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  1. Danish Quantum Optics Center University of Aarhus QuanTOp Niels Bohr Institute Copenhagen University Light-Matter Quantum Interface Eugene Polzik LECTURE 4 IHP Quantum Information Trimester

  2. Quantum memory for light: criteria • Memory must be able to store independently prepared • states of light • The state of light must be mapped onto the memory with • the fidelity higher than the fidelity of the best • classical recording • The memory must be readable B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik Nature, 432, 482(2004); quant-ph/0410072.

  3. Mapping a Quantum State of Light onto Atomic Ensemble Spin Squeezed Atoms 1 > 2 > 0 > Experiment: Hald, Sørensen, Schori, EP PRL 83, 1319 (1999) Very inefficient lives only nseconds, but a nice first try… The beginning. Complete absorption Squeezed Light pulse Proposal: Kuzmich, Mølmer, EP PRL 79, 4782 (1997) Atoms

  4. …and feedback applied Strong driving Weak quantum Projection measurement on light can be made… Passes through one… or more atomic samples Dipole off-resonant interaction entangles light and atoms Our light-atoms interface - the basics Light pulse – consisting of two modes

  5. x -45 45 Polarization – Stokes parameters y Circular polarizations Linear polarizations Polarization quantum variables – Light Propagation direction vertical horizontal

  6. x Quantum state (Wigner function) y z Canonical quantum variables for an atomic ensemble:

  7. Decoherence from stray magnetic fields Magnetic Shields Special coating – 104 collisions without spin flips Object – gas of spin polarized atoms at room temperature Optical pumping with circular polarized light

  8. Various states t Pulse: • Canonical quantum variables for light • Complementarity : amplitude and phase of • light cannot be measured together

  9. 450 -450 EOM l/4 Polarization homodyning - measure X (or P) Polarizing Beamsplitter 450/-450 Strong field A(t) x Quantum field a -> X,P Polarizing cube S1

  10. x,p Bell measurement Teleportation in the X,P representation

  11. Projection measurement X Today: another idea for (remote) state transfer and its experimental implementation for quantum memory for light See also work on quantum cloning: J. Fiurasek, N. Cerf, and E.S. Polzik, Phys.Rev.Lett.93, 180501 (2004)

  12. Implementation: light-to-matter state transfer - C squeeze atoms first No prior entanglement necessary = C F≈80% F→100% B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik Nature, 432, 482(2004); quant-ph/0410072.

  13. Quantum computing with linear operations Quantum buffer for light More efficient repeaters Quantum Key storage in quantum cryptography These criteria should be met for memory in:

  14. e.-m. vacuum Classical benchmark fidelity for transfer of coherent states Atoms Best classical fidelity 50% K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac, Phys. Rev. Lett. 94,150503 (2005),

  15. Preparation of the input state of light EOM Vacuum Input quantum field Coherent Squeezed Strong field A(t) Quantum field - X,P x Polarizing cube S1 P Polarization state X

  16. 450 -450 Physics behind the Hamiltonian: 1. Polarization rotation of light Polarizing Beamsplitter 450/-450 x Quantum field Polarizing cube

  17. EOM Physics behind the Hamiltonian: 2. Dynamic Stark shift of atoms Atoms atoms Strong field A(t) Quantum field - a x Polarizing cube y

  18. PL atoms Quantum memory – Step 1 - interaction Light rotates atomic spin – Stark shift XL Atomic spin rotates polarization of light – Faraday effect Output light Input light Entanglement

  19. PL XL c light out atoms Feedback to spin rotation Compare to the best classical recording Quantum memory – Step 2 - measurement + feedback Polarization measurement Fidelity – > 100% (82% without SS atoms)

  20. Experimental realization of quantum memory for light

  21. Memory in rotating spin states B B y z Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

  22. Memory in rotating spin states - continued B B x z y Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

  23. Encoding the quantum states in frequency sidebands

  24. Rotating frame spin Memory in atomic Zeeman coherences Cesium 4 3 2

  25. B B x z y

  26. Input pulse Readout pulse Magnetic feedback Nature, Nov. 25 (2004) quant-ph/0410072.

  27. Light Pin~ SYin Xin~ SZin p / 2 - rotation Stored state versus Input state: mean amplitudes X plane read write t output input Y plane Magnetic feedback

  28. Stored state: variances Absolute quantum/classical border 3.0 Perfect mapping Atoms <P2mem > Light <P2in >=1/2 <X2mem> <X2in> =1/2

  29. Experiment 0.68 Coherent states with 0 < n <4 Coherent states with 0 < n <8 0.66 F Experiment 0.64 0.64 0.62 0.62 Best classical mapping 0.58 0.58 0.56 0.56 Best classical mapping 0.54 Gain 0.65 0.7 0.75 0.8 0.85 0.9 0.82 0.84 0.86 0.88 0.9 Fidelity of quantum storage • State overlap averaged over • the set of input states

  30. Quantum memory lifetime

  31. 1-2Hz 3-6Hz 25-40Hz Dominating (T is time, typical 2ms) Atomic/shot ratio (retaining the dominating term) Decoherence up to around 0.5 Theoretical entanglement with no decoherence: Decoherence Limitations Typical estimate of linewidth: G[Hz] = 5 + 0.1*q[deg] + 1.0*P[mW] + 0.5*P[mW]*q[deg] Working values: Important for entanglement: Need k2 large and h low, impossible.

  32. Initial state of atoms coherent Input state State overlap 63% Fidelity 100% for a qubit input state 78% 90% Qubit fidelity Deterministic quantum memory for a light Qubit Initial state of atoms squeezed Realized by an extra QND measurement pulse A. Sørensen, NBI

  33. Quantum Memory for Light demonstrated • Deterministic Atomic Quantum Memory proposed and • demonstrated for coherent states with <n> in • the range 0 to 10; lifetime=4msec • Fidelity up to 70%, markedly higher than best • classical mapping

  34. Scalability – an array of dipole traps or solid state implementation – quantum holograms Detector array Spatial array of memory cells I. Sokolov and EP, to be submitted

  35. Future: Inverse Mapping AtomsLight Atoms Y Detector Proposals: Kuzmich, EP. 2001; Kraus, Giedke, Cirac 2001 Y l/4 wave plate Recent advanced proposals: K. Hammerer, K. Mølmer, EP, J.I. Cirac. Phys.Rev. A., 70, 044304 (2004). J. Sherson, K. Mølmer, A.Sørensen, J. Fiurasek, and EP quant-ph/0505170 Light pulse

  36. Quantum memory read-out: single pulse in squeezed state z Step 1 x y Step 2 Exchange y and z components: pass light through l/4 plate and probe along spin-y axis z y

  37. Light-Atoms Q-interface with cold atoms 6P Cesium clock levels F=4 F=3 D. Oblak C. Alzar, P. Petrov

  38. Memory Summary • New state transfer protocol →quantum memory for light • Experimental demonstration for coherent states • Nature, 432, 482(2004) • Prediction for a qubit state – bridging dicrete and • continuous variables • State retrieval protocols

  39. Figure of merit Probe depumping parameter: Criteria for light-ensemble interface • 2-level stable state with long coherence time • Initialization: collective coherent spin state (CSS) • Coupling of the CSS to light corresponding to • high optical density

  40. Multi-atom Cat states Color code “easy” hard Atomic teleportation 3-party entanglement/ Secret sharing Scaling/ solid state implementation Entangled atoms + Entangled light + Light/atoms QI exchange Quantum memory for light Distillation by local operations Continuous variable logic Discrete variable logic

  41. cold atomic cloud cavity enhanced interaction • enhanced phase shift • power build-up inside cavity compensate with smaller photon number T: mirror transmission a: absorption

  42. Coupling strength of the interface z y x Initial coherent spin state: Spin squeezed state Measurement on light results in distribution degree of squeezing in Jz Figure of merit for the quantum interface Z Duan, Cirac, Zoller, EP PRL (2000)

  43. Probe scattering parameter: Figure of merit for the quantum interface

  44. 0.3 Single pass interaction 30 50 10 Spontaneous emission probability degree of entanglement + h Figure of merit for the quantum interface Spontaneous emission – the fundamental limit K. Hamerrer, K. Mølmer, E. S. Polzik, J. I. Cirac. PRA 2004, quant-ph/0312156