IHP Quantum Information Trimester

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Niels Bohr Institute Copenhagen University
Light-Matter Quantum Interface
Eugene Polzik LECTURE 5
IHP Quantum Information Trimester
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Quantum teleportation
Light to light Entanglement resource
parametric downconversion process
Atoms to atoms Entanglement resource
measurement induced entanglement of two atomic
ensembles
Light atoms, etc
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More accurate description field modes in an
optical resonator
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Parametric downconversion in a resonator
(Optical Parametric Oscillator below threshold)
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Frequency tunable entangled light around 860nm
800MHz
107 photons per mode
AOM
Cavity modes
LO
AOM
LO-
Classical field
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Narrowband tunable entangled beams
Sorensen, Schori, Polzik PRA, 2002
Degree of entanglement 0.8 observed
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Teleportation principle (canonical variables)
L.Vaidman
Demonstrated experimentally for light variables
by Furusawa, Sørensen, Fuchs, Braunstein
Kimble, Polzik. Science 1998
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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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ix
X
P
ip
Alice
Mx
Dx
Dp
Mp
Bob
LOp
LOx
mBob
vacuum
In
Out
vacuum
c
LOV
rout
vingt
Classical teleportation
Victor
DV
_
Victor
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Furusawa et al, Science, Vol 282, Issue 5389,
706-709 , 23 October 1998
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Classical boundary
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Communication networks based on continuous spin
variables
Operations Light-atom teleportation
Resources local entanglement
Memory Bob
Memory Alice
EPR pulses
EPR spins
Quantum channel
Operation Teleportation of atoms
Resources shared entanglement
Memory Bob
Classical channel
Memory Alice
EPR spin Alice
EPR spin Bob
Coherent pulse
Symbols

• Continuous variables
• polarization state of light
• spin state of atoms

Input-Output interaction free
space off-resonant dipole interaction
conditional rotation detection of
light
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Light-to-Atoms Teleportation
Kuzmich, EP 2000
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Teleportation of atomic states
Light pulse
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Memory in rotating spin states - continued
x
z
y
1,4
1,2
1,0
0,8
Atomic Quantum Noise
2,4
0,6
2,2
0,4
2,0
0,2
1,8
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
1,6
Atomic density arb. units
Atomic noise power arb. units
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Teleportation of an entangled atomic state

• Every measurement changes the single cell
• spin, BUT does not change the measured sum
• Every pulse measures both y and z components of
  the sum entanglement is created

To complete teleportation of entanglement onto
cell 1 and cell 4 rotate spin 4 by ABC
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Tripartite entanglement
For atomic ensembles via quantum measurement
simple step from 2 to 3
N atoms, spins up
N/2 atoms, spins down
N/2 atoms, spins down
Fan HY, Jiang NQ, Lu HL Lance AM, Symul T, Bowen
WP, et al. Van Look et al
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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
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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