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
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