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V incent Josse L aurent Vernac A lberto Bramati M ichel Pinard E lisabeth Giacobino

Les Houches 2003. Continuous variable squeezing & entanglement. A urélien Dantan. V incent Josse L aurent Vernac A lberto Bramati M ichel Pinard E lisabeth Giacobino. Laboratoire Kastler-Brossel ENS, Paris. Introduction : quantum noise. Monomode field. Fresnel d iagram.

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V incent Josse L aurent Vernac A lberto Bramati M ichel Pinard E lisabeth Giacobino

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  1. Les Houches 2003 Continuous variable squeezing & entanglement Aurélien Dantan Vincent Josse Laurent Vernac Alberto Bramati Michel Pinard Elisabeth Giacobino Laboratoire Kastler-Brossel ENS, Paris

  2. Introduction : quantum noise Monomode field Fresnel diagram X, Y : quadrature operators “amplitude” “phase” : quadrature q

  3. Introduction : quantum noise Monomode field Fresnel diagram X, Y : quadrature operators “amplitude” “phase” : quadrature q Quantum noise  Heisenberg inequality  Phase/Photon number inequality

  4. Introduction : quantum noise Monomode field Fresnel diagram X, Y : quadrature operators “amplitude” “phase” : quadrature q Quantum noise Coherent state Standard Quantum Limit = Vacuum fluctuations= « shot noise »  Heisenberg inequality  Phase/Photon number inequality

  5. Introduction : quantum noise Monomode field Fresnel diagram X, Y : quadrature operators “amplitude” “phase” : quadrature q Quantum noise Squeezedstate  Heisenberg inequality Interest : Measurement sensitivity Quantum information  Phase/Photon number inequality

  6. Homodyne detection • Spectral noise density Analysis frequency: 1-15 MHz  Heisenberg inequality • Squeezed state generation c(2) -non linearity : parametric amplification (OPO, OPA) c(3) -non linearity : four wave mixing, Kerr effect (fibers, atoms) Introduction : quantum noise

  7. Polarization ellipsoid Stokes parameters Poincaré sphere Bowen etal. PRL 2002 Polarization (classical) Definition

  8. Quantum Stokes operators Polarization noise  Heisenberg inequalities Korolkova et al. PRA2002 Coherent polarization state x, y coherent states  Bowen et al. PRL 2002 Polarization (quantum)

  9. x-polarized beam : Stokes vector // S1 Heisenberg inequalities • Stokes vector fluctuations mean field amplitude length intensity azimuth amplitude orientation vacuum mode ellipticity phase Polarization squeezing: ?

  10. x-polarized beam : Stokes vector // S1 Heisenberg inequalities • Polarization squeezing ? xmodeamplitude squeezed amplitude squeezed y mode or or phase squeezed Polarization squeezing  NO  YES

  11. x-polarized beam : Stokes vector // S1 Heisenberg inequalities Polarization squeezing S3-polarization squeezed state Vacuum squeezing Polarization squeezing

  12. Direct detection  no LO required Korolkova et al. PRA 2002 • Atom-field interaction mapping of a quantum polarization state of light onto an atomic ensemble atomic ensembles entanglement, quantum networks,... [see P. Zoller’s lecture #3] Julsgaard et al. Nature2001 Why ?

  13. How ? • Indirect method Bowen etal. PRL 2002 Heersink et al.PRA 2003 60%  squeezed states produced independently • Direct method Cross-Kerr effect in optical fibers 50% Boivin et al.Opt. Comm. 1996 Josse etal. PRL 2003 Ries etal. PRA 2003 Cross-Kerr effect in atoms 20%  orthogonal vacuum squeezing

  14. homodyne detection interference signal Polarization squeezing with cold atoms

  15. Experimental results 10% polarization squeezing(3MHz) Josse etal. PRL 2003

  16. Experimental results S3-polarization squeezed state Josse etal. PRL 2003

  17. Inseparability criterion Duan et al. PRL 2000 Simon PRL 2000 Continuous variable inseparability criterion a and b entangled (Gaussian states) EPR-type operators ?

  18. Entanglement = sum of squeezings Non separable beams 2 uncorrelated squeezed modes : Ax and Ay, but for orthogonal quadratures  the 45° modesare the maximally entangled modes

  19. Inseparability criterion measurement Josse et al. quant-ph/0306152 Direct measurement  2 homodyne detections

  20. Conclusion • Applications: • measurementsensitivity • long distance quantum communication [see P. Zoller’s lecture], • quantum memory, quantum repeater... • teleportation with atomic ensembles [Polzik’s experiments 2001] • entanglement swapping [Glöckl et al. 2003]

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