A quantum optical beam

Classically an optical beam can have well defined amplitude AND phase simultaneously.

Quantum mechanics however imposes an uncertainty principle.– The deterministic classical

beam is blurred out by quantum noise.

V +V −≥1Uncertainty principle:

Coherent state Squeezed state

V+=V-=1 Ideal output of a low-

noise laser Same quantum noise as

vacuum

V+ or V- < 1 Very fragile in the

presence of loss

Laser outputs are typically very noisy at low frequency.

Measure squeezing of the beat of the carrier with frequencies outside this noise bandwidth.

Sideband squeezing

Coherent

Production of squeezing Produce squeezing in a below threshold

optical parametric amplifier (OPA)

Coherent

Production of squeezing Produce squeezing in a below threshold

optical parametric amplifier (OPA)

Amplitude squeezed

Coherent

Production of squeezing Produce squeezing in a below threshold

optical parametric amplifier (OPA)

Amplitude squeezedPhase squeezed

Comparison of OPAs and OPOs

OPAs are seeded with a bright beam whereas OPOs are vacuum seeded.

Advantages of OPAs:– Can lock the length of the resonator.– Bright squeezed output that can be

controlled in downstream applications. Advantage of OPOs:

– No classical noise coupled from the laser into the squeezed beam.

In our two OPAs this noise is correlated and can be cancelled by optical or electronic means.

Recovering buried squeezing

(D,D )(H,V)

(L,R)

S0 =IH +I V

S1 =IH −IV

S2 =ID −ID

S3=IR −I L

The Poincaré sphere

(D,D )(H,V)

(L,R)

S0 =IH +I V

S1 =IH −IV

S2 =ID −ID

S3=IR −I L

The Poincaré sphere

ˆ S 1,ˆ S 2[ ]=2iˆ S 3

ˆ S 2,ˆ S 3[ ]=2iˆ S 1

ˆ S 3,ˆ S 1[ ]=2iˆ S 2

Commutation Commutation rrelationelationssoof f StokesStokes operators operators

(D,D )(H,V)

(L,R)

S0 =IH +I V

S1 =IH −IV

S2 =ID −ID

S3=IR −I L

The Poincaré sphere

ˆ S 1,ˆ S 2[ ]=2iˆ S 3

ˆ S 2,ˆ S 3[ ]=2iˆ S 1

ˆ S 3,ˆ S 1[ ]=2iˆ S 2

Commutation Commutation rrelationelationssoof f StokesStokes operators operators Uncertainty relationsUncertainty relationsoof Stokes operatorsf Stokes operators

V1V2 ≥ ˆ S 32

V2V3≥ˆ S 1

2

V3V1≥ˆ S 2

2

(D,D )(H,V)

(L,R)

S0 =IH +I V

S1 =IH −IV

S2 =ID −ID

S3=IR −I L

The Poincaré sphere

ˆ S 1,ˆ S 2[ ]=2iˆ S 3

ˆ S 2,ˆ S 3[ ]=2iˆ S 1

ˆ S 3,ˆ S 1[ ]=2iˆ S 2

Commutation Commutation rrelationelationssoof f StokesStokes operators operators Uncertainty relationsUncertainty relationsoof Stokes operatorsf Stokes operators

V1V2 ≥ ˆ S 32

V2V3≥ˆ S 1

2

V3V1≥ˆ S 2

2

Polarisation squeezing A Stokes parameter is squeezed if its variance is

below the shot-noise of a coherent beam of equal power.

Polarisation state of acoherent beam

Polarisation state of acoherent beamPolarisation state of anamplitude squeezed beam

one Stokes parametersqueezed

Polarisation state of acoherent beamPolarisation state of anamplitude squeezed beam

one Stokes parametersqueezed

Polarisation state of asqueezed beam combined with a coherent beam

one Stokes parametersqueezed

[P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)]

Polarisation state of acoherent beamPolarisation state of anamplitude squeezed beam

one Stokes parametersqueezed

Polarisation state of asqueezed beam combined with a coherent beam

one Stokes parametersqueezed

[P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)]

Polarisation state of two phase squeezed beams combined

one Stokes parametersqueezed

Polarisation state of acoherent beamPolarisation state of anamplitude squeezed beam

one Stokes parametersqueezed

Polarisation state of asqueezed beam combined with a coherent beam

one Stokes parametersqueezed

[P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)]

Polarisation state of two phase squeezed beams combined

one Stokes parametersqueezed

Polarisation state of two amplitude squeezed beams combined

two Stokes parameterssqueezed

[W. Bowen et. al. http://xxx.lanl.gov/abs/quant-ph/0110129 (2001)]

Summary

We have produced two reliable strongly quadrature squeezed sources.

We produce new quantum polarisation states and investigate their properties.

We cancel the classical noise of our input laser beam to produce squeezing at low frequencies.

We have produced EPR entanglement and are presently characterising it.