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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

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Page 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,

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

Page 2: 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,

Frisno 8, february 2005 2

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

“Non-separables” states

Intense beams : quadratures of the

electromagnetic field

Quantum information with intense beams

Principes

Page 3: 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,

Frisno 8, february 2005 3

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Qualifying inseparability

InseparabilityL.M. Duan et al., C. Simon (PRL 2000)

Measuring entanglement

Frequency-degenerate operation required

Entanglement $ Squeezing

Page 4: 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,

Frisno 8, february 2005 4

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Covariance matrix formalism

Single-mode covariance matrix

Covariance matrix and squeezing

characterizes completely the state

Page 5: 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,

Frisno 8, february 2005 5

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Two-mode covariance matrix

Two-mode covariance matrix

Measuring entanglement

Page 6: 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,

Frisno 8, february 2005 6

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Parametric down-conversion

Triply resonant optical cavity

Principle of OPOs

OPO

Principles

Page 7: 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,

Frisno 8, february 2005 7

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Specificities of OPOs

Oscillation threshold

Emission of intense, coherent beams

Orthogonally-polarized beams

(“type II” phase matching)

Pin

Pout

Principles

Page 8: 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,

Frisno 8, february 2005 8

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

P um p(5 3 2 n m )

M 1 M 2 (2 ) cristal

(K T P )

Ensuring frequency-degenerate operation

Signal and idler frequency difference “arbitrary”Synchronizing/phase-locking two oscillatorsAdd a linear coupling

Frequency & phase - locking of signal and idler

P um p(5 3 2 n m )

M 1 M 2 (2 ) cristal

(K T P )

Waveplate( /4 )

SPL OPO

Mason & Wong, Opt. Lett. (1998)

Page 9: 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,

Frisno 8, february 2005 9

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Above threshold

Simultaneous measurement of amplitude correlations and phase anti-correlations

Abovethreshold

Excess phase noise

Page 10: 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,

Frisno 8, february 2005 10

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – “Aligned” waveplate

Measurement apparatus

Measurement results

Belowthreshold

F 4

@ 2 2 .5 °

F 3

F 5

O P O

local oscillator

Page 11: 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,

Frisno 8, february 2005 11

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – “aligned” waveplate

Covariance matrix

Inseparability

Belowthreshold

Page 12: 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,

Frisno 8, february 2005 12

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – rotated waveplate

Noise variances

Covariance matrix

Inseparability

Belowthreshold

F

Page 13: 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,

Frisno 8, february 2005 13

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – maximizing entanglement

Performing a non-local operation

InseparabilityCovariance matrix

F 4

F 1

F 5

F 3

O P O

F 4

F 1

F 5

F 3

O P Olocal

oscillator

Page 14: 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,

Frisno 8, february 2005 14

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

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

Page 15: 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,

Frisno 8, february 2005 15

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Perspectives

Working above threshold

Full measurement of the covariance

matrix

Higher dimensions

Page 16: 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,

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