Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Entanglement and Memory-ForceBound States

Beyond Bell Pairing in ContinuousInformation Spaces

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Introduction

Continuous degrees of freedom have the potential formassive information capacity.

Instances exist within current experimental control.

There is no easy method to analyzequantum information in a continuum

so surprises are possible!

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

The Schmidt theorem -> information eigenmodes, naturally discrete and unique.

The “participation ratio” K counts modes that will be effective beyond Bell-pair status.

Theory is in hand for broadband bi-photonentanglement (PRL, Law-Walmsley-Eberly).

K ≤ 5 in a normal BBO chi-2 setup.Lab advances by the Walmsley group have

been reported.

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Desirable “cross-modular’’ continua are engaged in experiments on entanglement of photons

with atomic center of mass, asreported by Pfau, et al., Chapman, et al., and

Kurtsiefer, et al. (1994-1997).

One entangled partner is detectable with nearly 100% efficiency (the atom) and

the other (the photon) is an ideally high-speedinformation carrier.

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

A generic continuum-entangling experiment:

The resulting photon-atom state amplitude:

C(

r q ,

r k ) =

g(r k ) a0(

r q +r k )

(Eq −Eq+k) / h+kc−ω0 +iγ

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Beyond Bell pairing, with the Schmidt decomposition:

Eigenvalues determine the participation ratio:

A new control parameter for entanglement:

K = 1 λ

n

2

∑

η =

ω

0

γ

h Δ p

mc

~

Δ ω

γ

Cθ(q,k) = λn ψ n(q,θ)φn(k,θ)∑

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Meaning of K

K = 1, no entanglement.

K = 2, Bell states.

K = 5, beyond Bell, more information.

K = 10, still more info.

Quantum info is alwaysdiscrete and countable.

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Surprising result beyond Bell pairing: the quantum Memory Force.

MF exists between the atom and the photon inthe absence of any classically describable force.

The Exchange Force of Pauli is a special case.EF applies only to pairs of identical particles. MF can apply to any pair of quantum systems,

(whether individual particles or not).

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Atom-photon entanglement and joint detection, a la Kurtsiefer, et al. (1997)

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Beyond Bell pairing:

Information eigenmodesare determined by theatom-photon quantum

memory.

The first 4 MF boundstates are shown here.(PRL, Chan-Law-Eberly).

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

First steps to treat 2-d info content are now underway.

Angular analysis of bi-photon beyond-Bell pairs shows a wealth of quantum patterns to exploit.

Center for Quantum InformationROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Prospects / Vision for QI Theory .

Explore and exploit quantum MF

Cross-platform instances, beyond-Bell pairing

• electron-photon Schmidt modes,

• quantum soliton pairs / optical fiber

• phased arrays / large particle number

Retain focus on high-dimensional contexts