Soliton response to transient trap variations

The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schrodinger stationary state solution in time can be effectively combined with the solutions of non-linear Schrodinger equation, for obtaining solutions of the Gross-Pitaevskii equation with time dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios

Mermin-Ho vortex in ferromagnetic spinor Bose-Einstein condensates

The Mermin-Ho and Anderson-Toulouse coreless non-singular vortices are demonstrated to be thermodynamically stable in ferromagnetic spinor Bose-Einstein condensates with the hyperfine state F=1. The phase diagram is established in a plane of the rotation drive vs the total magnetization by comparing the energies for other competing non-axis-symmetric or singular vortices. Their stability is also checked by evaluating collective modes.Comment: 4 pages, 4 figure

Bose-Einstein condensates with attractive interactions on a ring

Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme are used to attack the problem.Comment: 4 pages, 4 ps figures, RevTex, typographic errors correcte

Dimensional and Temperature Crossover in Trapped Bose Gases

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.Comment: One figure added, typos corrected, refernces adde

Effectively attractive Bose-Einstein condensates in a rotating toroidal trap

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.Comment: 4 pages, 4 ps figures, RevTe

In-situ velocity imaging of ultracold atoms using slow--light

The optical response of a moving medium suitably driven into a slow-light propagation regime strongly depends on its velocity. This effect can be used to devise a novel scheme for imaging ultraslow velocity fields. The scheme turns out to be particularly amenable to study in-situ the dynamics of collective and topological excitations of a trapped Bose-Einstein condensate. We illustrate the advantages of using slow-light imaging specifically for sloshing oscillations and bent vortices in a stirred condensate

Kinetic Theory of Collective Excitations and Damping in Bose-Einstein Condensed Gases

We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schr\"odinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In this manner we take into account both collisions between noncondensate-noncondensate and condensate-noncondensate atoms. We solve the linear response of these equations, using a time-dependent gaussian trial function for the condensate wave function and a truncated power expansion for the deviation function of the thermal cloud. As a result, our calculation turns out to be characterized by two dimensionless parameters proportional to the noncondensate-noncondensate and condensate-noncondensate mean collision times. We find in general quite good agreement with experiment, both for the frequencies and damping of the collective modes.Comment: 10 pages, 8 figure

't Hooft-Polyakov Monopoles in an Antiferromagnetic Bose-Einstein Condensate

We show that an antiferromagnetic spin-1 Bose-Einstein condensate, which can for instance be created with Na-23 atoms in an optical trap, has not only singular line-like vortex excitations, but also allows for singular point-like topological excitations, i.e., 't Hooft-Polyakov monopoles. We discuss the static and dynamic properties ofthese monopoles.Comment: Four pages of ReVTeX and 1 postscript figur

Extension of Bogoliubov theory to quasi-condensates

We present an extension of the well-known Bogoliubov theory to treat low dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretisation in cells of size $l$. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two and three dimensions with no ultraviolet or infrared divergence. Furthermore this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, the first order and second order correlations functions of the field. Explicit calculations are done for homogeneous systems.Comment: 32 pages, 2 figures; typos corrected in revised versio