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Diapositive 1 Quantum storage in cold atomic ensembles Elisabeth Giacobino Laboratoire Kastler Brossel, Ecole Normale Supérieure, Université Pierre et Marie Curie, Centre National de la Recherche Scientifique, Paris, France QuantumQuantum memorymemory :: aa quantumquantum interfaceinterface betweenbetween lightlight andand mattermatter Goal: To achieve storage and retrieval of quantum variables without measurement General Strategy: Mapping a quantum state of light into a quantum superposition of states in an atomic medium QuantumQuantum MemoriesMemories Objective : Storing without measuring and reading on demand, i.e. a coherent and reversible transfer Photonic Qubit between atoms and light. Strategy: Mapping light quantum superposition into quantum superposition of elements the storing medium |a> and |b> usually long lived states to avoid fast decoherence Two ground states connected via an excited state by a control field Other aims: , bandwidth, memory time, multimode… LightLight--MatterMatter InterfacesInterfaces :: HowHow ?? Photonic Qubit Mapping light quantum superposition into write QM quantum superposition of elements of the storing medium read Single Atom Atomic ensembles Requires a high- finesse cavity (CQED) Light easily interact with the sample Collective state (enhancement) Example for storage of a single photon Example for storage of a single photon QuantumQuantum MemoriesMemories :: anan OutlookOutlook Single Atom Cavity Quantum Electro-Dynamics (strong coupling) • Single trapped atom in a cavity (Kimble 2007, Rempe 2011) • Quantum dot « molecules » (Shields 2011) But mode matching is difficult QuantumQuantum MemoriesMemories :: anan OutlookOutlook Atomic Ensembles : Collective Excitation Dynamic EIT in warm vapors or cold atoms First experiments for optical pulses, based on EIT: 2001 : M. Lukin using Rb vapor, and L. Hau using cold sodium atoms Many experiments since then with efficiencies ranging from a few % to about 50% (M. Lukin, I. Novikova, J.W. Pan, I. Walmsley, P.Lett), but not always in the quantum regime Also : off-resonant Faraday rotation (Polzik, 2004) Best results to date ~90% efficiency (PK Lam, 2011) with echo-type technique (Moiseev and Krö ll, 2001) TheThe resourceresource :: ElectromagneticallyElectromagnetically inducedinduced transparencytransparency (EIT)(EIT)°° Control Reduced group velocity 7 ElectromagneticallyElectromagnetically inducedinduced transparencytransparency (EIT)(EIT) inin coldcold CsCs atomsatoms Absorption profiles for various values of Rabi frequency of the control field L. Giner et al, Phys. Rev. A 87, 013823 (2013) EITEIT basedbased quantumquantum memorymemory Atoms field transfer conditionsconditions :: ► coherence resonantly excited (2-photon resonance) ► low losses Raman or E.I.T. Expected performances : ► transfert efficiency ► storage time > ms ► reading/writing time s SimplifiedSimplified systemsystem :: 33--levellevel atomicatomic ensembleensemble inin aa cavitycavity • control field is strong : its Rabi frequency plays the role of a parameter • quantum field A has a very small mean value Then • all the atoms are pumped into evell 2 • JPA,, are decoupled from the other variables g 2 in P A () i c APA i pump signal P i () P ig N A i J F J ()i 0 J i P r f J FieldField toto atomicatomic spinspin couplingcoupling Field and optical dipole adiabatically follow the ground state evolution ~ in ( 0i J) x Ax x f ~ in ( 0i J) y Ay y f ~ 0 : ground state coherence relaxation rate 0 0 : effective optical pumping rate The two quadratures of the field are mapped onto the atomic spin OperationOperation ofof aa quantumquantum memorymemory DynamicDynamic EITEIT StorageStorage efficiencyefficiency I Efficiency out Iin Optical depth d I I0 e g2 N L d c From Grshkovo et al, PRA 76, 033805 (2007) Fidelity F in out in depends on the considered quantum state can be larger than the classical limit even for rather small efficiency ExperimentExperiment inin anan atomicatomic vaporvapor • when the signal pulse is inside the atomic medium, the control field is switched off. • the two quadratures of the signal field are then stored in two components of the ground state Zeeman coherence. • for read-out, the control field is turned on again and the medium emits a weak pulse, similar to the original signal pulse EnsembleEnsemble ofof ColdCold AtomsAtoms Magneto-optical trap 109 atoms in a mm3 volume large optical depth LKB PrinciplePrinciple ofof thethe experimentexperiment Cs MOT Level scheme Cs D2 line Trapping Repump Pump () Control Signal 17 TimingTiming ofof thethe experimentexperiment Magnetic field Trapping 650 µs lasers Repump 900 µs 25 ms Building of the cloud Memory operation and measurements 18 AtomicAtomic quantumquantum memorymemory forfor faintfaint pulsespulses (0.1(0.1 photon/pulse)photon/pulse) Memory time Efficiency 20 DecoherenceDecoherence duedue toto atomicatomic motionmotion Collective state Motional dephasing Retrieval efficiency 2 2 et / Temperature Angle between the beams DecoherenceDecoherence duedue toto magneticmagnetic fieldfield Residual magnetic field For Gaussian atomic distribution and magnetic field gradient B1 magnetic field gradient W Distribution of the atomic coherence σ 12 in space and time g2 2 N ~z z Effective length ~ Effective time t t duration First, the atomic coherence grows starting from the beginning of the medium. Later, layers deeper inside the medium start to participate in the process and the information moves further inside the ensemble. T. Golubeva et al, PRA 83, = 0 053810 (2011) Gradient echo memory Ping Koy Lam, Ben Buchler, Jevon Longdell (ANU, Australia) : Controlled reversible inhomogeneous broadening Ensemble of atoms with linearly varying Zeeman shift in the z direction: Increased efficiency From : M. Hosseini et al, Nature 461, 241 (2009) RecentRecent resultsresults andand performancesperformances Efficiency and lifetime -78% with EIT : Ite A. Yu (Taiwan) and Shengwang Du (Hong Kong) with cold Rb atoms, lifetime 54µs (2013) - 43% with Raman scheme and pulses Walmsley (Oxford) in hot Rb vapour (2012) -Best value 87% Ping-Koy Lam (Canberra) with GEM in Rb vapor, lifetime 50µs (80% in cold Rb, lifetime 195µs) (2011) - Lifetime 16 sec (n=0.26 at 1µsec) Kuzmich (USA) with cold Rb trapped in a lattice (2013) Experiments performed with faint pulses, not always in the quantum regime GoingGoing toto aa multimodemultimode basisbasis :: Laguerre-Gauss modes LaguerreLaguerre GaussianGaussian modesmodes A set of optical modes… : azimuthal index : radial index ‐3 ‐2 ‐1 0 1 2 3 0 1 2 LaguerreLaguerre GaussianGaussian modesmodes : azimuthal index : radial index Helical wavefront → Twisted photons (picture from M. Padgett) Each photon carries an orbital angular momentum OrbitalOrbital AngularAngular MomentumMomentum ofof lightlight • Laguerre-Gaussian and Hermite Gaussian modes infinite-dimensionnal Hilbert space for high density quantum information encoding ! Entanglement of high orbital angular momenta was demonstrated recently - A.C. Dada et al., Nature Phys. 7, 677 (2011) d= 12 - R. Fickler et al.,, Science 338, 640 (2012) d =100 PhotonsPhotons withwith orbitalorbital angularangular momentummomentum Qbit basis : Interference l=+1 l=-1 { |LGp=0 > , |LGp=0 > } between LG and TEM00 modes Laguerre-Gauss modes with l = ±1 Hermite-Gauss modes 1 i HGhor LG LG HGver LG LG 2 2 LightLight--mattermatter interfaceinterface forfor OAMOAM Storage of bright light beams(classical regime) Pugatch et al., Phys. Rev. Lett. 98, 203601 (2007) Moretti et al., Phys. Rev. A 79, 023825 (2009) Going down to the single‐photon level L. Veissier et al., IJQI 10, 1241011 (2012) Veissier et al., Opt. Lett. 38, pp. 712‐714 (2013) Ding et al., arXiv e‐print 1305.2675 (2013) StorageStorage ofof orbitalorbital angularangular momentummomentum ofof lightlight inin thethe singlesingle photonphoton regimeregime Signal pulse 0.5 µs ~ 0.7 photon per pulse The mode of the signal photons is prepared using a spatial light modulator (SLM). StorageStorage ofof orbitalorbital angularangular momentummomentum ofof lightlight inin thethe singlesingle photonphoton regimeregime Experimental set-up Signal from memory • fork phase holograms fork-hologram increase or reduce l by 1 • only the mode with l= 0 fork-hologram can couple efficiently into the subsequent single mode fibers and is Optical fiber detected with an APD. Optical fiber Count rates StorageStorage ofof LaguerreLaguerre GaussGauss photonsphotons Storage efficiency ~15% for LG modes L. Veissier et al., IJQI 10, 1241011 (2012) StorageStorage ofof HermiteHermite--GaussGauss photonsphotons Storage efficiency ~15% for HG modes L. Veissier et al, Opt. Lett. 38, 712 (2013) StorageStorage timetime Motional dephasing for atoms at 1 mK Gaussian distribution with Further cooling to increase 1/e decay constant of 15 µs the storage time OAMOAM encodedencoded qubitqubit OAM encoded qubit Equally‐weighted superpositions As for polarization qubit Stokes parameters i Pauli matrices Three linearly independent measurements ExperimentalExperimental setset--upup forfor fullfull qubitqubit characterizationcharacterization Signal attenuated Ti:Sapph laser Control : diode laser The visibility of a qbit is measured at the output of the interferometer MeasuringMeasuring thethe interferometerinterferometer phasephase • Reference light sent backwards (12 ms over 15) • Bright beam but low power (1 nW) • Forms a HG mode after recombining on BS 1, with symmetry axis related to ∆ϕ • Detected by CCD camera (recording
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