The SqueezedThe Squeezed Atom LaserAtom Laser

Simon Haine and Joe HopeAustralian Centre for Quantum-Atom Optics,

Australian National UniversityCanberra

ANU Atom OpticsANU Atom Optics Theory:Joe Hope, Mattias Johnsson, Simon HaineSebastian Wuester, Craig Savage

Atom Laser Experiment:Nick Robins, Cristina Figl, Matthew Jeppesen,Julien Dugue, John Close

ANUANU Quantum OpticsQuantum OpticsSqueezing at Rubidium Wavelengths Experiment:Katie Pilypas, Magnus Hsu, Gabriel Hetet, OliverGlockl, Charles Harb, Pingkoy Lam, Hans Bachor

!

V ( ˆ X +) =1

V ( ˆ X ") =1

!

V ( ˆ X +) <1

V ( ˆ X ") >1

!

V ( ˆ X +) >1

V ( ˆ X ") <1

Squeezing

Amplitude and Phase are conjugate observables

Can’t have a state with perfectly well definedamplitude and phase

Motivation:Precision measurement:

- Atom lasers useful for precision measurement.

- Atomic shot noise will limit the sensitivity of any measurement.

- Squeezing will reduce shot noise.

Fundamental:

- Tests of entanglement with massive particles.

Why atom laser?

- Can use amplitude and phase quadratures as conjugate observables.

How to get squeezing:

Use atomic nonlinearity somehow

Two choices:

!

H =U ˆ " + ˆ " + ˆ " ˆ "

Use squeezed light

Squeezed light (almost) on tap at ANU

Kerr squeezing, 4-wave mixing

Molecular dissociation!

H = "( ˆ # m

+ ˆ # a

ˆ # a

+ ˆ # a

+ ˆ # a

+ ˆ # m

)

BEC

!

1

!

2

!

3

!

"1

!

"2

!

h(k probe "kcontrol )

Control

probe

(Control)(probe)

(trapped)(untrapped)

Raman Atom Laser

• Each outcoupled atom receives a momentumkick of

• In certain regimes, each photon for the probebeam gives you one outcoupled atom.

!

h(k probe "kcontrol )

ATOM

LASE

RSQ

UEEZED

squeezed

!

ˆ E

!

"!

ˆ " 3

!

ˆ " 1

!

ˆ " 2

• Adiabatically eliminate excitedstate

!

ˆ " 3

( )

• Assume control field andcondensate field are largeand coherent (semiclassicalapproximation)

!

ˆ " 1

!

"

Single mode model

Rabi floppingHui Jing et al. PRA 63,015601, (2000).

Need to consider the multimode dynamics of the probe beam and the atom laser beam!

ˆ E " ˆ E (x)

!

ˆ " # ˆ " (x) etc.

approximations…

• Far detuned - ignore spontaneous emission

• Condensate and control field remain in coherent state.

Outcoupled atoms

Optical probe field

Trapped atoms

Heisenberg Equations of Motion:

Solution:

x (mm)0.50.40.30.20.10-0.1

Den

sity

BEC

Probe beam x c/v x100

Atom Laser x 100

• Qauntum efficiency of outcoupling (atoms/photon) ~1

- (Vacuum Rabi frequency ~1/Tleave)

• Probe beam weak (Nprobe << Ncondensate)

• Appropriate two-photon detuning

Quantum Fluctuations

Sque

ezin

g

S. A. Haine and J. J. HopeLas. Phys. Lett. 2 597 (2005)

!

v( ˆ N ) =

ˆ N 2" ˆ N

2

ˆ N

!

!

v( ˆ N )

!

v( ˆ N ) = 0

!

v( ˆ N ) = 1

Perfect squeezing

No squeezing

t (ms)

Quadrature Quadrature SqueezingSqueezing

• Homodyne detector required to measure quadratures.- could use bright atom laser from same BEC as local oscillator.

!

V ( ˆ X +)

!

V ( ˆ X +)V ( ˆ X

") #1

Commutationrelations give:

Atom-Light Entanglement

squeezing

squeezing

vacuum squeezing squeezing

vacuum

squeezing

Entanglement?

!

" = 0

!

" ="opt

!

" = 1

2"opt

!

"

!

"

!

0

!

0

!

0

!

0

!

0

!

"

!

"

!

"

enta

ngle

men

t

100/0 0/100 50/50

Atom-Light Entanglement

x (mm)

0.50.40.30.20.10-0.1

Den

sity

BEC

Probe beam x c/v x100

Atom Laser x 100

Infer results of measurements on the atomic beam

!

Vinf

( ˆ X +)V

inf( ˆ X

") <1

Measure quadraturesof the light beam

Entangled if:

S. A. Haine, M. K. Olsen, J. J. Hope, quant-ph/0601029 (2005).

Pump (β)χ (2)

a1

a2 ψ(k1 )

ψ(k2 )

Control

beamBEC

Entangled atom laser beamsEntangled atom laser beams

OPO

• By making measurements on one beam, can infer results ofmeasurements on the other beam to better than the uncertainty principle.

• Fundamental tests of entanglement with massive particles.

• Practical applications: Precision measurement below the quantum limit,teleportation.

Flux SqueezingFlux Squeezing

Flux difference

!

V ( ˆ J 1" ˆ J

2)

!

ˆ J 1

!

ˆ J 2

EPR CriterionEPR Criterion

!

V ( ˆ X +)V ( ˆ X

") #1

Commutation relations give:

!

Vinf

( ˆ X +)V

inf( ˆ X

") <1

To demonstrate the EPRcriterion:

Amplitude and phase quadratures:

Measure left beam Infer results of measurements on theright beam

S. A. Haine and J. J. HopePhys. Rev. A 72, 033601 (2005)

Ent

angl

emen

t

!

Vinf

( ˆ X +)V

inf( ˆ X

") <1

To demonstrate the EPRcriterion:

How hard is this experiment?How hard is this experiment?

Things we need:

- Raman atom laser.

- Squeezed light at atom optics frequencies- on the way

- Atom detection with high quantum efficiency.- hard, but has been done before

- Homodyne detector for quadrature squeezing.- we have some ideas.

Summary:

• Can use squeezed light to generate asqueezed atom laser.

• Can generate entangled atom laser beams,and entanglement between atomic beam andoptical beam.

• Should be possible with realistic parameters.

?

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Thank you