We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultracold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement.

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Nonequilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, such as two-dimensional incompressible fluids and wave-particle interaction in a plasma.

We find two types of moving dark soliton textures in elongated condensates: nonstationary kinks and proper dark solitons. The latter have a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.

We have studied the dynamics of large vortex lattices in a dilute-gas Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal structure, large-amplitude quadrupolar shape oscillations of the condensate are shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an $m=-2$ mode, we observe shifting of lattice planes, changes of lattice structure, and sheetlike structures in which individual vortices appear to have merged. Excitation of an $m=+2$ mode dissolves the regular lattice, leading to randomly arranged but still strictly parallel vortex lines.

Three apparently unrelated problems which have no solution using classical tools are described: the “$N$-strangers,” “secret sharing,” and “liar detection” problems. A solution for each of them is proposed. Common to all three solutions is the use of quantum states of total spin zero of $N$ spin-$(N-1)/2$ particles.

We propose the use of a combined optical dipole trap to achieve Fermi degeneracy by sympathetic cooling with a different bosonic species. Two far-detuned pairs of laser beams focused on the atomic clouds are used to confine the two atomic species with different trapping strengths. We show that a deep Fermi degeneracy regime can be potentially achieved earlier than Bose-Einstein condensation, as discussed in the favorable situation of a ${}^{\mathrm{6}}\mathrm{L}\mathrm{i}–{}^{\mathrm{23}}\mathrm{N}\mathrm{a}$ mixture. This opens up the possibility of experimentally investigating a mixture of superfluid Fermi and normal Bose gases.

We present a simple criterion based on the Einstein relation for determining whether diffusion in systems governed by a generalized Langevin equation with long-range memory is normal, superdiffusive, or subdiffusive. We support our analysis with numerical simulations.

We relate the entropies of ensembles of atoms in optical lattices to atoms in simple traps. We then determine which ensembles of lattice-bound atoms will adiabatically transform into a Bose condensate. This shows a feasible approach to Bose condensation without evaporative cooling.

We study spontaneous directionality in the bosonic amplification of atom pairs emitted from an elongated Bose-Einstein condensate, an effect analogous to superradiant emission of atom-photon pairs. Using a simplified model, we make analytic predictions regarding directional effects for both atom-atom and atom-photon emission. These are confirmed by numerical mean-field simulations, demonstrating the feasibility of nearly perfect directional emission along the condensate axis. The dependence of the emission angle on the pump strength for atom-atom pairs is significantly different than for atom-photon pairs.

We present the first spatially resolved images of spin waves in a gas. The complete longitudinal and transverse spin field as a function of time and space is reconstructed. Frequencies and damping rates for a standing-wave mode are extracted and compared with theory.

We introduce a variant of the asymmetric random average process with continuous state variables where the maximal mass transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a pure high flow phase and a mixed phase, whereby the latter consists of a homogeneous high flow and a condensed low flow substate without translation invariance. The finite system alternates between these substates which both have diverging lifetimes in the thermodynamic limit, so ergodicity is broken in the infinite system. However, the scaling behavior of the lifetimes in dependence of the system size is different due to different underlying flipping mechanisms.

In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.

The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.

We construct Greenberger-Horne-Zeilinger (GHZ) contradictions for three or more parties sharing an entangled state, the dimension of each subsystem being an even integer $d$. The simplest example that goes beyond the standard GHZ paradox (three qubits) involves five ququats ($d=4$). We then examine the criteria that a GHZ paradox must satisfy in order to be genuinely $M$ partite and $d$ dimensional.

Phase transitions create a domain structure with defects, which has been argued by Zurek and Kibble (ZK) to depend in a characteristic way on the quench rate. We present an experiment to measure the ZK scaling exponent $\sigma$. Using long symmetric Josephson tunnel junctions, for which the predicted index is $\sigma =0.25$, we find $\sigma =0.27\pm 0.05$. Further, we agree with the ZK prediction for the overall normalization.

We report on the specific features of the sign problem in the classical auxiliary field methodology and the strategies employed for its alleviation. In particular, we focus on a new technique based on the method of Gaussian equivalent representation of Efimov and Nogovitsin [Physica (Amsterdam) 234A, 506 (1996)] with which we could ameliorate the convergence properties significantly. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach.

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here, one does not have a partition function; instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first- and the second-order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

We present a calculation of a solitary wave propagating along a cylindrical Bose-Einstein trap. For sufficiently strong couplings of experimental interest, it is found to be a hybrid of a one-dimensional (1D) soliton and a three-dimensional vortex ring. The calculated energy-momentum dispersion exhibits characteristics similar to those of a mode proposed sometime ago by Lieb within a 1D model, as well as some rotonlike features.

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long-wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving at certain speeds, the dot can extract a desired number of atoms from the condensate through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.