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

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

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

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

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

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

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

Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 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)

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

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

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

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

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

Quantum Information Measuring Entanglement OPOs Optimizing entanglement Conclusions Perspectives Frisno 8, february 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

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