Quantum mechanical wonders

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Niels Bohr Institute Copenhagen University
Light-Matter Quantum Interface
Eugene Polzik LECTURE 4
IHP Quantum Information Trimester
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Quantum memory for light criteria

• Memory must be able to store independently
  prepared
• states of light

• The state of light must be mapped onto the
  memory with
• the fidelity higher than the fidelity of the
  best
• classical recording

• The memory must be readable

B. Julsgaard, J. Sherson, J. Fiuráek , I. Cirac,
and E. S. Polzik Nature, 432, 482 (2004)
quant-ph/0410072.
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Mapping a Quantum State of Light onto Atomic
Ensemble
The beginning. Complete absorption
Squeezed Light pulse
Proposal Kuzmich, Mølmer, EP PRL 79, 4782
(1997)
Atoms
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Our light-atoms interface - the basics
Light pulse consisting of two modes
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Polarization quantum variables Light
Propagation direction
vertical
horizontal
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Canonical quantum variables for an atomic
ensemble
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Object gas of spin polarized atoms at room
temperature
Optical pumping with circular polarized light
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• Canonical quantum variables for light
• Complementarity amplitude and phase of
• light cannot be measured together

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Polarization homodyning - measure X (or P)
Polarizing Beamsplitter 450/-450
Strong field A(t)
x
Quantum field a -gt X,P
Polarizing cube
S1
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Teleportation in the X,P representation
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Today another idea for (remote) state
transfer and its experimental implementation for
quantum memory for light
See also work on quantum cloning J. Fiurasek, N.
Cerf, and E.S. Polzik, Phys.Rev.Lett. 93,
180501 (2004)
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Implementation light-to-matter state transfer
No prior entanglement necessary
C
F80
F?100
B. Julsgaard, J. Sherson, J. Fiuráek , I. Cirac,
and E. S. Polzik Nature, 432, 482 (2004)
quant-ph/0410072.
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These criteria should be met for memory in
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Classical benchmark fidelity for transfer of
coherent states
Atoms
Best classical fidelity 50
K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac,
Phys. Rev. Lett. 94,150503 (2005),
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Preparation of the input state of light
Strong field A(t)
Quantum field - X,P
x
Polarizing cube
S1
P
Polarization state
X
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Physics behind the Hamiltonian 1. Polarization
rotation of light
Polarizing Beamsplitter 450/-450
x
Quantum field
Polarizing cube
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Physics behind the Hamiltonian 2. Dynamic Stark
shift of atoms
Atoms
atoms
Strong field A(t)
Quantum field - a
x
Polarizing cube
y
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Quantum memory Step 1 - interaction
Light rotates atomic spin Stark shift
XL
Atomic spin rotates polarization of light
Faraday effect
Output light
Input light
Entanglement
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Quantum memory Step 2 - measurement feedback
Polarization measurement
Fidelity gt 100 (82 without SS atoms)
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Experimental realization of quantum memory for
light
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Memory in rotating spin states
y
z
Atomic Quantum Noise
2,4
2,2
2,0
1,8
1,6
1,4
1,2
Atomic noise power arb. units
1,0
0,8
0,6
0,4
0,2
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
Atomic density arb. units
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Memory in rotating spin states - continued
x
z
y
Atomic Quantum Noise
2,4
2,2
2,0
1,8
1,6
1,4
1,2
Atomic noise power arb. units
1,0
0,8
0,6
0,4
0,2
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
Atomic density arb. units
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Encoding the quantum states in frequency sidebands
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Memory in atomic Zeeman coherences
Cesium
4
3
2
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x
z
y
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Nature, Nov. 25 (2004) quant-ph/0410072.
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Stored state versus Input state mean amplitudes
X plane
read
write
t
output
input
Y plane
Magnetic feedback
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Stored state variances
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Fidelity of quantum storage

• State overlap averaged over
• the set of input states

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Quantum memory lifetime
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Decoherence Limitations
Typical estimate of linewidth
GHz 5 0.1qdeg 1.0PmW
0.5PmWqdeg
Working values
Important for entanglement
Need k2 large and h low, impossible.
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Deterministic quantum memory for a light Qubit
Initial state of atoms
squeezed
Realized by an extra QND measurement pulse
A. Sørensen, NBI
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Quantum Memory for Light demonstrated

• Deterministic Atomic Quantum Memory proposed and
• demonstrated for coherent states with ltngt in
• the range 0 to 10 lifetime4msec

• Fidelity up to 70, markedly higher than best
• classical mapping

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Scalability an array of dipole traps or solid
state implementation quantum holograms
Detector array
Spatial array of memory cells
I. Sokolov and EP, to be submitted
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Y
l/4 wave plate
Recent advanced proposals K. Hammerer, K.
Mølmer, EP, J.I. Cirac. Phys.Rev. A., 70, 044304
(2004). J. Sherson, K. Mølmer, A.Sørensen, J.
Fiurasek, and EP quant-ph/0505170
Light pulse
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Quantum memory read-out single pulse in squeezed
state
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Light-Atoms Q-interface with cold atoms
6P
Cesium clock levels
F4
F3
D. Oblak C. Alzar, P. Petrov
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• Memory Summary
• New state transfer protocol ? quantum memory for
  light
• Experimental demonstration for coherent states
• Nature, 432, 482 (2004)
• Prediction for a qubit state bridging dicrete
  and
• continuous variables
• State retrieval protocols

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Criteria for light-ensemble interface

• 2-level stable state with long coherence time
• Initialization collective coherent spin state
  (CSS)
• Coupling of the CSS to light corresponding to
• high optical density

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Atomic teleportation
3-party entanglement/ Secret sharing
Scaling/ solid state implementation
Entangled atoms Entangled light Light/atoms QI
exchange
Quantum memory for light
Distillation by local operations
Continuous variable logic
Discrete variable logic
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cavity enhanced interaction

• enhanced phase shift
• power build-up inside cavity
• compensate with smaller photon number

T mirror transmission a absorption
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Coupling strength of the interface
Z
Duan, Cirac, Zoller, EP PRL (2000)
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Figure of merit for the quantum interface
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Spontaneous emission the fundamental limit
K. Hamerrer, K. Mølmer, E. S. Polzik, J. I.
Cirac. PRA 2004, quant-ph/0312156