characterization and optimization of entangled states produced by a self-phase-locked opo j. laurat,...

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

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

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

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

Frisno 8, february 2005 5

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Two-mode covariance matrix

Two-mode covariance matrix

Measuring entanglement

Frisno 8, february 2005 6

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Parametric down-conversion

Triply resonant optical cavity

Principle of OPOs

OPO

Principles

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

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)

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

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

Frisno 8, february 2005 11

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – “aligned” waveplate

Covariance matrix

Inseparability

Belowthreshold

Frisno 8, february 2005 12

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Below threshold – rotated waveplate

Noise variances

Covariance matrix

Inseparability

Belowthreshold

F

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

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

Frisno 8, february 2005 15

QuantumInformation

MeasuringEntanglement

OPOs

Optimizingentanglement

ConclusionsPerspectives

Perspectives

Working above threshold

Full measurement of the covariance

matrix

Higher dimensions