IHP Quantum Information Trimester

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Niels Bohr Institute Copenhagen University
Light-Matter Quantum Interface
Eugene Polzik
IHP Quantum Information Trimester
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Light-Matter interface for
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What do we want to achieve?
Quantum memory for light
Classical approach - measure and
write Problem Cannot measure an unknown state
Example single polarized photon
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What do we want to achieve?
Quantum memory retrieval
Atoms
Classical approach - measure and write Same
Problem Cannot measure an unknown state
Example atom in an unknown superposition of two
states
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Distant quantum network retrieval memory
Atoms 1
Atoms 2
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Another option for networks distant
teleportation of atomic states
Atoms to be teleported
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Outline

• Quantum variables pairs of non-commuting
  operators for
• atomic ensembles and for pulses of light
• Off-resonant interaction Hamiltonian
• Atoms-light quantum interface - protocols
• Entanglement and teleportation measurement
  based approach
• Quantum memory for light
• other

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Quantum description of light
Spatial, temporal and frequency modes
Comparison with atoms
Annihilation and creation operators. Quadrature
phase operators
Coherent states Gaussian states Fock
states Entangled states
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Field vector potential
Classical mode functions
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• Complimentary quantum variables for light
• E.-m. field is quantum amplitude and phase
  quadratures of
• light cannot be measured together

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Photon number phase uncertainty
Coherent state
A
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Coherent state
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Measurement of the quadrature phase operators
with 50/50 beamsplitter Homodyning
Quadratic photodetectors Strong LO lots of
photons Quantum efficiency up to 99 At least
106 photons needed in the LO
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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
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A short story about quantum limitation
on communication rates
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Youngs Interference
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Youngs experiment with a weak flux of light

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What if the source of light emits two colors
red and blue?
The two colors are separated its called
wavelength multiplexing in modern communication
But what if only a few photons OR JUST ONE -
are detected?
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Modern communication uses pulses of light
traveling in glass fibers
Light is a wave of electromagnetic field
and in phase
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Fourier limit on the information processing rate
State-of-the-art RD (NEC et al) February
2002 100 GHz ?0.8nm 40 channels cover 1530
1562 nm
Is it a true limit?
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Heisenberg limit on the information processing
rate
n photons, frequency n, duration t
n

• Transmission rate
• 10-40 GHz
• 100 GHz
• doubles every year
• 2020 1017 Hz (?)

Is it the limit for quantum networks?
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• Some special quantum states
• Real life noise measurements
• Dissipation and losses
• Detectors and efficiency
• Spatial modes
• Quantum measurements with light
• Photon counting
• Coincidence measurements
• Spectrum of photocurrent noise

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Continuous quantum variables - light
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The story of losses
Also inefficient detectors, tdetector Q.E.
vacuum
input
output
t/r
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Spatial modes
Optical resonators. Gaussian spatial modes
Z
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Light to atoms coupling
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Cavity QED
Ensemble approach
Strong coupling to a single atom - qubit
Collective ensemble quantum variables
Caltech optical l
Paris microwave MPQ optical MPQ, Innsruck
ions Stanford - solid state
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Spin polarized atomic ensemble
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Single spin
Then y and z projections will be undetermined
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Collective spin state of an oriented 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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Ensemble of N atomic spins and noise
x

What is the spin projection along Y or Z?
Zero?
Not really!
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Ensemble ground-state spin variables
z
Optical pumping
x
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Complimentary quantum variables for an atomic
ensemble
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Macroscopic spin ensemble coherent spin
state
x
X
z
y
State preparation (optical pumping)

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6P3/2
Cesium as a spin ½ system
6S1/2
Spherical chicken
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