this paper at https://doi.org/10.1038/s42005- 26. Budker, D. & Jackson Kimball, D. F. Optical Magnetometry (Cambridge 019-0170-4. University Press, New York, 2013). 27. Kitching, J. et al. Microfabricated atomic magnetometers and applications. in Competing interests: The authors declare no competing interests. Frequency Control Symposium, IEEE International, 789–794 (IEEE, 2008). 28. Walker, T. G. & Larsen, M. Spin-exchange-pumped NMR gyros. Adv. Mol. Reprints and permission information is available online at http://npg.nature.com/ Opt. Phys. 65, 373–401 (2016). reprintsandpermissions/ 29. Bulatowicz, M. et al. Laboratory search for a long-range T-Odd, P-Odd interaction from axionlike particles using dual-species nuclear magnetic Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in resonance with polarized 129Xe and 131Xe gas. Phys. Rev. Lett. 111, 102001 published maps and institutional affiliations. (2013). 30. Katz, O. & Firstenberg, O. Light storage for one second in room-temperature alkali vapor. Nat. Commun. 9, 2074 (2018). Open Access This article is licensed under a Creative Commons 31. Martin, C., Walker, T., Anderson, L. W. & Swenson, D. R. Laser optical Attribution 4.0 International License, which permits use, sharing, pumping of potassium in a high magnetic field using linearly polarized light. adaptation, distribution and reproduction in any medium or format, as long as you give Nucl. Instrum. Methods Phys. Res. Sect. A 335, 233 (1993). appropriate credit to the original author(s) and the source, provide a link to the Creative 32. Ben-Kish, A. & Romalis, M. V. Phys. dead-zone-free atomic magnetometry Commons license, and indicate if changes were made. The images or other third party with simultaneous excitation of orientation and alignment resonances. Rev. material in this article are included in the article’s Creative Commons license, unless Lett. 105, 193601 (2010). indicated otherwise in a credit line to the material. If material is not included in the 33. Novikova, I., Mikhailov, E. E. & Xiao, Y. Excess optical quantum noise in article’s Creative Commons license and your intended use is not permitted by statutory atomic sensors. Phys. Rev. A 91, 051804(R) (2015). regulation or exceeds the permitted use, you will need to obtain permission directly from 34. Cohen-Tannoudji, C. & Dupont-Roc, J. Experimental study of Zeeman light the copyright holder. To view a copy of this license, visit http://creativecommons.org/ fi shifts in weak magnetic elds. Phys. Rev. A 5, 968 (1972). licenses/by/4.0/. 35. Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633 (2005). © The Author(s) 2019

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