Given many realizations of a state or a channel as a resource, two parties can generate a secret key as well as entanglement. We describe protocols to perform the secret key distillation (as it turns out, with optimal rate). Then we show how to achieve optimal entanglement generation rates by “coherent” implementation of a class of secret key agreement protocols, proving the long-conjectured “hashing inequality.”

We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.

We study the nonlinear excitations of a vortex line in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the classical Euler dynamics of the vortex results in a description of the vortex line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which allows for both bright and gray soliton solutions. We discuss these solutions in detail and predict that it is possible to create vortex-line solitons with current experimental capabilities.

The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect two-photon coalescence even for nonperfect photons.

In 1972 May showed that for a large linear system with random coupling the system size and the average coupling strength must together satisfy a simple inequality to ensure the stability of the equilibrium point. Here we extend the analysis to delay coupled systems. Our calculations establish that the same inequality obtained by May constrains the stability for systems randomly coupled through discrete and distributed delays.

We demonstrate a robust implementation of a deterministic linear-optical controlled-not gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45 °-oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The optical controlled-not gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.

We demonstrate that the fusion algebra of conformal defects of a two-dimensional conformal field theory contains information about the internal symmetries of the theory and allows one to read off generalizations of Kramers-Wannier duality. We illustrate the general mechanism in the examples of the Ising model and the three-state Potts model.

We propose a quantum computing architecture based on the integration of nanomechanical resonators with Josephson-junction phase qubits. The resonators are GHz-frequency, dilatational disk resonators, which couple to the junctions through a piezoelectric interaction. The system is analogous to a collection of tunable few-level atoms (the Josephson junctions) coupled to one or more electromagnetic cavities (the resonators). Our architecture combines desirable features of solid-state and optical approaches and may make quantum computing possible in a scalable, solid-state environment.

We reexamine dipolar motion of condensate atoms in one-dimensional optical lattices and harmonic magnetic traps including quantum fluctuations within the truncated Wigner approximation. In the strong tunneling limit we reproduce the mean field results with a sharp dynamical transition at the critical displacement. When the tunneling is reduced, on the contrary, strong quantum fluctuations lead to finite damping of condensate oscillations even at infinitesimal displacement. We argue that there is a smooth crossover between the chaotic classical transition at finite displacement and the superfluid-to-insulator phase transition at zero displacement. We further analyze the time dependence of the density fluctuations and of the coherence of the condensate and find several nontrivial dynamical effects, which can be observed in the present experimental conditions.

We show that time- and phase-resolved two-color nonlinear wave packet interferometry can be used to reconstruct the probability amplitude of an optically prepared molecular wave packet without prior knowledge of the underlying potential surface. We analyze state reconstruction in pure- and mixed-state model systems excited by shaped laser pulses and propose nonlinear wave packet interferometry as a tool for identifying optimized wave packets in coherent control experiments.

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.

We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or $\mathrm{S}\mathrm{U}(1,1)$ quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or $\mathrm{S}\mathrm{U}(1,1)$ degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.

Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.

This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics.

We report Bose-Einstein condensation of weakly bound ${}^6\mathrm{L}\mathrm{i}_2$ molecules in a crossed optical trap near a Feshbach resonance. We measure a molecule-molecule scattering length of ${170}_{-60}^{+100}\mathrm{n}\mathrm{m}$ at $770\mathrm{G}$, in good agreement with theory. We study the 2D expansion of the cloud and show deviation from hydrodynamic behavior in the BEC-BCS crossover region.

The collective mode frequencies in isotropic and deformed traps are calculated for general polytropic equation of states, $P\propto n^{\gamma +1}$, and expressed in terms of $\gamma$ and the trap geometry. For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the effective power $\gamma \simeq 0.5–1.3$ is calculated from Jastrow type wave-function ansatz, and from the crossover model of Leggett. The resulting mode frequencies are calculated for these phases around the BEC-BCS crossover.

We study the zero-temperature ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the dipolar interactions break the rotational symmetry of the Hamiltonian and induce new quantum phases. Different phases can be reached by tuning the effective strength of the dipolar interactions via modifying the trapping geometry. The experimental feasibility of detecting these phases is investigated. The spin-mixing dynamics is also studied.

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.

Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic ${\mathrm{A}\mathrm{l}}_{0.4}{\mathrm{G}\mathrm{a}}_{0.6}\mathrm{A}\mathrm{s}/\mathrm{\text{air}}$ structure for the generation of $1.5\mu \mathrm{m}$ light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.

We report the implementation of quantum dense coding on individual atomic qubits with the use of two trapped ${}^9\mathrm{B}\mathrm{e}^{+}$ ions. The protocol is implemented with a complete Bell measurement that distinguishes the four operations used to encode two bits of classical information. We measure an average transmission fidelity of 0.85(1) and determine a channel capacity of 1.16(1).