c.w. chou, h. deng, k.s. choi, h. de riedmatten, j. laurat, s. van enk, h.j....

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

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

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.

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.

One Approach : « DLCZ »One Approach : « DLCZ »

Atomic ensembles in the single excitation regime

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

• « DLCZ building block » : writing, reading, memory time

• Number-state entanglement between two ensembles

• Polarization entanglement between two nodes (4 ensembles)• Towards entanglement swapping

OutlineOutline

« 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)

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

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

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

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

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)



• 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)

Atoms

Light

entangled

Atoms

Light

entangled

50/50 Beam splitter

Entanglement between Two Entanglement between Two EnsemblesEnsembles

1 photon detected 1 atom transferred

50/50 Beam splitter


+

here

here

therethere

Entangled

L

R

1 photon detected 1 atom transferred


where = there

General (and ideal) case

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

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

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%)



• Polarization entanglement between two nodes (4 ensembles)• Towards entaglement swapping

OutlineOutline

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

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

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

Results : Preparation and Bell Results : Preparation and Bell ViolationViolation


Asynchronous Preparation

Preparation x 35Final state x 20


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)

Results : Preparation and Bell Results : Preparation and Bell ViolationViolation Asynchronous

Preparation

Bell Violation (CHSH)

Preparation x 35Final state x 20


Large violation : quantum key

distribution with security at minimum

against individual attacks


• 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)



• Polarization entanglement between two nodes (4 ensembles)• Towards entanglement swapping

OutlineOutline

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:

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

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

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

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

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


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


c.w. chou, h. deng, k.s. choi, h. de riedmatten, j. laurat, s. van enk, h.j....

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