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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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slide1

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]

slide2

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

slide3

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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
slide4

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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

slide5

One Approach : « DLCZ »

Atomic ensembles in the single excitation regime

slide6

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
slide7

Outline

  • « DLCZ building block » : writing, reading, memory time
  • Number-state entanglement between two ensembles
  • Polarization entanglement between two nodes (4 ensembles)
  • Towards entanglement swapping
slide8

Large ensemble of atoms

  • With a L-type level configuration

« Building Block » (DLCZ)

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

slide9

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

slide10

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

slide11

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

slide12

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)

slide13

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)

slide14

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)

slide15

Light

Atoms

entangled

Entanglement between Two Ensembles

entangled

Atoms

Light

50/50

Beam splitter

slide16

Entanglement between Two Ensembles

1 photon detected  1 atom transferred

50/50

Beam splitter

slide17

here

here

General (and ideal) case

there

there

where

there

=

Entanglement between Two Ensembles

1 photon detected  1 atom transferred

L

Entangled

R

+

slide18

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
slide19

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

slide20

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

slide21

Outline

  • « DLCZ building block » : writing, reading, memory time
  • Number-state entanglement between two ensembles
  • Polarization entanglement between two nodes (4 ensembles)
  • Towards entaglement swapping
slide22

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

slide23

“Effective” state giving one click on each side

Polarization Entanglement

3 m

Node R

Node L

2L

2LU

2RU

2R

LU

RU

2LD

2RD

LD

RD

slide24

Preparation x 35

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)

slide25

Results : Preparation and Bell Violation

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)

slide26

Results : Preparation and Bell Violation

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)

slide27

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)

slide28

Outline

  • « DLCZ building block » : writing, reading, memory time
  • Number-state entanglement between two ensembles
  • Polarization entanglement between two nodes (4 ensembles)
  • Towards entanglement swapping
slide29

2LU

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

slide30

Towards Entanglement Swapping

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

slide31

3m

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
slide32

Raman

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

slide33

Typical storage time

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

slide34

LU

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

slide35

Experimental Setup

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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