We extend our recent work on the two-fluid hydrodynamics of a Bose-condensed gas by including collisions involving both condensate and noncondensate atoms. These collisions are essential for establishing a state of local thermodynamic equilibrium between the condensate and noncondensate. Our theory is more general than the usual Landau two-fluid theory, to which it reduces in the appropriate limit, in that it allows one to describe situations in which a state of complete local equilibrium between the two components has not been reached. The exchange of atoms between the condensate and noncondensate is associated with a new relaxational mode of the gas.

We study the nature of the phase transition of the $q$-state Potts model with long-range ferromagnetic interactions decaying as $1/r^{d+\sigma }$, in dimension $d=1\mathrm{}$, using a histogram Monte Carlo (MC) technique. The model can exhibit a first-order transition or a second-order phase transition with nonstandard critical exponents. The critical value of $q$ above which a first-order transition occurs decreases with decreasing $\sigma$, from $q_c=8\mathrm{}$ for $\sigma =1\mathrm{}$ to $q_c=2\mathrm{}$ for $\sigma =0.3\mathrm{}$. Detailed results for various $\sigma$ will be shown and discussed. Mean-field calculation confirms the tendency of our MC results.

Optical excitations in a Bose gas are demonstrated to be sensitive to many-body effects. At low temperature the momentum relaxation is provided by momentum exchange collisions, rather than by elastic collisions. A collective excitation mode forms, which in a nondegenerate gas is manifest in a collision shift and dramatic narrowing of spectral lines. In the Bose-Einstein condensate state, each spectral line splits into two components. The doubling of the optical excitations results from the physics analogous to that of the second sound. We present a theory of the line doubling, and calculate optical absorption spectrum for a uniform density system.

We investigate decoherence in the limit where the interaction with the environment is weak and the evolution is dominated by the self-Hamiltonian of the system. We show that in this case quantized eigenstates of energy emerge as pointer states selected through the predictability sieve.

We study the flow of a weakly interacting Bose-Einstein condensate around an obstacle by numerical solution of the Gross-Pitaevskii equation. We observe vortex emission and the formation of bow waves leading to pressure drag. We compare the drag law with that of an ideal Bose gas, and show that interactions reduce the drag force. This reduction can be explained in terms of a “collisional screening” of the obstacle.

The de Broglie–Bohm causual (hydrodynamic) formulation of quantum mechanics is computationally implemented in the Lagrangian (moving with the fluid) viewpoint. The quantum potential and force are accurately evaluated with a moving weighted least squares algorithm. The quantum trajectory method is then applied to barrier tunneling on smooth potential surfaces. Analysis of the tunneling mechanism leads to a novel and accurate approximation: shortly after the wave packet is launched, completely neglect all quantum terms in the dynamical equations for motion along the tunneling coordinate.

Both in atomic and in mesoscopic physics it is interesting to consider the energy time dependence of a parametrically driven chaotic system. We assume an Hamiltonian $H(Q,P;x(t\left)\right)$ where $x\left(t\right)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy spreading is studied. Dissipation is the associated irreversible growth of the average energy. It is found that a dimensionless velocity $v_{\mathrm{PR}}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence. A perturbative regime and a nonperturbative semiclassical regime are distinguished.

Vortex states of weakly interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.

We have performed a pure optical frequency measurement of the $2S-12D$ two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, $R_{\infty }=109\mathrm{}737.31568516\left(84\right){\mathrm{cm}}^{-1\mathrm{}}$ (relative uncertainty of $7.7\times {10}^{-12\mathrm{}}$) and for the $1S$ and $2S$ Lamb shifts $L_{1S}=8172.837\mathrm{}\left(22\right)\mathrm{MHz}$ and $L_{2S-2P}=1057.8446\mathrm{}\left(29\right)\mathrm{MHz}$ [respectively, $L_{1S}=8183.966\mathrm{}\left(22\right)\mathrm{MHz}$, and $L_{2S-2P}=1059.2337\mathrm{}\left(29\right)\mathrm{MHz}$ for deuterium]. These are now the most accurate values available.

In Ramsey atomic interferometry, a superposition of atomic states is produced by a mechanism completely equivalent (for experimental purposes) to interaction with a classical field. Since this property holds, in the case of Rydberg atoms, for temperatures close to absolute zero and field intensities of the order of a single photon, the question arises as to why the quantum nature of the field can be neglected. We model the passage of an atom through a Ramsey zone and show that, in order to explain the phenomenon, correlation properties between three subsystems and strong cavity dissipation turn out to be the essential physical ingredients leading to classical behavior.

We study propagation of light in a Fermi-Dirac gas. We analytically obtain the leading density correction to the optical linewidth at zero temperature. This correction is a direct consequence of the quantum statistical correlations of atomic positions that modify the optical interactions between the atoms at small interatomic separations. The gas exhibits a dramatic line narrowing already at very low densities.

We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy. The algorithm—which is as simple as variational Monte Carlo—for bosons provides exact expectation values of local observables, as well as their static and dynamic (in imaginary time) response functions, without mixed-estimate nor population-control biases. Our method is demonstrated with a few case applications to ${}^4\mathrm{He}$.

We show that in second-order phase transformations that are induced by an inhomogeneous quench the density of topological defects is drastically suppressed as the velocity with which the quench propagates falls below a threshold velocity. This threshold is approximately given by the ratio of the healing length to relaxation time at freeze-out, which is the instant when the critical slowing down results in a transition from the adiabatic to the impulse behavior of the order parameter.

Properties of a Bose-Einstein condensate were studied by stimulated, two-photon Bragg scattering. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum uncertainty of the condensate. The coherence length of the condensate was shown to be equal to its size. Bragg spectroscopy can be used to determine the dynamic structure factor over a wide range of energy and momentum transfers.

We introduce an open-loop control scheme for stochastic resonators; the scheme permits the enhancement or suppression of the spectral response to threshold-crossing events triggered by a time-periodic signal in background noise. The control is demonstrated in experiments using a Schmitt trigger. A generic two-state theory captures the essential features observed in our experiments and in numerical simulations; this suggests the generality of the effect.

We investigate the thermodynamic stability of quantized vortices in a dilute Bose gas confined by a rotating harmonic trap at finite temperature. Interatomic forces play a crucial role in characterizing the resulting phase diagram, especially in the large $N$ Thomas-Fermi regime. We show that the critical temperature for the creation of stable vortices exhibits a maximum as a function of the frequency of the rotating trap, and that the corresponding transition is associated with a discontinuity in the number of atoms in the condensate. Possible strategies for approaching the vortical region are discussed.

We consider the role of weak interatomic interactions on the fluctuations of the number of condensed atoms within canonical and microcanonical ensembles. Unlike the corresponding case of the ideal gas this is not a clean, well-defined problem of mathematical physics. Two related reasons are the following: there is no unique way of defining the condensate fraction of the interacting system and no exact energy levels of the interacting system are known.

The Casimir force between an aluminum-coated plate with small sinusoidal corrugations and a large sphere was measured for surface separations between 0.1 and 0.9 μm using an atomic force microscope. The measured force shows significant deviation from the perturbative theory. The measured Casimir force between the same sphere and flat plate shows good agreement with the same theory in the limit of zero amplitude of corrugation. These together demonstrate the nontrivial boundary dependence of the Casimir force.

In this Letter we present a novel quantum Monte Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $\exp (-\beta \hat{H})$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.

We argue that the phase transition in the mean-field $\mathrm{XY}$ model is related to a particular change in the topology of its configuration space. The nature of this topological change can be discussed on the basis of elementary Morse theory using the potential energy per particle $V$ as a Morse function. The value of $V$ where such a topological change occurs equals the thermodynamic value of $V$ at the phase transition and the number of (Morse) critical points grows very fast with the number of particles $N$. Furthermore, as in statistical mechanics, the way the thermodynamic limit is taken is crucial in topology.