The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal tes...

In the first part of this article we briefly overview the fundamentals of Bose-Einstein condensation and survey a series of results concerning the effective equations which describe the dynamics of elongated and oblate Bose-Einstein condensates. In the second part of the paper we show how one can construct effective oneand two-dimensional polynomial Schrödinger equations which describe the long...

A set of exact closed-form Bloch-state solutions to the stationary GrossPitaevskii equation are obtained for a Bose-Einstein condensate in a one-dimensional periodic array of quantum wells, i.e. a square-well periodic potential. We use these exact solutions to comprehensively study the Bloch band, the compressibility, effective mass and the speed of sound as functions of both the potential dept...

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover...

The past decade has seen marked advances in cooling techniques, making possible the realization of Bose-Einstein condensates and degenerate Fermi gases, most notably in the alkali gases. In this paper we review the properties of these systems and the experimental techniques which have made them possible. We then discuss the recent use of a Feshbach resonance in Fermi systems, which allows one t...

The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed ...

We study pion condensation and the phase structure in a two-flavor Nambu-Jona-Lasinio model in the presence of baryon chemical potential μ and isospin chemical potential μI at zero and finite temperature. There is a competition between the chiral condensate and a Bose-Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin ch...

We report the creation of a Bose-Einstein condensate using buffer-gas cooling, the first realization of BEC using a broadly general method which relies neither on laser cooling nor unique atom-surface properties. Metastable helium (He*) is buffer-gas cooled, magnetically trapped, and evaporatively cooled to quantum degeneracy. 10 atoms are initially trapped, leading to Bose-Einstein condensatio...

We report the formation of Bose-Einstein condensates into nonequilibrium states. Our condensates are much longer than equilibrium condensates with the same number of atoms, show strong phase fluctuations, and have a dynamical evolution similar to that of quadrupole shape oscillations of regular condensates. The condensates emerge in elongated traps as the result of local thermalization when the...

We present the random phase approximation (RPA) theory of the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to ...