University of Aarhus

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Danish Quantum Optics Center
Entanglement and quantum communication with
non-exotic means
Copenhagen interpretation
University of Aarhus
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Entanglement - qubits
2 quantum coins
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Entanglement collective variables
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Now, imagine 1012 spins in each ensemble

• Only interactions/measurements of
• the collective spin of each ensemble are
  necessary
• Atoms are indistinguishable - high symmetry of
  the system
• - robustness against losses of spins
• No free lunch
• limited capabilities compared to ideal maximal
  entanglement

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Outline Continuous quantum variables Atoms
Collective spin of the sample Light Stokes
parameters of the pulse Hald, Sorensen, Schori,
Polzik PRL 83, 1319 (1999) Entangling atoms via
interaction with light Theory Kuzmich, Polzik
PRL 85, 5639 (2000) Duan,Cirac, Zoller, Polzik
PRL 85, 5643 (2000) Experiment entangled state
of two Cs gas samples two macroscopic
entangled objects Julsgaard, Kozhekin, Polzik
Nature 413, 400 (2001). Quantum communication
protocols with entangled atomic
samples Proposals Kuzmich, Polzik PRL 85, 5639
(2000) Duan,Cirac, Zoller, Polzik PRL 85, 5643
(2000)
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Quantum limits on the communication rate
n photons, frequency n, duration dt
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Teleportation of light Innsbruck Rome Caltech-Aarh
us
Quantum State (information) Processing
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Why use ensembles of atoms?

• Quantum information processing often requires
  efficient interaction between light and atoms
• Entangled (squeezed) states of atomic ensembles
  are required in applications such as
• frequency standards

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gt
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Spin memory with Coherent Spin States
Quasi-continuous encoding
90
180
0
270

• Densely coded states are impossible to read
• but possible to transfer via teleportation

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Entangled or inseparable continuous variable
systems

• EPR example 1935

2 particles entangled in position/momentum

• EPR state of light Ou, Pereira, Kimble 1992

Simon PRL (2000) Duan, Giedke, Cirac, Zoller PRL
(2000) Necessary and sufficient condition for
entanglement
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EPR state of two macro-spin systems
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Two samples oppositely polarized
x
Two entangled samples
y
z
y
z
-x
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Total z and y components of two ensembles
with equal and opposite macroscopic spins can be
determined simulteneously with arbitrary
accuracy
x
x
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Light / Atom - Interaction
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Entangled state of 2 macroscopic objects
J1
J2
Polarization detection
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Detecting quantum fluctuations of the spin
Probe polarization noise spectrum
0,0008
B
Atomic density (a.u.)
probe
Density
arb. units
----------------------------------
1.00

0.02
0,0006
z
0.56

0.01
0.21

0.01
1.0
y
0.5
0.2
Noise power arb. units
0,0004
0,0002
Shot noise level
,
0,0000
Larmor frequency W320kHz
300000
310000
320000
330000
340000
RF frequency
Frequency (Hz)
Atomic Quantum Noise
2,4
2,2
2,0
1,8
1,6
1,4
Atomic noise power arb. units
1,2
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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700MHz
6
P
PBS
3/2
Entangling and
verifying beams
out
S
y
m
4
m
4
W
325kHz
F
4
6
S
1/2
F
3
Entangling and
verifying pulses
B
-field
Time
0.5 ms
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2.0
1.5
CSS
1.0
Entangled spin state
2
F
x
Atoms
0.5
Light
(1pulse)
S

(1pulse)
y
0.0
0
2
4
6
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Protocols (proposals)

• Teleportation of atomic states
• Light-to-atoms teleportation
• Atom-to-light teleportation

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Parametric downconversion in a resonator (OPO)
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Frequency tunable entangled and squeezed light
around 860nm
800MHz
107 photons per mode
Classical field
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8
6
4
2
0
-2
-4
-6
-1
0
1
2
3
4
5
6
p
Phase
Radians
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Quantum state of light stored in long lived spins
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Quantum Teleportation of Light
Furusawa et al Science, 1998 Caltech-Aarhus-Bangor
Classical channels
Ap
Ax
Actuators
Quantum channel
Ea
Eb
p
EPR source
?in
x
Eb
Ap
Ax
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Teleportation of an entangled atomic state
2
1

• 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 Spin 1 to cell
4 rotate spin 4 by ABC
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Operation Teleportation of atoms
Resources shared entanglement
Memory Bob
Memory Alice
EPR spin Alice
EPR spin Bob

• Distance limitations
• Losses of light fiber (3 dB) 1 km at 850 nm
• 10 km at 1500 nm
• space 100 km (diffraction)

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Communication networks based on continuous spin
variables
Operation Storage of light and read-out from
atomic memory
Resources local entanglement
Memory Bob
Memory Alice
EPR pulses
EPR spins

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

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Brian Julsgaard
Christian Schori