Functional Quantum Nodes for Entanglement Distribution over Scalable Quantum Networks

We demonstrate entanglement distribution between two remote quantum nodes located 3 meters apart. This distribution involves the asynchronous preparation of two pairs of atomic memories and the coherent mapping of stored atomic states into light fields in an effective state of near maximum polarization entanglement. Entanglement is verified by way of the measured violation of a Bell inequality, and can be used for communication protocols such as quantum cryptography. The demonstrated quantum nodes and channels can be used as segments of a quantum repeater, providing an essential tool for robust long-distance quantum communication.Comment: 10 pages, 7 figures. Text revised, additional information included in Appendix. Published online in Science Express, 5 April, 200

Solution of the Three--Anyon Problem

We solve, by separation of variables, the problem of three anyons with a harmonic oscillator potential. The anyonic symmetry conditions from cyclic permutations are separable in our coordinates. The conditions from two-particle transpositions are not separable, but can be expressed as reflection symmetry conditions on the wave function and its normal derivative on the boundary of a circle. Thus the problem becomes one-dimensional. We solve this problem numerically by discretization. $N$-point discretization with very small $N$ is often a good first approximation, on the other hand convergence as $N\to\infty$ is sometimes very slow.Comment: 15 pages, LaTeX2.0

Calabi-Yau Black Holes and Enhancement of Supersymmetry in Five Dimensions

BPS electric and magnetic black hole solutions which break half of supersymmetry in the theory of N=2 five-dimensional supergravity are discussed. For models which arise as compactifications of M-theory on a Calabi-Yau manifold, these solutions correspond, respectively, to the two and five branes wrapping around the homology cycles of the Calabi-Yau compact space. The electric solutions are reviewed and the magnetic solutions are constructed. The near-horizon physics of these solutions is examined and in particular the phenomenon of the enhancement of supersymmetry. The solutions for the supersymmetric Killing spinor of the near horizon geometry, identified as $AdS_{3}\times S^{2}$ and $AdS_{2} \times S^{3}$ are also given.Comment: 12 pages, Latex file. CAMS/AU

Control of decoherence in the generation of photon pairs from atomic ensembles

We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et. al for long distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than 10 microseconds, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.Comment: 16 pages, 11 figures, submitted for publicatio

Direct measurement of decoherence for entanglement between a photon and stored atomic excitation

Violations of a Bell inequality are reported for an experiment where one of two entangled qubits is stored in a collective atomic memory for a user-defined time delay. The atomic qubit is found to preserve the violation of a Bell inequality for storage times up to 21 microseconds, 700 times longer than the duration of the excitation pulse that creates the entanglement. To address the question of the security of entanglement-based cryptography implemented with this system, an investigation of the Bell violation as a function of the cross-correlation between the generated nonclassical fields is reported, with saturation of the violation close to the maximum value allowed by quantum mechanics.Comment: 4 pages, 3 figures. Minor changes. Published versio

Towards experimental entanglement connection with atomic ensembles in the single excitation regime

We present a protocol for performing entanglement connection between pairs of atomic ensembles in the single excitation regime. Two pairs are prepared in an asynchronous fashion and then connected via a Bell measurement. The resulting state of the two remaining ensembles is mapped to photonic modes and a reduced density matrix is then reconstructed. Our observations confirm for the first time the creation of coherence between atomic systems that never interacted, a first step towards entanglement connection, a critical requirement for quantum networking and long distance quantum communications

Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons

Methods in Riemann-Finsler geometry are applied to investigate bi-Hamiltonian structures and related mKdV hierarchies of soliton equations derived geometrically from regular Lagrangians and flows of non-stretching curves in tangent bundles. The total space geometry and nonholonomic flows of curves are defined by Lagrangian semisprays inducing canonical nonlinear connections (N-connections), Sasaki type metrics and linear connections. The simplest examples of such geometries are given by tangent bundles on Riemannian symmetric spaces $G/SO(n)$ provided with an N-connection structure and an adapted metric, for which we elaborate a complete classification, and by generalized Lagrange spaces with constant Hessian. In this approach, bi-Hamiltonian structures are derived for geometric mechanical models and (pseudo) Riemannian metrics in gravity. The results yield horizontal/ vertical pairs of vector sine-Gordon equations and vector mKdV equations, with the corresponding geometric curve flows in the hierarchies described in an explicit form by nonholonomic wave maps and mKdV analogs of nonholonomic Schrodinger maps on a tangent bundle.Comment: latex 2e 50 pages, the manuscript is a Lagrange-Finsler generalization of the solitonic Riemannian formalism from math-ph/0608024, v3 modified following requests of Editor/Referee of J. Geom. Phys., new references and discussion provided in Conclusio

Free Relativistic Anyons with Canonical Spin Algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra $\left\{ S_\mu , S_\nu \right\}\,=\,\epsilon_{\mu \nu \gamma}S^\gamma$. It is shown that it is a general consequence of these features that the Poincar\`e invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.Comment: Complete version with reference