Entanglement of Collective Quantum Entanglement of Collective Quantum Variables for Quantum Memory and Variables for Quantum Memory and

TeleportationTeleportation

N. P. Bigelow

The Center for Quantum Information

The University of Rochester

ΨUR

CQI

A Tall Pole Item in QIA Tall Pole Item in QI

How to Realize Robust, Long- Lived

Entanglement of Many Particles for

Quantum Information Storage and Processing

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CQI

We performed the first experimental demonstration of We performed the first experimental demonstration of

long-lived entanglementlong-lived entanglement of the spins of 10 of the spins of 101212 neutral, neutral,

ground-state atoms in a simple atomic vapor cell ground-state atoms in a simple atomic vapor cell

by using the interaction of the atomic sample by using the interaction of the atomic sample

with polarized laser lightwith polarized laser light

Accomplishments to Date

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Simple, Long-lived On-Demand Entanglement Simple, Long-lived On-Demand Entanglement is Required for Practical Quantum Information Networks:is Required for Practical Quantum Information Networks:Quantum Memory, Teleportation and Quantum RepeatersQuantum Memory, Teleportation and Quantum Repeaters

Objectives–to create entanglement of a macroscopic sample of matter – a collection of trillions of atoms–to create entangled samples separated by large distances–to teleport the quantum state of massive particles – a sample of atoms–To develop quantum devices for purification and transmission of entanglement over long distancesRelevanceExtensible entanglement is an enabling technology for QI toolbox: information storage and transmittal

Present Status–We have demonstrated the entanglement of more than 1012 atoms using coherent laser light

Milestones for Future Work–Create entangled atomic samples that are widely separated in space–Teleport the quantum state of massive matter–Quantum repeaters

Approach–To couple light to the collective quantum variables of a macroscopic sample –To create on-demand entanglement using interaction of the atoms with laser light–To use measurements of quantum “noise” as an entanglement detector

There is a beneficial synergy with other CQI projectsThere is a beneficial synergy with other CQI projects

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Important Quantum Information Protocols: Important Quantum Information Protocols: Entanglement Purification and Quantum RepeatersEntanglement Purification and Quantum Repeaters

Issue and Objective: • Optical states (photonic channels) are ideal for transferring information

as light is the best long distance carrier of information. • To date, the majority of quantum communications experiments on

entanglement involve entangled states of light. • Unfortunately, entanglement is degraded exponentially with distance due

to losses and channel noise. • Solutions protocols have been devised evoking concepts of

entanglement purification and quantum repeaters strategies that avoid entanglement degradation while increasing the

communication time only polynomially with distance.

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Requirements for implementing these QI Devices:• Long lived entanglement - quantum memory

• Generation of entanglement between distant qubits

What platform to use? What tool in our toolbox?

Quantum Information Processing: Quantum Information Processing: Light and/or Atoms?Light and/or Atoms?

Light as the Quantum System

To date, the majority of quantum communications experiments on

entanglement involve entangled states of light

Entanglement of discrete photonic variables (spin-1/2) and continuous

variables (quadrature phases) has been demonstrated. Continuous variables

are advantageous because they provide access to an infinite dimensional state

space.

It is hard to “store” light ΨUR

Matter (Atoms) as the Quantum System

Entanglement of massive particles with multiple internal degrees of

freedom is more difficult but recognized as mandatory for realizing the entanglement lifetimes needed for information storage and processing

Record so far: four trapped ions (C. Sackett et al. At NIST Boulder –

Nature 2000)

How to entangle many, many atoms? How to entangle many, many atoms?

Can we do so in a simple way?Can we do so in a simple way?

Can we introduce a “new” physics Can we introduce a “new” physics

approach to the QI toolbox?approach to the QI toolbox?

How to have How to have longlong coherence times? coherence times?ΨUR

Some Needs for the QI Toolbox

Entangling the Collective Quantum Entangling the Collective Quantum Variables of the Atomic VaporVariables of the Atomic Vapor

• For a sample of many atoms, the accepted approach to entanglement is to build it up on a atom-by-atom basis – difficult (loss of single atom destroys entanglement, very sensitive to environment, spontaneous emission..)

• Our approach is to couple strongly to the collective variables of the ensemble using an optical interaction

• Readily achieve the required strong coupling without using a cavity or a trap

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we use the collective spin of the sample – the

“super moment” reflecting the

quantum sum of the individual

magnetic moments of the atom in the gas

What is Collective Spin?

By Entangling Collective Variables Long By Entangling Collective Variables Long Lived Entanglement Can be Realized Lived Entanglement Can be Realized

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rS = ˆ s ii

∑

• Entanglement of the Collective Spin is robust because the loss of coherence of one spin of our billions or trillions has little effect on the overall collective spin state – a robustness factor due to the intrinsic symmetry of collective state

• In a glass vapor cell, spin lifetimes are set by wall collisions and inhomogeneous magnetic fields–many milliseconds to seconds.

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•Collective Variables (in atomic physics)Spin-waves in H(Cornell U) and He-3 (ENS) [c. 1980](Stimulated Raman Scattering (Mostowski, Raymer…) [c. 1980] Present work [c. 1998]Light Storage - Hau, Fleischhauer, Lukin, Polzik..….[c. 2000]QI Theory: Cirac, Zoller…..[c. 2001/02]

Possible Applications to “Other” Solid State Systems – e.g. an electron gas

Entanglement can be produced by the Entanglement can be produced by the interaction of atoms with polarized lightinteraction of atoms with polarized light

AtomAAAs

Photons

Photons

Entangled Atoms

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Kuzmich, Bigelow, Mandel, EPL, 42, 481 (1998)Duan, Cirac, Zoller, Polzik, PRL 85, 5643 (2000)

Entanglement is produced through a QND interaction – a non-local

Bell measurement

Entanglement is produced Entanglement is produced using only coherent lightusing only coherent light

AtomAAAs

Photons

Photons

Entangled Atoms

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ˆ H I

=r S •

r J → ˆ σ x

s ˆ σ xJ

r S

r S

r J

r J

Optically Thick Sample Optically Thick Sample ++ Forward Scattering of Optical Field Forward Scattering of Optical FieldAnalogue of 2-mode squeezed stateAnalogue of 2-mode squeezed state

Forward scattered mode is keyForward scattered mode is key

r ′ S

r ′ J

Forward scattering, indistinguishability Forward scattering, indistinguishability & QND Hamiltonian & QND Hamiltonian

How Can We Probe the Collective Spin?How Can We Probe the Collective Spin?

How Can We Sense Entanglement?How Can We Sense Entanglement?

Collective quantum state not necessarily Collective quantum state not necessarily detectable in single particle propertiesdetectable in single particle properties

(a “bug” and a “feature”)(a “bug” and a “feature”)

Recall the quantum mechanics of a spinRecall the quantum mechanics of a spinand the connection to “noise”and the connection to “noise” ΨUR

Measurement Variances as a Probe of Entanglement

A Quantum Spin has Uncertainties A Quantum Spin has Uncertainties Relating its Knowable ComponentsRelating its Knowable Components

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Quantum Uncertainty Disc for Transverse Spin Component

Quantum Uncertainty Transverse Spin

Component

y

z

δz2

How to Probe Entanglement of the How to Probe Entanglement of the Collective Atomic SpinCollective Atomic Spin

An Ideal EPR StateOf Entangled Spins (Gaussian

Quantum Variables) Obeys

Duan, Giedke, Cirac, Zoller PRL 84, 2722 (2000); Simon & Peres-Horodecki PRL 84, 2726 (2000)

Non-factorable state

δr S y,z

2 ≤δr S ⊥

2

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Quantum Uncertainty Disc for Transverse Spin Component

Non-classical quantum variance (noise) only visible in the Non-classical quantum variance (noise) only visible in the collective spincollective spinExample of how quantum properties are observable in collective properties but Example of how quantum properties are observable in collective properties but

not single particlenot single particle

Variance of Collective Spin – Variance of Collective Spin – A Probe of EntanglementA Probe of Entanglement

When the Spins of the Sample are appropriately Entangled

The Spin Measurement Variance (noise) of

One Transverse Quadrature Can be Reduced Below the

“Quantum Limit”So, We Use Quantum Spin

Variance as Our Probe

(recall noise measurements presented by Yamamoto, discussed by Marcus)

Bigelow, Nature 409, 27 (2001)

Spin VarianceSpin Variance Measurement of Entanglement Measurement of Entanglement

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To characterize the quantum spin To characterize the quantum spin variance or noise of the collective variance or noise of the collective spin, a “thermal” sample is first used spin, a “thermal” sample is first used to calibrate the system (spin “light to calibrate the system (spin “light bulb”. bulb”.

Then, the system is (1) prepared in a Then, the system is (1) prepared in a Coherent Spin State - a minimum Coherent Spin State - a minimum uncertainty state (e.g. completely uncertainty state (e.g. completely polarized), then (2) entangled and (3) polarized), then (2) entangled and (3) the spin fluctuation is re-measuredthe spin fluctuation is re-measured

Process can be performed pulsed (ns Process can be performed pulsed (ns or slower), or CWor slower), or CW

Dx polarizingbeamsplitter

coated Cs cell

l/ 4

-

Our Entanglement Figure of Our Entanglement Figure of Merit is 70% out of 100%Merit is 70% out of 100%

• The SQL is the variance level for a sample of spins in a coherent, but not entangled, state known as a Coherent Spin State (CSS) - analogous to a coherent state of light

• The data is spin variance for the entangled sample and the line for the non- entangled sample

• ms coherence time set by transit time of atoms through laser beams (vs. <ns lifetimes)

Kuzmich, Mandel, Bigelow, PRL, 85, 1594 (2000)

The atoms are contained The atoms are contained in small glass cellsin small glass cells

The apparatus is compactThe entire

entanglement apparatus already fits

on a 3 x 2 ft optical bench, including lasers

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The cells are constructed with a custom dry-film coating to The cells are constructed with a custom dry-film coating to minimize wall relaxation - many ms lifetimesminimize wall relaxation - many ms lifetimes

Entanglement Can Be Realized in Entanglement Can Be Realized in Even Smaller Cells!Even Smaller Cells!

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Logical Extrapolation – Entanglement Logical Extrapolation – Entanglement of “Separated Ensembles”of “Separated Ensembles”

• Following our work, Polzik’s group in Aarhus used this approach to entangle atoms in two distinct and separated atomic cells (Nature 2001) - Effectively same as our single cell experiment with an added wall

NY Times, Nature, Scientific American

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D2

D1

D2

D1

≈

What Does the Future Include?: Teleportation of massive particle states

• We intentionally work with states that are well suited to teleportation – analogue to two-mode squeezed state

• Teleportation protocol established: Duan, Cirac, Zoller, Polzik, PRL 85, 5643 (2000)

D2

D1

D3

D41

2

3

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What Does the Future Include?Raman Processes and Photon Counting:

Parallel Geometry and Conditional Measurement

g1 g2

e

filter

mirrors

beamsplitter

1D

2D

• Photon counting techniques have proven invaluable in quantum information entanglement experiments

• Conditional measurement and photon counting can be used to realize alternative approaches to collective variable quantum information generation and processing

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Ψ 12± = 1

2S1†±e

iϕS2† ⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟0a 1

0a 2

1

2

What Does the Future Include?Raman Processes and Photon Counting:

Entanglement Swapping

• Coherent Raman pulse to top two cells (at common location distant from bottom two cells - three locations total)

• Click at D1 or D2 and entanglement is transferred from L1-L2 and R1-R2 to L2-R2 – entanglement transfer achieved

mirror

beam

splitterD1 D2

mirror

entangled entangled

L2

L1 R1

R2

What Does the Future Include?:Raman Processes - Spontaneous and Stimulated

(I. Cirac, QO5 Summer 2001)

• Treatment does not emphasize coherent processes - use multi-level properties of the atomic media to enhance performance and increase noise immunity

• Simple – modify laser frequencies/add additional diode laser• Use Raman scattering in forward direction

– Inherent increase in noise immunity if ground states are non-degenerate– Stimulated processes give large signals– Coherent processes minimize spontaneous forward scattering

g1 g2

e

g

e

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What Does the Future Include?

• Teleportation of massive particle states

• Exploit coherent atomic interaction

• Entanglement purification and repeater implementation

• Demonstration of a compact apparatus – M<20 lbs– P<100 watts

• Application of quantum control

• Realization in solids

• Quantum imprinting on the collective spin state

• Transfer to QI technology - error management, etc.

• Measures of entanglement –Schmidt rank, entropy…

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Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley

Published Record of Our WorkPublished Record of Our Work

• Kuzmich, Bigelow, Mandel, EPL, 42, 481

• Kuzmich et al., PRA 60, 2346

• Kuzmich, Mandel, Bigelow, PRL, 85, 1594

• Bigelow, Nature, 409, 27

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CQI

Simple, On-Demand Entanglement Simple, On-Demand Entanglement of Trillions of Neutral Atoms :of Trillions of Neutral Atoms :

Quantum Memory, Teleportation and Quantum RepeatersQuantum Memory, Teleportation and Quantum Repeaters

Objective–to create entanglement of a macroscopic collection of atoms–to create entangled samples separated by large distances–to teleport the quantum state of massive particles – a sample of atomsRelevanceEstensible entanglement is an enabling technology for QI information storage and transmittal

Present Status–We have demonstrated the entanglement of more than 1012 atoms using coherent laser lightMilestones for Future Work–Create entangled atomic samples that are widely separated in space–Teleport the state of massive matter–Quantum repeaters

Approach–To couple to the collective quantum variables of a macroscopic sample –To create on-demand entanglement using interaction of the atoms with laser light–To use measurements of quantum “noise” to probe entanglement

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

ΨUR

CQI