The Squeezed The Squeezed Atom Laser Atom Laser Simon Haine and Joe Hope Australian Centre for Quantum-Atom Optics, Australian National University Canberra
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