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Quantum Networks with Atomic Ensembles. 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 Information Paraty, August 14, 2007.

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Quantum Networks with Atomic Ensembles

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 Information

Paraty, August 14, 2007

Daniel Felinto*

[email protected]


B

A

  • Theoretical issues

    • Does it “work” – capabilities beyond any classical system

      • Quantum computation, communication, & metrology

  • Experimental implementation

    • Physical processes for reliable generation, processing, & transport

    • of quantum states

      • A quantum interface between matter and light

« Quantum Networking »

Fundamental scientific questions and Diverse experimental challenges

Quantum channel–

transport / distribute

quantum entanglement

Quantum node

generate, process, store

quantum information

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


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  • Purify the entanglement

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F<1

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F~1

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Quantum Repeaters : Principles

  • Divide into segments and generate entanglement

Fidelity close to 1, long distance… But time exponentially large with the distance

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L0

L0

L0

L

Entanglement (often) and purification (always) are probabilistic : each step ends at different times.

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  • Connect the pairs


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  • Purify the entanglement

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F<1

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F~1

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Quantum Repeaters : Principles

  • Divide into segments and generate entanglement

Fidelity close to 1, long distance… But time exponentially large with the distance

.

.

L0

L0

L0

L

Entanglement (often) and purification (always) are probabilistic : each step ends at different times.

.

.

« Scalability » :requires the storage of heralded entanglement

  • Connect the pairs

: Quantum Memories


One Approach : « DLCZ »

Atomic ensembles in the single excitation regime


Entanglement-based cryptography

Entanglement connection

Quantum teleportation

Entanglement of two ensembles

Capabilities Enabled by DLCZ Roadmap

  • Beyond the original protocols of DLCZ

  • Implementation of quantum memory

  • Realization of fully controllable

  • source for single photons

  • A source for entangled photon pairs

  • Universal quantum computation via

  • the protocol of Knill, LaFlamme, Milburn

  • Scalable long-distance

  • quantum communication via

  • quantum repeater architecture

  • Distribution of entanglement

  • over quantum networks


Outline

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

  • Number-state entanglement between two ensembles

  • Polarization entanglement between two nodes (4 ensembles)

  • Towards entanglement swapping


« Building Block » (DLCZ)

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


Nonclassical correlations between field 1 and the ensemble

: the excitation probability

Write

Collective atomic state

Write

Field 1

Field 1

Creating a Single Atomic Excitation


Nonclassical correlations between field 1 and the ensemble

Field 2

Read

read

Read

Field 2

Nonclassical correlations between fields 1 and 2

Retrieving the Single Excitation


Si APD

30 ns, Very weak

200 µm

Experimental Setup

Counter-propagating and off-axis configuration

H

Field 2

Read V

Write H

Field 1

V


Field 2

Read

Suppression of the

two-photon component

Multi-excitations

Coherent state limit

Plateau :

Single excitation

Sub-Poissonian

qc~ 50%

?

a = 0.7 ± 0.3%

Background noise

Conditional Field-2

Retrieval efficiency

of the stored excitation

J. Laurat et al., “Efficient retrieval of a single excitation stored in an atomic ensemble”, Opt. Express 14, 6912 (2006)


Programmable Delay

10 to 20 µs

Write

Field 1

Storage Time of the Single Excitation

Reading

Writing

Field 2

Read

H. De Riedmatten et al., “Direct measurement of decoherence for entanglement between a photon and a stored excitation”, PRL 97, 113603 (2006)

D. Felinto et al., “Control of decoherence in the generation of photon pairs from atomic ensembles”, Phys. Rev. A 72, 053809 (2005)


Outline

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

  • Number-state entanglement between two ensembles

  • Polarization entanglement between two nodes (4 ensembles)

  • Towards entaglement swapping

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)


Light

Atoms

entangled

Entanglement between Two Ensembles

entangled

Atoms

Light

50/50

Beam splitter


Entanglement between Two Ensembles

1 photon detected  1 atom transferred

50/50

Beam splitter


here

here

General (and ideal) case

there

there

where

there

=

Entanglement between Two Ensembles

1 photon detected  1 atom transferred

L

Entangled

R

+


Map matter state

to field state

atoms L

entangled?

  • Coherence d

  • Individual statistics pij

atoms R

/

Concurrence

C > 0  Entanglement of formation E > 0

W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998)

How to Verify the Entanglement ?

  • Tomography


Experimental Density Matrix

Populations

Coherence

D1c

D1b

<1, suppression of 2-photon events relative to

single-excitation events

p=9.10-4

160 Hz preparation rate

J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528


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%)

Scaling with Excitation Probability

Decreasing excitation probability

J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528


Outline ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

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

  • Number-state entanglement between two ensembles

  • Polarization entanglement between two nodes (4 ensembles)

  • Towards entaglement swapping


ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%) R

L

2LU

2RU

DLa

DRa

BS

BS

2LD

2RD

DLb

DRb

“Effective” state giving one click on each side

How Having one Click on Each Side ?

3 m

Entangled !

Node R

Node L

Entangled !

LU

RU

LD

RD


“Effective” state giving one click on each side ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Polarization Entanglement

3 m

Node R

Node L

2L

2LU

2RU

2R

LU

RU

2LD

2RD

LD

RD


Preparation x 35 ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

p11 : Probability of both pairs

are prepared in an entangled state

Duration that the first entanged pair is stored before retrieval

Results : Preparation and Bell Violation

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)


Results : Preparation and Bell Violation ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Asynchronous Preparation

Preparation x 35

Final state x 20

Duration that the first entanged pair is stored before retrieval

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)

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)


Results : Preparation and Bell Violation ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Asynchronous Preparation

Preparation x 35

Final state x 20

Bell Violation (CHSH)

Large violation : quantum key distribution with security at minimum against individual attacks

Duration that the first entanged pair is stored before retrieval

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)


  • 2 nodes separated by 3m ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

  • 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)


Outline ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

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

  • Number-state entanglement between two ensembles

  • Polarization entanglement between two nodes (4 ensembles)

  • Towards entanglement swapping


2 ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%) LU

2RU

2LD

2RD

Entangled !

One click at Node L projects the Node R into:

Towards Entanglement Swapping

3 m

Entangled !

Node R

Node L

Entangled !

LU

RU

LD

RD


Towards Entanglement Swapping ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Populations

Coherence

  • From two entangled pairs with h(2)~0.15 and 90% vacuum

  • The transfert succeeds only 50% of the time, while the weight of two-photon events stays the same.

  •  Overall, h(2) multiplied by 4

<1, suppression of 2-photon events relative to

single-excitation events

J. Laurat et al., Towards entanglement swapping with atomic ensembles in the single excitation regime, arXiv:0704.2246


3m ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Node L

Node R

2R

2L

Field 1

LU

RU

LD

RD

In a Nutshell…

  • Q. Repeaters, DLCZ

  • …and Building Block

Writing

Reading

Field 2

Write

  • Photon pair : a<1%

  • Efficient retrieval : 50%

  • Memory time ~ 10 µs

Read

  • Number-state entanglement

  • Heralded and stored

  • C=0.9±0.3 for the atoms

  • Polarization Entanglement

  • 2 nodes, 4 ensembles

  • Asynchronous preparation

  • Bell violation

  • Towards swapping

  • Coherence transfert


Raman ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

E

 1/

t

Decoherence

1) MOT magnetic field

Each atom sees a different field  Inhomogeneous broadening of the ground states

B

z

t ~ 100 ns

Solution : Switching off the trapping field


Typical storage time ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

t ~ 10 µs

~ 100 m

MOT temperature 500 K  t ~ 200 s

Storage Time of the Excitation

« Timing » and linewidth

Perspectives ?? Better cancellation of residual fields

@ 40 Hz

MOT off 6 ms


LU ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

LD

Experimental Setup

Repumper

Write

PBS

BSW

Read

LU

BSR

RU

LD

RD

D2LV

D2RV

BS1

D2LH

D2RH

l/2

l/4

D1Va

D1Vb

Compensator

Beam displacer

D1Ha

D1Hb


Experimental Setup ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%)

Interferometers Entangling the (U, D) Pairs

Repumper

Write

PBS

BSW

Read

LU

BSR

RU

LD

RD

D2LV

D2RV

BS1

D2LH

D2RH

l/2

l/4

D1Va

D1Vb

Compensator

Beam displacer

D1Ha

D1Hb


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