The superfluid-Mott insulator phase transition in a Bose-Einstein condensate of neutral atoms with doubly degenerate internal ground states in an optical lattice is theoretically investigated. The optical lattice is created by two counterpropagating linearly polarized laser beams with the angle $\theta$ between the polarization vectors (lin-angle-lin configuration). The phase diagram of the system and the critical values of the parameters are worked out. It is shown that the sign of the detuning plays an important role and that there is a strong suppression of the Mott transition in the case of blue detuning. Varying the laser intensity and/or the angle $\theta$ one can manipulate the Mott insulator to superfluid quantum phase transition as well as prepare the condensate in physically distinguishable “ferromagnetic” and “antiferromagnetic” superfluid states.

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a $(1+1)$-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.

We investigate the relationship between the coherence of a partially Bose-condensed spinor gas and its temperature. We observe cooling of the normal component driven by decoherence as well as the effect of temperature on decoherence rates.

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.

We demonstrate the first step of a complete program, which consists in establishing an x-ray energy standard scale with the use of few-body atoms, in the few keV range. Light pionic and muonic atoms as well as one and two-electron ions from electron-cyclotron ion sources are used. The transition energies are calculable from quantum-electrodynamics, meaning that only a very limited subset need be measured and compared with theory, while providing a large number of standard lines. Here we show that circular transitions in pionic neon atoms, completely stripped from their electrons, reveal spectral lines which are narrow, symmetric, and well reproducible. We use these lines for the energy determination of transition energies in complex electronic systems, like the $\mathrm{K}{\alpha }_{1,2}$ transitions in metallic Ti, which may serve as secondary standard.

We develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.

We create weakly bound ${\mathrm{L}\mathrm{i}}_2$ molecules from a degenerate two component Fermi gas by sweeping a magnetic field across a Feshbach resonance. The atom-molecule transfer efficiency can reach $85\%$ and is studied as a function of magnetic field and initial temperature. The bosonic molecules remain trapped for 0.5 s and their temperature is within a factor of 2 from the Bose-Einstein condensation temperature. A thermodynamical model reproduces qualitatively the experimental findings.

We report on the production of a pure sample of up to $3\times {10}^5$ optically trapped molecules from a Fermi gas of ${}^6\mathrm{L}\mathrm{i}$ atoms. The dimers are formed by three-body recombination near a Feshbach resonance. For purification, a Stern-Gerlach selection technique is used that efficiently removes all trapped atoms from the atom-molecule mixture. The behavior of the purified molecular sample shows a striking dependence on the applied magnetic field. For very weakly bound molecules near the Feshbach resonance, the gas exhibits a remarkable stability with respect to collisional decay.

Using a variational ansatz for the wave function of the Bose-Einstein condensate, we develop a quantum theory of vortices and quadrupole modes in a one-dimensional optical lattice. We study the coupling between the quadrupole modes and Kelvin modes, which turns out to be formally analogous to the theory of parametric processes in quantum optics. This leads to the possibility of squeezing vortices. We solve the quantum multimode problem for the Kelvin modes and quadrupole modes numerically and find properties that cannot be explained with a simple linear-response theory.

We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-$Q$ cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.

Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry.

We study a non-Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable system with periodical driving. In the limit of a small amplitude of the external signal we derive expressions for the spectral power amplification and the signal to noise ratio as well as for the interspike interval distribution.

We discuss a proposal for the efficient generation of the maximally entangled atomic $N$-GHZ state in a spinor-1 condensate by driving internal state atomic Raman transitions using (classical) laser fields. We illustrate the dynamics in terms of a quantum Zeno subspace and identify the resultant atomic elastic collision in facilitating the deterministic entanglement creation. Our proposal can be readily implemented in several laboratories where ferromagnetic spinor condensates (of ${}^{87}\mathrm{R}\mathrm{b}$ atoms) are investigated.

We discuss the long-range nature of the molecules produced in recent experiments on molecular Bose-Einstein condensation. The properties of these molecules depend on the full two-body Hamiltonian and not just on the states of the system in the absence of interchannel couplings. The very long-range nature of the state is crucial to the efficiency of production in the experiments. Our many-body treatment of the gas accounts for the full binary physics and describes properly how these molecular condensates can be directly probed.

The discrete spectrum of the nonlinear eigenvalue problem associated to the one-dimensional Gross-Pitaevskii equation with a smooth potential is studied in the quasiclassical limit. We particularly focus on the corrections to the Bohr-Sommerfeld quantization rule for the excited energy levels due to the nonlinearity. Explicit predictions are obtained analytically for these corrections and are supported by numerical computations.

A proof of Bell’s theorem without inequalities is presented which exhibits three remarkable properties: (a) reduced local states are immune to collective decoherence; (b) distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups; (c) local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfills (a), (b), and (c).

The experimental evidence and characterization of “vibrational resonance” in a bistable vertical cavity laser are reported. The system is driven by two periodic forcings, with frequencies differing by several orders and studied in the case of both symmetrical and asymmetrical quasipotentials. The phenomenon shows up in the dynamics of the polarized laser emission as a resonance in the low-frequency response and signal-to-noise ratio, depending on the amplitude of an applied high-frequency modulation. The possibility to use the phenomenon for low-level detection is experimentally demonstrated.

We compute the force on a small neutral polarizable object moving at velocity relative to a photon gas equilibrated at a temperature . We find a drag force linear in . Its physical basis is related to that in recent formulations of the dissipative component of the Casimir force, i.e., the change in photon momentum in emission and absorption between the moving body and the stationary thermal bath. We estimate the strength of this universal drag force for different dielectric response functions and comment on its relevance in various contexts, especially to radiation-matter coupling in the cosmos.

We develop an analytically solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations, we obtain the steady-state probabilities. Generally, the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space, we find the null curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force.

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and $L$ local, in the sense of containing interaction terms involving at most $L$ bodies, for some fixed $L$. We construct quantum states $\psi$ which are “far away” from all the eigenstates $\mathbf{E}$ of any nontrivial $L$-local Hamiltonian, in the sense that $\Vert \psi -\mathbf{E}\Vert$ is greater than some constant lower bound, independent of the form of the Hamiltonian.