Bose-Einstein condensation has been achieved in a magnetic surface microtrap with $4\times {10}^5{}^{87}\mathrm{Rb}$ atoms. The strongly anisotropic trapping potential is generated by a microstructure which consists of microfabricated linear copper conductor of widths ranging from 3 to $30\mu \mathrm{m}$. After loading a high number of atoms from a pulsed thermal source directly into a magneto-optical trap the magnetically stored atoms are transferred into the microtrap by adiabatic transformation of the trapping potential. In the microtrap the atoms are cooled to condensation using forced rf-evaporation. The complete in vacuo trap design is compatible with ultrahigh vacuum below $2\times {10}^{-11\mathrm{}}\mathrm{mbar}$.

We study the relation between distillability of multipartite states and violation of Bell’s inequality. We prove that there exist multipartite bound entangled states (i.e., nonseparable, nondistillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell’s inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.

The interaction of an electron with a polar molecule is shown to be the simplest realization of a quantum anomaly in a physical system. The existence of a critical dipole moment for electron capture and formation of anions, which has been confirmed experimentally and numerically, is derived. This phenomenon is a manifestation of the anomaly associated with quantum symmetry breaking of the classical scale invariance exhibited by the point-dipole interaction. Finally, analysis of symmetry breaking for this system is implemented within two different models: point dipole subject to an anomaly and finite dipole subject to explicit symmetry breaking.

Classical heat engines produce work by operating between a high temperature energy source and a low temperature entropy sink. The present quantum heat engine has no cooler reservoir acting as a sink of entropy but has instead an internal reservoir of negentropy which allows extraction of work from one thermal bath. The process is attended by constantly increasing entropy and does not violate the second law of thermodynamics.

The Dirac equation for a charged particle in a static electromagnetic field is written for the special case of a spherically symmetric potential. Besides the well-known Dirac-Coulomb and Dirac-oscillator potentials, we obtain a relativistic version of the $S$-wave Morse potential. This is accomplished by adding a simple exponential potential term to the Dirac operator, which in the nonrelativistic limit reproduces the usual Morse potential. The relativistic bound-states spectrum and spinor wave functions are obtained.

We propose a method to study the time evolution of Bose-Einstein condensed gases perturbed from an initial thermal equilibrium, based on the Wigner representation of the $N$-body density operator. We show how to generate a collection of random classical fields sampling the initial Wigner distribution in the number conserving Bogoliubov approximation. The fields are then evolved with the time dependent Gross-Pitaevskii equation. We illustrate the method with the damping of a collective excitation of a one-dimensional Bose gas.

Collapse, or a gravitational-like phase transition, is found in microcanonical ensembles of particles with an attractive ${1/r}^{\alpha }$ potential not only for $\alpha =1\mathrm{}$ but for all $0<\mathrm{}\alpha <3\mathrm{}$. The phase behavior of the system is complex: If an effective sufficiently short-range cutoff is applied, the density of the collapsed phase is finite everywhere; if not, the collapse results in a density singularity. Also, with increasing effective cutoff range, the gravitational phase transition will cross over to a normal first-order phase transition.

We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.

We have developed an evaporative cooling technique that accelerates the rotation of an ultracold ${}_{}{}^{87}{}_{}{}^{}R\mathrm{b}$ gas, confined in a static harmonic potential. As a normal gas is evaporatively spun up and cooled below quantum degeneracy, it is found to nucleate vorticity in a Bose-Einstein condensate. Measurements of the condensate’s aspect ratio and surface-wave excitations are consistent with effective rigid-body rotation. Rotation rates of up to $94\%$ of the centrifugal limit are inferred. A threshold in the normal cloud’s rotation is observed for the intrinsic nucleation of the first vortex. The threshold value lies below the prediction for a nucleation mechanism involving the excitation of surface waves of the condensate.

A number-conserving hybrid Bose-Fermi variational theory is developed and applied to investigation of the Bose-Einstein condensate crossover to the Tonks gas in toroidal and long cylindrical traps of high aspect ratio, where strong many-body correlations and condensate depletion occur.

The properties of a rotating Bose-Einstein condensate confined in a prolate cylindrically symmetric trap are explored both analytically and numerically. As the rotation frequency increases, an ever greater number of vortices are energetically favored. Though the cloud anisotropy and moment of inertia approach those of a classical fluid at high frequencies, the observed vortex density is consistently lower than the solid-body estimate. Furthermore, the vortices are found to arrange themselves in highly regular triangular arrays, with little distortion even near the condensate surface. These results are shown to be a direct consequence of the inhomogeneous confining potential.

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the nonlinear Schrödinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.

The quantum and thermal fluctuations of the phase are investigated in a cold Bose gas confined by a double well trap. The coherence of the system is discussed in terms of the visibility of interference fringes in both momentum and coordinate space. The visibility is calculated at zero as well as at finite temperature. The thermal fluctuations are shown to affect significantly the transition from the coherent to the incoherent regime even at very low temperatures. The coherence of an array of multiple condensates is also discussed.

A simple, approximate boost rule is derived for two spinless particles that is sufficient to keep the mass invariant and to relate interactions, vertex functions, wave functions, and $t$ matrices of the instantaneous two-body problem in an arbitrary frame to those in the c.m. frame. The boost generator $\mathbf{K}$ that is used provides a solution to the Poincaré algebra except for the commutator between two components of $\mathbf{K}$, for which it provides an approximate solution.

We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics. These systems generalize the way in which ordinary Langevin equations underlie ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.

We measure the angular divergence of a quasicontinuous, rf-outcoupled, free-falling atom laser as a function of the outcoupling frequency. The data are compared to a Gaussian-beam model of laser propagation that generalizes the standard formalism of photonic lasers. Our treatment includes diffraction, magnetic lensing, and interaction between the atom laser and the condensate. We find that the dominant source of divergence is the condensate-laser interaction.

Collisional avalanches are identified to be responsible for an 8-fold increase of the initial loss rate of a large ${}^{87}\mathrm{Rb}$ condensate. We show that the collisional opacity of an ultracold gas exhibits a critical value. When exceeded, losses due to inelastic collisions are substantially enhanced. Under these circumstances, reaching the hydrodynamic regime in conventional Bose-Einstein condensation experiments is highly questionable.

We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear completely positive maps on density matrices is derived from the following assumptions: (1) physical states are described by rays in a Hilbert space, (2) probabilities for measurement outcomes at any given time are calculated according to the usual trace rule, and (3) superluminal communication is excluded. This result also constrains possible nonlinear modifications of quantum physics.

We propose a direct, coherent coupling scheme that can create massively entangled states of Bose-Einstein condensed atoms. Our idea is based on an effective interaction between two atoms from coherent Raman processes through a (two atom) molecular intermediate state. We compare our scheme with other recent proposals for the generation of massive entanglement of Bose condensed atoms.