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IHP Quantum Information Trimester

Danish Quantum Optics Center University of Aarhus. QuanTOp. Niels Bohr Institute Copenhagen University. Light-Matter Quantum Interface. Eugene Polzik LECTURE 5. IHP Quantum Information Trimester. Quantum teleportation. Light – to – light

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IHP Quantum Information Trimester

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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 5 IHP Quantum Information Trimester

  2. Quantum teleportation Light – to – light Entanglement resource – parametric downconversion process Atoms – to – atoms Entanglement resource – measurement induced entanglement of two atomic ensembles Light – atoms, etc

  3. Parametric Hamiltonian, no dissipation: Equations of motion for field operators: Hamiltonian commutes with the photon number difference operator: In photon number basis: "photon pairs" Workhorse of photon entanglement experiments!

  4. Entangled cavity modes Parameter: More accurate description : field modes in an optical resonator

  5. w + When the two fields are separated correlations – entanglement are observed: P=Im(E)=i( a+ - a) E- X- X+ X = Re(E)= a+ + a E+ P- P+ Parametric downconversion in a resonator (Optical Parametric Oscillator below threshold)

  6. - - Frequency tunable entangled light around 860nm 800MHz 107 photons per mode AOM Cavity modes LO+ AOM LO- Classical field

  7. 8 6 Entangled cavity modes 4 2 0 -2 -4 -6 -1 0 1 2 3 4 5 6 2 [dB(2 SQL)] Necessary and sufficient condition for entanglement p Phase [ Radians] ) 2 - -X + (X d Narrowband tunable entangled beams Sorensen, Schori, Polzik PRA, 2002 Degree of entanglement 0.8 – observed

  8. Einstein-Podolsky-Rosen entangled state Teleportation principle (canonical variables) L.Vaidman Demonstrated experimentally for light variables byFurusawa, Sørensen, Fuchs, Braunstein Kimble, Polzik. Science 1998

  9. 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),

  10. _ _ _ ix X P ip Alice Mx Dx Dp Mp Bob LOx LOp mBob vacuum In Out vacuum c rout LOV |vin> Classical teleportation Victor DV _ Victor

  11. LOV _ DV Victor _ Bob _ _ Mx Out rout mBob Mp Pump 2 ix b EPR beams ip ii Classical Information OPO LOp i Dp Pump 1 a Alice Dx c LOx In Victor |vin>

  12. 2 units of Vacuum = 4.8 dB Quantum teleportation Furusawa et al, Science, Vol 282, Issue 5389, 706-709 , 23 October 1998

  13. Classical boundary

  14. Communication networks based on continuousspin variables Operations: Light-atom teleportation Resources: local entanglement Memory Bob Memory Alice EPR pulses EPR spins Quantum channel Operation: Teleportation of atoms Resources: shared entanglement Memory Bob Classical channel Memory Alice EPR spin Alice EPR spin Bob Coherent pulse Symbols : Input-Output interaction: free space off-resonant dipole interaction • Continuous variables: • polarization state of light • spin state of atoms conditional rotation detection of light

  15. z x k=1 y Light-to-Atoms Teleportation Kuzmich, EP 2000

  16. Atoms 2 Atoms X Atoms 1 Detector Proposals: Duan, Cirac, Zoller, EP 2000 Kuzmich, EP. 2000 Teleported entangled Classical signal Teleportation of atomic states Light pulse

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

  18. Teleportation of an entangled atomic state • Every measurement changes the single cell • spin, BUT does not change the measured sum • Every pulse measures both y and z components of the sum – entanglement is created To complete teleportation of entanglement onto cell 1 and cell 4: rotate spin 4 by A+B+C:

  19. Tripartite entanglement For atomic ensembles via quantum measurement: simple step from 2 to 3 N atoms, spins up N/2 atoms, spins down N/2 atoms, spins down Fan HY, Jiang NQ, Lu HL Lance AM, Symul T, Bowen WP, et al. Van Look et al

  20. 2 1 3 N and S condition for 3-party pairwise entanglement:

  21. 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)

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

  23. 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

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

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