1. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Entanglement and Memory-Force Bound States Beyond Bell Pairing in Continuous Information Spaces

2. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Introduction Continuous degrees of freedom have the potential for massive information capacity. Instances exist within current experimental control. There is no easy method to analyze quantum information in a continuum so surprises are possible!

3. Center for Quantum Information ROCHESTER 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-photon entanglement (PRL, Law-Walmsley-Eberly). K ≤ 5 in a normal BBO chi-2 setup. Lab advances by the Walmsley group have been reported.

4. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Desirable “cross-modular’’ continua are engaged in experiments on entanglement of photons with atomic center of mass, as reported 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-speed information carrier.

5. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES A generic continuum-entangling experiment: The resulting photon-atom state amplitude:

6. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Beyond Bell pairing, with the Schmidt decomposition: Eigenvalues determine the participation ratio: A new control parameter for entanglement:

7. Center for Quantum Information ROCHESTER 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 always discrete and countable.

8. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES

9. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Surprising result beyond Bell pairing: the quantum Memory Force. MF exists between the atom and the photon in the 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).

10. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Atom-photon entanglement and joint detection, a la Kurtsiefer, et al. (1997)

11. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Beyond Bell pairing: Information eigenmodes are determined by the atom-photon quantum memory. The first 4 MF bound states are shown here. (PRL, Chan-Law-Eberly).

12. Center for Quantum Information ROCHESTER 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.

13. Center for Quantum Information ROCHESTER 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