Related papers: Two-species Bose-Einstein condensate in an optical…
Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions,…
In the hydrodynamic approximation we obtain analytic solutions to the Gross-Pitaevskii equation with positive scattering length which describe expansions of the Bose-Einstein condensates in quasi-one and quasi-two dimensional geometries.…
We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the…
The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analyzed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process.…
We consider stationary states of an effectively one-dimensional Bose-Einstein condensate in a quasiperiodic lattice. We formulate sufficient conditions for a one-to-one correspondence between the stationary states with a fixed chemical…
We study the behavior of a Bose-Einstein condensate held in an optical lattice. We first show how a self-trapping transition can be induced in the system by either increasing the number of atoms occupying a lattice site, or by raising the…
A simple picture describes the results of recent treatments of partially-condensed, dilute, trapped Bose gases at temperature T > 0. The condensate wavefunction is nearly identical to that of a T=0 condensate with the same number of…
We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modelled as a coupled discrete nonlinear Schr \"{o}dinger equation. The excitation spectrum and the modulational instability…
Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas…
The dynamics of a bright matter wave soliton in a quasi 1D Bose-Einstein condensate with periodically rapidly varying trap is considered. The governing equation is derived based on averaging over fast modulations of the Gross-Pitaevskii…
In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors…
We study Bose-Einstein condensate of atomic Boson gases trapped in a composite potential of a harmonic potential and an optical lattice potential. We found a series of collective excitations that induces localized vortex oscillations with a…
We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as…
We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from…
We study the nonequilibrium dynamics of a Bose-Einstein condensate which is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the…
The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose--Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the…
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their…
The internal one-particle density matrix is discussed for Bose-Einstein condensates with finite number of particles in a harmonic trap. The outcome of the digonalization of the density matrix depends on the choice of the internal…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODE) for dynamics of one and two individual vortices in the rotating BECs with those of the partial…