C.W. Chou, H. Deng, K.S. Choi, H. de Riedmatten, J. Laurat, S. van Enk, H.J....
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C.W. Chou, H. Deng, K.S. Choi, H. de Riedmatten, J. Laurat, S. van Enk, H.J. Kimble
Caltech Quantum Optics
*Presently at Departamento de Física, UFPE
International Workshop on Quantum InformationParaty, August 14, 2007
Daniel Felinto*[email protected]
Quantum Networks with Atomic Ensembles
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AB
Quantum channel –
transport / distribute quantum
entanglement
Quantum nodegenerate, process, store
quantum information
Theoretical issues• Does it “work” – capabilities beyond any classical system
• Quantum computation, communication, & metrologyExperimental implementation
• Physical processes for reliable generation, processing, & transportof quantum states
• A quantum interface between matter and light
Goal : develop the ressources that enable quantum repeaters, thereby allowing entanglement-based communication tasks on distance scales larger than set by the attenuation length of
fibers
« Quantum Networking »« Quantum Networking »Fundamental scientific questions and Diverse experimental Fundamental scientific questions and Diverse experimental
challengeschallenges
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Quantum Repeaters : PrinciplesQuantum Repeaters : Principles1) Divide into segments and
generate entanglement
L0 L0 L0
L
2) Purify the entanglement F<1
F~1
3) Connect the pairs
Fidelity close to 1, long distance… But time
exponentially large with the distance
Entanglement (often) and purification
(always) are probabilistic : each step ends at different times.
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Quantum Repeaters : PrinciplesQuantum Repeaters : Principles1) Divide into segments and
generate entanglement
L0 L0 L0
L
2) Purify the entanglement F<1
F~1
3) Connect the pairs
« Scalability » : requires the storage of heralded
entanglement
: Quantum Memories
Fidelity close to 1, long distance… But time
exponentially large with the distance
Entanglement (often) and purification
(always) are probabilistic : each step ends at different times.
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One Approach : « DLCZ »One Approach : « DLCZ »
Atomic ensembles in the single excitation regime
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Capabilities Enabled by DLCZ Capabilities Enabled by DLCZ RoadmapRoadmapBeyond the original protocols of DLCZBeyond the original protocols of DLCZ • Implementation of quantum memory• Realization of fully controllablesource for single photons• A source for entangled photon pairs…• Universal quantum computation via the protocol of Knill, LaFlamme, Milburn
• Scalable long-distancequantum communication via quantum repeater architecture• Distribution of entanglementover quantum networks
Entanglement-based cryptography
Quantum teleportation
Entanglement connection
Entanglement of two ensembles
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• « DLCZ building block » : writing, reading, memory time
• Number-state entanglement between two ensembles
• Polarization entanglement between two nodes (4 ensembles)• Towards entanglement swapping
OutlineOutline
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« Building Block » (DLCZ)« Building Block » (DLCZ)
• Large ensemble of atoms• With a -type level configuration
Duan, Lukin, Cirac and Zoller, “Long-distance quantum communication with atomic ensembles and linear optics”, Nature 414, 413 (2001)
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Creating a Single Atomic Excitation Creating a Single Atomic Excitation
Nonclassical correlations between field 1 and the ensemble
Field 1
Field 1
Write
WriteCollective atomic state
: the excitation probability
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Retrieving the Single ExcitationRetrieving the Single Excitation
Read
Read
Field 2
Field 2
read
Nonclassical correlations between fields 1 and 2
Nonclassical correlations between field 1 and the ensemble
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Experimental SetupExperimental Setup
Field 1
Field 2
Write HRead V
V
H
Si APD
Counter-propagating and off-axis configuration
30 ns, Very weak200 µm
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Conditional Field-2Conditional Field-2
cqReadField 2
Retrieval efficiencyof the stored excitation
?
J. Laurat et al., “Efficient retrieval of a single excitation stored in an atomic ensemble”, Opt. Express 14, 6912 (2006)
Suppression of the two-photon component
Coherent state limit
Sub-Poissonian
= 0.7 ± 0.3%
qc ~ 50%
Plateau : Single
excitation
Background noise
Multi-excitations
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Storage Time of the Single Storage Time of the Single ExcitationExcitation
Field 1Write ReadField 2
Programmable Delay10 to 20 µs
Writing Reading
D. Felinto et al., “Control of decoherence in the generation of photon pairs from atomic ensembles”, Phys. Rev. A 72, 053809 (2005)
H. De Riedmatten et al., “Direct measurement of decoherence for entanglement between a photon and a stored excitation”, PRL 97, 113603 (2006)
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• « DLCZ building block » : writing, reading, memory time
• Number-state entanglement between two ensembles
• Polarization entanglement between two nodes (4 ensembles)• Towards entaglement swapping
OutlineOutline
C.W. Chou, H. de Riedmatten, D. Felinto, S.V. Polyakov, S. van Enk, H.J. Kimble, Measurement-induced entanglement for excitation stored in remote atomic ensembles, Nature 438, 828 (2005)
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Atoms
Light
entangled
Atoms
Light
entangled
50/50 Beam splitter
Entanglement between Two Entanglement between Two EnsemblesEnsembles
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1 photon detected 1 atom transferred
50/50 Beam splitter
Entanglement between Two Entanglement between Two EnsemblesEnsembles
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+
here
here
therethere
Entangled
L
R
1 photon detected 1 atom transferred
Entanglement between Two Entanglement between Two EnsemblesEnsembles
where = there
General (and ideal) case
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How to Verify the Entanglement ?How to Verify the Entanglement ?•Tomography
2L
2R
• Individual statistics pij
• Coherence d2L
2R
où
Concurrence /C > 0 Entanglement of formation E > 0
W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998)
atoms L
atoms R
entangled?
,L R
L
R
Map matter state to field state
2 ,2L R
2L
2R
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Experimental Density MatrixExperimental Density MatrixPopulations Coherence
<1, suppression of 2-photon events relative to single-excitation events
2L
2R
2L
2R
D1c
D1b
J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528
p=9.10-4
160 Hz preparation rate
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Scaling with Excitation ProbabilityScaling with Excitation Probability
J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528
Decreasing excitation probability
Asymptotic value (no two-photon
component) given in the ideal case by the retrieval efficiency (13.5%) times the
overlap of the detected photons
(95%)
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• « DLCZ building block » : writing, reading, memory time
• Number-state entanglement between two ensembles
• Polarization entanglement between two nodes (4 ensembles)• Towards entaglement swapping
OutlineOutline
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How Having one Click on Each Side ?How Having one Click on Each Side ?
Entangled !
Entangled !DRa
DRb
BSDLa
DLb
BS
LU
LD RD
RU
“Effective” state giving one click on each side
R2RU
2RD
2LU
2LD
L
Node L Node R3 m
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Polarization EntanglementPolarization Entanglement
2RU
2RD
2LU
2LD
LU
LD RD
RU
“Effective” state giving one click on each side
2L 2R
Node L Node R3 m
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Results : Preparation and Bell Results : Preparation and Bell ViolationViolation
Duration that the first entanged pair is stored before retrieval
Asynchronous Preparation
C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)
p11 : Probability of both pairs are prepared in an entangled state
Preparation x 35
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Results : Preparation and Bell Results : Preparation and Bell ViolationViolation
Duration that the first entanged pair is stored before retrieval
Asynchronous Preparation
Preparation x 35Final state x 20
C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)
D. Felinto, C.W. Chou, J. Laurat, H. de Riedmatten, H. Kimble, “Conditional control of the quantum states of remote atomic memories for Q. networking”, Nature Physics 2, 844 (2006)
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Results : Preparation and Bell Results : Preparation and Bell ViolationViolation Asynchronous
Preparation
Bell Violation (CHSH)
Preparation x 35Final state x 20
Duration that the first entanged pair is stored before retrieval
Large violation : quantum key
distribution with security at minimum
against individual attacks
C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)
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• 2 nodes separated by 3m
• 2 ensembles per node
• Asynchronous preparation (memory) of 2 parallel
number-state entangled pairs
• Polarization coding and passive phase stability
Polarization entanglement distribution, violating Bell, in
a scalable fashion
C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over Scalable Quantum Networks, Science 316, 1316 (2007)
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• « DLCZ building block » : writing, reading, memory time
• Number-state entanglement between two ensembles
• Polarization entanglement between two nodes (4 ensembles)• Towards entanglement swapping
OutlineOutline
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Towards Entanglement SwappingTowards Entanglement Swapping
Entangled !
Entangled !LU
LD RD
RU
2RU
2RD
Node L Node R
Entangled !
3 m
2LU
2LD
One click at Node L projects the Node R into:
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Towards Entanglement SwappingTowards Entanglement SwappingPopulations Coherence
<1, suppression of 2-photon events
relative to single-excitation
events
2L
2R
2L
2R
• The transfert succeeds only 50% of the time, while the weight of two-
photon events stays the same.
Overall, h(2) multiplied by 4
J. Laurat et al., Towards entanglement swapping with atomic ensembles in the single excitation regime, arXiv:0704.2246
• From two entangled pairs
with h(2)~0.15 and 90% vacuum
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In a Nutshell…In a Nutshell…
Field 1Write ReadField 2
Writing Reading• Q. Repeaters, DLCZ …and Building Block
• Number-state entanglement
Photon pair : <1% Efficient retrieval : 50% Memory time ~ 10 µs
Heralded and stored C=0.9±0.3 for the atoms
• Polarization Entanglement 2 nodes, 4 ensembles Asynchronous preparation Bell violation LU
LD RD
RU
2L 2R
Node L Node R3m
• Towards swapping Coherence transfert
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Decoherence Decoherence 1) MOT magnetic field
Each atom sees a different field Inhomogeneous
broadening of the ground states
t
z
B
Solution : Switching off the trapping field
~ 100 ns
E
1/
Raman
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Storage Time of the ExcitationStorage Time of the Excitation
MOT off 6 ms
@ 40 Hz
« Timing » and linewidth
Perspectives ?? Better cancellation of residual
fields
~ 100 m
MOT temperature 500 K ~ 200 s
Typical storage time
~ 10 µs
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Write Repumper
Read
/2/4
PBS
Compensator
Beam displacer
LU
LD
RU
RD
D2RV
D2RH
D2LV
D2LH
D1Va
D1Ha D1Hb
D1Vb
BSW
BS1
BSR
LU
LD
Experimental SetupExperimental Setup
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Write
Interferometers Entangling the (U, D) Pairs
Repumper
Read
/2/4
PBS
Compensator
Beam displacer
LU
LD
RU
RD
D2RV
D2RH
D2LV
D2LH
D1Va
D1Ha D1Hb
D1Vb
BSW
BS1
BSR
Experimental SetupExperimental Setup