We experimentally demonstrate electromagnetically induced transparency and
light storage with ultracold 87Rb atoms in a Mott insulating state in a three
dimensional optical lattice. We have observed light storage times of about 240
ms, to our knowledge the longest ever achieved in ultracold atomic samples.
Using the differential light shift caused by a spatially inhomogeneous far
detuned light field we imprint a "phase gradient" across the atomic sample,
resulting in controlled angular redirection of the retrieved light pulse.Comment: 4 pages, 4 figure

Bloch, I.

Davidson, N.

Kuhr, S.

Pugatch, R.

Schnorrberger, U.

Thompson, J. D.

Trotzky, S.

English

arXiv

We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold Rb-87 atoms in a Mott insulating state in a three-dimensional optical lattice. We have observed light storage times of similar or equal to 240 ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a ``phase gradient'' across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse

Name not available

Electromagnetically induced transparency and light storage in an atomic Mott insulator

Thompson, J.

MPG.PuRe

Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator

University of Strathclyde Institutional Repository

arXiv:0903.0135v1  [quant-ph]  1 Mar 2009Electromagnetically Induced Transparency and Light Storagein an Atomic Mott InsulatorU. Schnorrberger1, J. D. Thompson1,2, S. Trotzky1, R. Pugatch3, N. Davidson3, S. Kuhr1, and I. Bloch1,41Johannes Gutenberg-Universita¨t, Institut fu¨r Physik, Staudingerweg 7, 55128 Mainz, Germany2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA3Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel4Max-Planck-Institut fu¨r Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany(Dated: March 1, 2009)We experimentally demonstrate electromagnetically induced transparency and light storage withultracold 87Rb atoms in a Mott insulating state in a three dimensional optical lattice. We haveobserved light storage times of ≃ 240 ms, to our knowledge the longest ever achieved in ultracoldatomic samples. Using the differential light shift caused by a spatially inhomogeneous far detunedlight field we imprint a “phase gradient” across the atomic sample, resulting in controlled angularredirection of the retrieved light pulse.PACS numbers: 37.10.Jk, 42.50.GyCoherent interaction between light and matter plays animportant role in many quantum information and quan-tum communication schemes [1, 2]. In particular, it isdesirable to transfer quantum states from photonic, “fly-ing” qubits to matter-based systems for storage and pro-cessing [3]. In this context, electromagnetically inducedtransparency (EIT) has proven extremely useful, sinceit allows an incoming light pulse to be converted intoa stationary superposition of internal states and backinto a light pulse [4, 5, 6, 7]. This effect has success-fully been used to map quantum states of light onto coldatomic ensembles [8] or even to transmit quantum infor-mation between two such remote quantum memories [9].EIT and light storage have been realized in crystals [10],atomic vapors [7, 11] and in ultracold atomic ensembles[6, 12, 13]. In crystals, storage times of several secondshave been achieved [14]. In vapor cells, inelastic colli-sions with other atoms or with the walls usually limitthe coherence times to a few milliseconds [15, 16]. Incold atomic samples the light storage times are also on amillisecond timescale [6]. Using magnetically insensitivestates, storage times of up to 6 ms were recently observedeven for single quantum excitations in cold atomic gases,limited by loss of atoms [17] or thermal diffusion [18].Ultracold atoms in a Mott insulator (MI) state withunity filling in a deep 3D optical lattice are ideal forlight storage, as they experience no diffusion and no col-lisional interaction. In the present work, we demonstrateEIT and long light storage in such an environment. Theminimal dephasing observed allows for many possibilitiesfor processing stored information using advanced manip-ulation techniques for atomic many-body states in opti-cal lattices (see Ref. [19] and references therein). Lightpulses can be stored in an atomic spin wave in the MI,transformed, and then efficiently mapped back into pho-tonic modes. As an example of such a spin-wave manip-ulation, we imprint a “phase gradient” across the atomicsample using a spatially varying differential light shift ofthe two ground state levels. This spatial phase gradi-ent results in a controlled change of the direction of theλ/4 λ/4λ/4λ/2 APDProbe beamCouplingbeamProbebeamCoupling beamVacuum cellPolarizerΩc,σ-Ωp,σ+F'=1mF' =0795 nmF=2mF =1F=1mF = -15S1/25P1/2ab312PolarizerFIG. 1: (a) EIT Λ-system in 87Rb (D1-line). The transitionbetween the two ground states |1〉 and |2〉 is insensitive tomagnetic field fluctuations to first order at B ≃ 3.23 G. (b)Experimental setup. Probe and coupling beam are used in acollinear configuration and are focussed onto the atoms in theoptical lattice.restored pulse. By controlling non-classical atomic spinexcitations, atoms in optical lattices could even be turnedinto novel non-classical light sources [20, 21] or lead todeterministic photonic phase gates at the single photonlevel [3].In our experiment we begin with ultracold 87Rb atomsin the |F = 1,mF = −1〉 ≡ |1〉 state in an optical lat-tice consisting of three mutually orthogonal retroreflectedlaser beams each with 1/e2-radius ≈ 150 µm. Two of thelattice beams are red detuned (λy,z = 844 nm), while thethird is blue detuned (λx = 765 nm). In a sufficientlydeep lattice (30 Er; Er = h2/2mλ2z is the recoil energy),the many-body ground state is a MI with a well-definednumber of atoms on each lattice site.For EIT, we use a Λ-system consisting of the two Zee-man sublevels |1〉 and |F = 2,mF = +1〉 ≡ |2〉 of the5S1/2 ground state, and the |F′ = 1,mF = 0〉 ≡ |3〉 levelof the 5P1/2 excited state [Fig. 1(a)]. At a field of2δ / 2pi (Hz)Rel. population in F = 2   -20 0 200.00.20.40.6 δ / 2pi (MHz)  -100 0 100 2000.20.30.4  0.5FIG. 2: Observation of EIT in a Mott insulator. Shown isthe fraction of atoms transferred from F = 1 to F = 2 bya 200 ms probe laser pulse, as a function of the two-photondetuning δ = ωp −ωc−ω21. The observed EIT window has awidth of 81(10) Hz. The inset shows the total lineshape. Thered line is a prediction from a rate equation model (see text).B ≃ 3.23 G, the states |1〉 and |2〉 have the same first-order Zeeman shift [22]. The coupling laser light withRabi frequency Ωc is σ−-polarized and is resonant withthe |2〉 ↔ |3〉 transition. The probe laser (Rabi frequencyΩp, frequency ωp, σ+-pol.) is phase locked to the cou-pling laser with a difference frequency corresponding tothe ground state hyperfine splitting. We use a collineararrangement of probe- and coupling beams [Fig. 1(b)] inorder to avoid momentum transfer to the atoms. Thetwo beams are overlapped on a Glan-Thompson polar-izer before a λ/4 waveplate converts the linear into cir-cular polarizations. A lens system focusses the beamsonto the atomic sample. The coupling beam has a 1/e2-radius of ≃ 150 µm, much larger than the diameter ofthe atomic sample (typically 26 µm), in order to facili-tate the alignment and to create a spatially homogeneouscoupling laser field. The probe laser beam has a radiusof ≃ 40 µm. The outgoing beams are separated usingpolarization optics (suppression ratios of 103 − 104) andthe probe beam is directed onto an avalanche photodiode(APD, Analog Modules 712A-4).We first observe EIT, in particular the existence ofa narrow transmission window, in an atomic sample of≃ 9 × 104 atoms, which in our system corresponds to aMI with only singly occupied sites. The atomic sample isan ellipsoid with radii rx = 8.6 µm and ry,z = 13.1 µm.We shine in the coupling laser (Ωc = 2π×26(5) kHz) anda weak probe laser pulse (Ωp = 2π×7(2) kHz) for 200 ms.Due to the small system size and low powers necessaryto achieve such a narrow EIT window, a direct measure-ment of probe transmission through the atom cloud isdifficult in our case. Instead, we measure the fraction ofatoms transferred by the probe laser to the F = 2 man-ifold. We first detect the number of atoms N2 in F = 2by resonant absorption imaging. A second image is taken500 µs later with a repumper in order to also detect theatoms in the F = 1 manifold (N = N2+N1). The graphsin Fig. 2 show the relative population transfer N2/N asa function of the two-photon detuning. We observe anEIT transmission window (81(10) Hz FWHM) at the cen-ter of the absorption line. We calculate the fraction ofatoms pumped from |1〉 into the F = 2 manifold by arate equation model. It includes the analytic expressionfor the linear susceptibility given in Ref. [4] and also ac-counts for the inhomogeneous optical depth (OD), whicharises from the ellipsoidal cloud shape. To explain theobserved population transfer to F = 2 also at the cen-ter of the EIT window, we include a decay rate of the|1〉−|2〉 coherence γ21 = 2π×10 Hz and transfer to F = 2by a fraction of π-polarized probe laser light (Ωpip ) onthe |1〉 →|F ′ = 1,mF = −1〉 transition. The best agree-ment with the data is obtained with Ωc = 2π × 27 kHz,Ωp = 2π × 3.9 kHz and Ωpip = 0.2Ωp (red line in Fig. 2),which are close to the measured values.As a second experiment, we demonstrate the storageof light pulses (Fig. 3). After turning on the couplingbeam, we apply a Gaussian-shaped probe pulse with2.8 µs FWHM. At the peak of this pulse, we shut offthe probe and coupling beams simultaneously, within lessthan 50 ns. After waiting for a variable storage time,we turn on the coupling beam again and monitor therestored probe pulse on an APD. The second, retrievedpulse is much smaller than the first, incident pulse. Fromthe ratio of their areas, we estimate the storage efficiencyto be 3% for a large thermal cloud [Fig. 3(a)] and 0.3%for the MI. The small efficiency is partly caused by themismatch of the size of the probe beam and the atomic-6 -4 -2 0 200.51.0Normalized intensityt (µs)aCouplingProbeTotal retrievedsignal (rel. u.)Storage time (ms)Retrievedsignal (a. u.)t (µs)0 1b c0 200 400 6000.11FIG. 3: Light storage. (a) Intensity of coupling (probe)beams, recorded on a photodiode before (after) the atomicsample during a light storage experiment with 3 µs stor-age time in a thermal cloud (Ωc = 2pi × 4.9 MHz, Ωp =2pi × 920 kHz, ≃ 106 atoms) (b) Retrieved pulses for storagetimes of tS = 1 ms, 200 ms, 400 ms (from top to bottom)in a Mott insulator. Traces are offset for better visibility(Ωc = 2pi × 4.5 MHz, Ωp = 2pi × 1.5 MHz, ≃ 9× 104 atoms).(c) Retrieved signal (relative to the signal at tS = 3 µs) as afunction of tS . The line is an exponential fit with decay timeτ = 238(20) ms.3sample (18% geometrical overlap for the MI), leakage ofthe probe beam due to the finite OD of the sample (peakOD α = 6.3, see definition in Ref. [2]), and due to sponta-neous emission during writing and retrieval phases. Fromnumerical simulations based on the equations in [23], weestimate the efficiencies due to leakage and spontaneousemission as 11% for short storage times (3 µs). The samesimulations were used to reproduce the retrieved pulseshapes shown in Fig. 3(b) with no free parameters otherthan the amplitude. Not included in the simulations areeffects due to imperfect polarizations of probe and cou-pling beams.We use the energy (integrated intensity) of the restoredpulse as a measure of the stored light signal. As shownin Fig. 3(c), fitting an exponential decay to the retrievedpulse power as a function of storage time yields a decaytime constant of τ = 238(20) ms. To independently mea-sure the coherence time of the |1〉 + |2〉 superposition,we performed a Ramsey experiment on the same statesusing an rf+microwave two-photon transition [22]. Thevisibility of the Ramsey fringes decays with a time con-stant of 2τ = 436(22) ms, indicating that the decay ofthe stored light pulse is not caused by residual couplinglight present during the storage time. The factor of twoarises since the Ramsey fringe contrast measures the de-cay of the quantum amplitude coherence [24], whereas inthe EIT signal we measure an intensity. A π-echo pulsedoes not restore the Ramsey signal contrast, so the de-cay time has to be attributed to an irreversible dephasingmechanism. We have ruled out magnetic field noise bymeasuring coherence times away from the “magic” fieldat 3.23 G. The coherence times are nearly unchanged at6 G and 2 G, where the differential shift of the |1〉 ↔ |2〉transition is at least an order of magnitude more sen-sitive to magnetic field fluctuations. We measured thecoherence time vs lattice depth and found a maximumat 30 − 40 Er for our experimental parameters. Thisindicates that the source of the coherence decay is dueto heating in the optical lattice and to finite tunneling.The latter leads to an increased probability of havingmore than one atom per lattice site. In this case theinteraction energy in the doubly occupied sites leads toan onsite dephasing with respect to the singly occupiedsites. Increasing the lattice depth improves the coher-ence times due to the suppression of tunneling, but inturn the heating due to spontaneous light scattering andtechnical noise increases. Our analysis suggests that bysimply using farther detuned lattices, even longer lightstorage times can be achieved.In a non-collinear geometry, the difference in thewavevectors of coupling and probe beams, kc − kp, isstored as a spatial gradient in the phase of the atomicsuperposition state [6]:|D〉 =Ωc |1〉 − Ωpei(kc−kp)r |2〉√Ω2c +Ω2p. (1)Here we reverse the logic leading to Eq. (1), and showGradient beamprofileAtoms-40 -20 0 20 40 602001000Intensity (a.u.)cβkpoutkpin∆kbλ/4& CouplingbeamProbeaEMCCDCameraDeflectedProbe δy∆LGradientδy (µm)dβ (mrad)Interaction time (µs)0 40 80 120 1600102030 100 µs0 µs50 µsFIG. 4: Angular deflection of a stored light pulse. (a) Thedeflected light pulse is detected with an EMCCD camera. (b)A detuned laser beam with a spatially varying intensity pro-file across the atoms creates a spatial phase gradient via thedifferential light shift. (c) Row sums of the CCD images fromthe deflected light pulse for different interaction times. Eachcurve is averaged over 5 runs and the background due to thecoupling beam is subtracted. (d) Deflection angle β as a func-tion of the interaction time tint with the gradient beam. Theblue line is a linear fit.that imprinting a phase gradient on a stored-light statecan change the direction of the restored pulse. This issimilar to the work demonstrating deflection of light in avapor cell by a magnetic gradient field [25] or by an inho-mogeneous laser beam [26]. In our experiment, we firststore a pulse in a MI with ≃ 2.5×105 atoms, and a latticedepth of 30 Er using the sequence described above (Ωc =2π×4.3 MHz, Ωp = 2π×3.8 MHz). Before retrieving thepulse after 10 ms storage time, we shine in an additionalσ+ polarized laser (w0 = 42(8) µm), aligned 20(5) µmaway from the center of the atomic cloud [Fig. 4(b)].The laser is red detuned from the |2〉↔|3〉 transition by−20 GHz, which causes spatially inhomogeneous lightshifts ∆1,2(~r) of the two ground state levels due to theGaussian intensity profile. Shining in this laser for an4interaction time tint induces a local dephasing between|1〉 and |2〉 of φ(~r) = [∆1(~r) − ∆2(~r)]tint/h¯. In our ex-periment, the maximum laser intensity is 2.3(2) W/cm2,which produces a differential light shift of ∆1 − ∆2 =2π × 7.7 kHz at the center of the atomic cloud. Theinteraction time tint is varied from 0 to 150 µs. Thedeflection angle isβ ≃∆kkpwith ∆k =d(∆1 −∆2)dytinth¯, (2)where kp = 2π/λ is the wavevector of the probe laserbeam.The deflected pulse is detected using an electron mul-tiplying CCD (EMCCD, ANDOR iXon DV885), seeFig. 4(a). In order to reveal the deflection, the cam-era is placed out of the focal plane by translating thelast lens before the camera. The detected signal on theEMCCD camera for tint = 0 µs contains about 1.1× 105counts (corresponding to 3.4 × 103 photons). This sig-nal was then summed along the z-direction and averagedover 5 − 12 runs for better visibility. To each of theseintegrated pulses we fit a 1D Gaussian and determinethe position shift δy of the deflected beam. From δy andthe camera position with respect to the focal plane, wedetermine the deflection angle β. The result is summa-rized in Fig. 4(d) together with a linear fit. The fittedslope dβ/dtint = 155(5) µrad/µs is close to the valueof 232(46) µrad/µs calculated from our experimental pa-rameters. The error takes into account the uncertaintiesof the gradient beam power, waist and the alignment.In summary we have demonstrated EIT, light storageand retrieval from an atomic Mott insulator. We haveobserved very long storage times of about 240 ms, wherethe storage time is limited by heating from the latticeand by tunneling. We also demonstrated that a storedpulse can be controlled and redirected by imprinting aspatial phase gradient with a laser beam.In the future, it would be interesting to extend thistechnique to more complex light fields in order to pro-cess and manipulate information stored in spin struc-tures, which can then be analyzed by measuring the di-rection and shape of the retrieved pulse. In contrasttwo the usual manipulation of the spins by microwaveradiation, EIT also allows the imprinting of elaboratephase structures generated by holograms such as imagesor vortices [27]. This could facilitate the study of far-from equilibrium spinor gases, or allow the storage of adoubly charged m = 2 vortex in the MI phase, where itis expected to be stable in contrast to a BEC [28]. An-other interesting prospect is to use the MI as a genuinequantum memory to store and to retrieve single photons[17, 18]. By using an optimized geometry with a higherOD, storage of an entire pulse or pulse sequence can beachieved. As an alternative to storing light pulses, onecan also directly create an atomic superposition. Turn-ing on the coupling field then leads to the creation of aprobe field. We are currently exploring the use of such acreated light pulse as a novel probe for classical or entan-gled atomic spin states in an optical lattice. Ultimately,the generation of such non-classical spin states and thedirect mapping onto photonic states could lead to a newgeneration of non-classical light sources [20, 21].We acknowledge support by DIP, DFG, EU (IPSCALA), AFOSR, and DARPA (OLE) and the FulbrightAssociation (J.D.T.). We thank A. V. Gorshkov for help-ful discussions.[1] L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Na-ture 414, 413 (2001).[2] M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).[3] M. Masˇalas and M. Fleischhauer Phys. Rev. A 69,061801(R) (2004).[4] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev.Mod. Phys. 77, 633 (2005).[5] M. D. Lukin, S. F. Yelin, and M. Fleischhauer, Phys.Rev. Lett. 84, 4232 (2000); M. Fleischhauer and M. D.Lukin, Phys. Rev. Lett. 84, 5094 (2000).[6] C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature409, 490 (2001).[7] D. F. Phillips et al., Phys. Rev. Lett. 86, 783 (2001).[8] H. J. Kimble, Nature 453, 1023 (2008).[9] T. Chanelie`re et al., Nature 438, 833 (2005).[10] A. V. Turukhin et al., Phys. Rev. Lett. 88, 023602 (2002).[11] M. M. Kash et al., Phys. Rev. Lett. 82, 5229 (1999).[12] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi,Nature 397, 594 (1999).[13] V. Ahufinger et al., Opt. Commun. 211, 159 (2002).[14] J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson,Phys. Rev. Lett. 95, 063601 (2005).[15] M. Klein, I. Novikova, D. F. Phillips, and R. L.Walsworth, J. Mod. Opt. 53, 2583 (2006).[16] B. Julsgaard et al., Nature 432, 482 (2004).[17] B. Zhao et al., Nature Phys. 5, 95 (2009).[18] R. Zhao et al., Nature Phys. 5, 100 (2009).[19] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys.80, 885 (2008).[20] D. Porras and J. I.Cirac, Phys. Rev. A 78, 053816 (2008).[21] L. H. Pedersen and K. Mølmer, Phys. Rev. A 79, 012320(2009).[22] D. M. Harber, H. J. Lewandowski, J. M. McGuirk, andE. A. Cornell, Phys. Rev. A 66, 053616 (2002).[23] N. B. Phillips, A. V. Gorshkov, and I. Novikova, Phys.Rev. A 78, 023801 (2008).[24] A. Widera et al., Phys. Rev. Lett. 92, 160406 (2004).[25] L. Karpa and M. Weitz, Nature Phys. 2, 332 (2006).[26] V. A. Sautenkov, H. Li, Y. V. Rostovtsev, M. O. Scully,arXiv:quant-ph/0701229v1 (2007).[27] R. Pugatch et al., Phys. Rev. Lett. 98, 203601 (2007).[28] Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004); J. A.M. Huhtama¨ki et al., Phys. Rev. Lett. 97, 110406 (2006).

Bloch, Immanuel

Max Planck Society eDoc Server

http://dx.doi.org/10.1103/PhysRevLett.103.033003

Electromagnetically Induced Transparency and Light Storage in an Atomic
  Mott Insulator

Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator

Abstract

Similar works

Full text

Available Versions

Name not available

MPG.PuRe

University of Strathclyde Institutional Repository

MPG.PuRe

Max Planck Society eDoc Server