Squeezing, Entanglement and Teleportation - LIGO

Manipulating the Quantum Noise :
Squeezing, Entanglement and Teleportation
LIGO-G030221-00-Z
Roman Schnabel,
Warwick P. Bowen,
Nicolas Treps,
Timothy C. Ralph,
Ping Koy Lam,
Hans-Albert Bachor.
1

Quadrature Amplitudes
Coherent
state
δÊ 1
E 0
E
δÊ 2
t
Variance
Var
2
ˆ 2 ˆ ˆ 2
( Eˆ
) ( ˆ
i
= Var δ Ei
) = δEi
− δEi
= δEi
Heisenberg uncertainty relation
δEˆ
2
1
⋅
δEˆ
2
2
≥
(
hω
) 2
4πV
2

Squeezed
beam
3

OPA Quadrature Squeezing
OPA:
Optical
Parametric
Amplifier
E
δEˆ2
≅ ˆ ϕ =
Eˆ
0
t
E
E
t
ϕ
4

The Homodyne Detector
Interfering
50/50 beam splitter
Phase shift θ
Intense local oscillator
(Squeezed) Coherent signal State beam
Electrical
current
2 2 2
V( iˆ
) ≅ E δEˆ
cos θ δEˆ
LO
⋅ +
−
1
2
2
sin
2
θ
Squeezing 5

Noise Power of Coherent and Squeezed Light
2
δÊ 2
11.2 dB
2
δEˆcoh
3.1 dB
2
δÊ 1
θ=0 θ=π/2
Squeezing 6

Quadrature Noise Operators
δXˆ
δXˆ
1
2
†
( Ω) = δaˆ
( Ω) + δaˆ
( Ω)
†
( Ω) = i δaˆ
( Ω) −δaˆ
( Ω)
( )
δ ˆX 2
( Ω)
1
Noise operator
diagrams for a
coherent and
phase squeezed
beam
Linearized annihilation and
creation operators
aˆ
( Ω) = α + δaˆ
( Ω)
†
aˆ
( Ω'
),
δaˆ
( Ω)
=
[ δ
] δ ( Ω − Ω'
)
-1
-1
1
δ ˆX ( Ω)
1
Squeezing 7

Bright squeezed beams I II
8

Quadrature Entanglement
Loss
δ ˆ
A
X 1, 2
λ/2
2
∆ δ ˆX
A±
B
1,2
I
V
( ˆ + ˆ −
X , X ) = 0.44 ± 0.01
( ˆ +
, ˆ −
X X ) = 0.58 ± 0. 02
c
λ/2
Loss
g
δ ˆ
B
X 1, 2
Entanglement 9

Teleportation of Quantum Information
• Can all information of a quantum system be gathered
No!
• Can information be copied exactly
No!
• Can all the information be classically transmitted with
arbitrarily high accuracy
Yes, under certain
conditions!
[Bennett et al. 1993]
10

Teleportation of a Quadrature State
Xˆ
Xˆ
1
2
=
=
1
2
1
2
in A
( Xˆ
−δXˆ
)
1
in A
( Xˆ
+ δXˆ
)
2
1
2
ˆX 1
ˆX 2
[A. Furusawa et al., 1998], [Bowen et al. 2002]
Teleportation 11

Teleporter Input and Output States
ˆX
1
ˆX
2
Classical limit
No-cloning limit
ˆX
1
ˆX
2
Classical limit
No-cloning limit
Perfect teleportation
W.P. Bowen et al., Phys. Rev. A, accepted (2003)
Entanglement 12

Summary
• Experiments were introduced where the
quantum noise of a cw laser beam was
manipulated and characterized.
• Squeezing and entanglement of quadrature
operators were demonstrated.
• Entanglement was used to teleport a side-
band modulation signal of a cw laser beam.
13