1. Characterization and optimization of entangled states produced by a self-phase-locked OPO J. Laurat, G. Keller, J.A.O. Huguenin T. Coudreau, N. Treps, C. Fabre Laboratoire Kastler Brossel, ENS, CNRS, UPMC

2. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20052 “Non-separables” states Intense beams : quadratures of the electromagnetic field Quantum information with intense beams Principes

3. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20053 Qualifying inseparability Inseparability L.M. Duan et al., C. Simon (PRL 2000) Measuring entanglement  Frequency-degenerate operation required Entanglement $ Squeezing

4. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20054 Covariance matrix formalism Single-mode covariance matrix Covariance matrix and squeezing  characterizes completely the state

5. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20055 Two-mode covariance matrix Measuring entanglement

6. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20056 Parametric down-conversion Triply resonant optical cavity Principle of OPOs OPO Principles

7. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20057 Specificities of OPOs Oscillation threshold Emission of intense, coherent beams Orthogonally-polarized beams (“type II” phase matching) Principles

8. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20058 Ensuring frequency-degenerate operation Signal and idler frequency difference “arbitrary” Synchronizing/phase-locking two oscillators Add a linear coupling Frequency & phase - locking of signal and idler SPL OPO Mason & Wong, Opt. Lett. (1998)

9. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 20059 Above threshold Simultaneous measurement of amplitude correlations and phase anti-correlations Above threshold Excess phase noise

10. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200510 Below threshold – “Aligned” waveplate Measurement apparatus Measurement results Below threshold

11. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200511 Below threshold – “aligned” waveplate Covariance matrix Inseparability Below threshold

12. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200512 Below threshold – rotated waveplate Noise variances Covariance matrix Inseparability Below threshold

13. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200513 Below threshold – maximizing entanglement Performing a non-local operation Inseparability Covariance matrix local oscillator

14. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200514 Conclusions Self-Phase Locked OPO a good tool to produce entangled states Self-Phase Locked OPO a good tool to show the general properties of entangled states Polarization elements a good tool to manipulate entanglement

15. Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 200515 Perspectives Working above threshold Full measurement of the covariance matrix Higher dimensions