C.W. Chou, H. Deng, K.S. Choi, H. de Riedmatten, D. Felinto, H.J. Kimble

Caltech Quantum OpticsFRISNO 2007, February 12, 2007

Julien Lauratjlaurat@caltech.edu

Julien Lauratjlaurat@caltech.edu

Quantum Communication with Atomic Ensembles

Quantum Communication with Atomic Ensembles

EntanglementEntanglement : : ParadoxParadox to Applicationsto Applications

…Product states

… Entangled states

A B

.Cryptography Teleportation

Classical communication.

Entanglement : Non classical correlations

between distant systems

.EPR correlations

. .EPR correlations

.

…… AtAt Long DistancesLong Distances

A quantum state can’t be amplified

Fibre Optique

TelecomRepeater

Problem : DecoherenceCaltech

Les Houches.Result : Entanglement decays exponentially with the distance

Solution : Repeater

…… AtAt Long DistancesLong Distances

Caltech .

. QuantumRepeater .

Goal : Connect with a fidelity close to 1 in a “not too long” time

Les Houches

Problem : Decoherence

Result : Entanglement decays exponentially with the distance

Solution : Repeater

Quantum Quantum RepeatersRepeaters : : PrinciplesPrinciples

1) Divide into segments andgenerate 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 withthe distance

Entanglement (often) andpurification (always) are probabilistic : each stepends at different times.

. . ..

Quantum Quantum RepeatersRepeaters : : PrinciplesPrinciples

1) Divide into segments andgenerate entanglement

. .. .. .L0 L0 L0

L

2) Purify the entanglement. .. .. .. .. .. .. .. .. . F<1

. .. .. . F~1

3) Connect the pairs. .. .. .. .. . ..

« Scalability » : requiresthe storage of the

entanglement

: Quantum Memories

Fidelity close to 1, long distance… But time

exponentially large withthe distance

Entanglement (often) andpurification (always) are probabilistic : each stepends at different times.

Quantum NetworkQuantum Network

• Cavity QED

Ideal system but difficult to scale up.

• Single atom

• Atomic Ensembles

Continuous Variables

Single Excitation

Requirement :Atom-light interface

Quantum nodegenerate, process, store

quantum information

Quantum channel –transport / distribute

quantum entanglement

Quantum networks enabled by distributed entanglement

«« DLCZ DLCZ »»

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

• Entanglement between twoensembles

• Simultaneous storage of twoexcitations in two remote ensembles

• Polarization entanglement betweentwo nodes

OutlineOutline

Real-time ConditionalControl of Quantum

Memories

«« Building Block Building Block »» (DLCZ)(DLCZ)

• Large ensemble of atoms

• With a Λ-type level configuration

Duan, Lukin, Cirac and Zoller, “Long-distance quantum communication with atomic ensembles and linear optics”, Nature 414, 413 (2001)

CreatingCreating a Single a Single AtomicAtomic Excitation Excitation

Nonclassical correlations between field 1 and the ensemble

Field 1

Field 1

Write

WriteCollective atomic state

: the excitation probability

RetrievingRetrieving thethe Single ExcitationSingle Excitation

Read

Read

Field 2

Field 2

read

Nonclassical correlations between fields 1 and 2

Nonclassical correlations between field 1 and the ensemble

ExperimentalExperimental SetupSetup

Field 1

Field 2

Write H

Read V

V

H

Si APD

Counter-propagating and off-axis configuration

30 ns, Very weak200 µm

ConditionalConditional FieldField--22

cqRead

Field 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

α = 0.7 ± 0.3%

qc ~ 50%

Plateau :Single excitation

Background noise

Multi-excitations

StorageStorage TimeTime

Field 1Write ReadField 2

Programmable DelayAround 10µs

Writing Reading

D. Felinto et al., Phys. Rev. A 72, 053809 (2005)

H. De Riedmatten, J. Laurat, C.W. Chou, E.W. Schomburg, D. Felinto H.J. Kimble, “Direct measurement of decoherence for entanglement between a photon and a stored excitation”, PRL 97, 113603 (2006)

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

• Entanglement between twoensembles

• Simultaneous storage of twoexcitations in two remote ensembles

• Polarization entanglement betweentwo nodes

OutlineOutline

Atoms

Light

entangled

Atoms

Light

entangled

50/50 Beam splitter

EntanglementEntanglement betweenbetween TwoTwo EnsemblesEnsembles

1 photon detected ⇔ 1 atom transferred

50/50 Beam splitter

EntanglementEntanglement betweenbetween TwoTwo EnsemblesEnsembles

HowHow to to VerifyVerify thethe EntanglementEntanglement ??

•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 Rρ

L

R

Map matter state to field state

2 ,2L Rρ

2L

2R

ExperimentalExperimental DensityDensity MatrixMatrix

Populations Coherence

<1, suppression of 2-photon events relative to single-excitation events

2L

2R

2L

2R

D1c

D1b

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

• Entanglement between twoensembles

• Simultaneous storage of twoexcitations in two remote ensembles

• Polarization entanglement betweentwo nodes

OutlineOutline

Real-Time ConditionalControl of Quantum

Memories

SimultaneousSimultaneous StorageStorage ofof Single Single Excitations in Excitations in TwoTwo RemoteRemote MemoriesMemories

LWrite

Field 1

Repumper

Write

Repumper

Field 1 R

44-fold increase in p11!(N=23, 12µs)

p11 : Probability of both ensembles are prepared with one excitation, heralded by the two field-1 clicks.

FirstFirst Application : HOMApplication : HOM

Field 2 Field 2λ/2

BS

L R

V=0.77±0.06(Integrated data)

28-fold increase in p1122!(N=23, 12µs)

Two independent sources of single photons

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)

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

• Entanglement between twoensembles

• Simultaneous storage of twoexcitations in two remote ensembles

• Polarization entanglement betweentwo nodes

OutlineOutline

How How HavingHaving oneone Click on Click on EachEach SideSide ??

Entangled !

Entangled !DRa

DRb

BSDLa

DLb

BS

LU

LD RD

RU

“Effective” state giving one click on each side

ϕR2RU

2RD

2LU

2LD

ϕL

Node L Node R

3 m

PolarizationPolarization EntanglementEntanglement

2RU

2RD

2LU

2LD

LU

LD RD

RU

“Effective” state giving one click on each side

2L 2R

Node L Node R

3 m

Write Repumper

Read

λ/2λ/4

PBS

Compensator

Beam displacer

LU

LD

RU

RD

D2RV

D2RH

D2LV

D2LH

D1Va

D1Ha D1Hb

D1Vb

BSW

BS1

BSR

LU

LD

ExperimentalExperimental SetupSetup

Write

Interferometers Entangling the (U, D) Pairs

Repumper

Read

λ/2λ/4

PBS

Compensator

Beam displacer

LU

LD

RU

RD

D2RV

D2RH

D2LV

D2LH

D1Va

D1Ha D1Hb

D1Vb

BSW

BS1

BSR

ExperimentalExperimental SetupSetup

ResultsResults : Bell Violation: Bell Violation

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, arxiv\quant-ph 0702057

• 2 nodes separated by 3m

• 2 ensembles per node

• Asynchronous preparation(memory) of 2 parallel

entangled pairs

• Polarization coding

Polarizationentanglement distribution, violating Bell, in a scalable

fashion

In a In a NutshellNutshell……

Field 1WriteRead

Field 2

Writing Reading• Q. Repeaters, DLCZ …et Building Block

• Entanglement

Photon pair : α<1%Efficient retrieval : 50%Memory time ~ 10 µs

• Conditional Control

HeraldedWithout postselection, C~0.1

Asynchronous preparation

• Polarisation Entanglement2 nodes, 4 ensemblesBell violation

LU

LD RD

RU2L 2R

Node L Node R3m