Vortex oscillations in confined Bose-Einstein condensate interacting with 1D optical lattice

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 characteristic wavelength. The oscillations might be observed experimentally when radial confinement is tight. We present the excitation spectra of the vortex oscillation modes and propose a way to experimentally excite the modes.Comment: 5 pages, 7 figures. Title, abstract and references are update

Stability of small amplitude normal modes of a Bose-Einstein condensate with a singly quantized vortex confined in an optical lattice

We study the dynamics of a BEC with a singly quantized vortex, placed in the combined potential of a 1-D (2-D) optical lattice and an axi-symmetric harmonic trap. A time-dependent variational Lagrangian analysis shows that an optical lattice helps to stabilize the vortex which in absence of the optical lattice is unstable. We find that the normal modes are stable only if the depth of the optical potential is more than a certain critical value. This critical value of the optical potential depends on the interaction parameter.In general higher the interaction parameter,lower the value of the optical potential required to stabilize the vortex. The BEC with the singly quantized vortex is found to be relatively more unstable in a 2-D optical lattice compared to a 1-D optical lattice.Comment: Revised version with 11 pages including 1 figur

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.Comment: 10 pages, 1 figure. Published versio

Analysis of an atom laser based on the spatial control of the scattering length

In this paper we analyze atom lasers based on the spatial modulation of the scattering length of a Bose-Einstein Condensate. We demonstrate, through numerical simulations and approximate analytical methods, the controllable emission of matter-wave bursts and study the dependence of the process on the spatial dependence of the scattering length along the axis of emission. We also study the role of an additional modulation of the scattering length in time.Comment: Submitted to Phys. Rev.

Small deviations of iterated processes in space of trajectories

We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different

Bose-Einstein condensation in shallow traps

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 introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure

The validity of the Landau-Zener model for output coupling of Bose condensates

We investigate the validity of the Landau-Zener model in describing the output coupling of Bose condensates from magnetic traps by a chirped radiofrequency field. The predictions of the model are compared with the numerical solutions of the Gross-Pitaevskii equation. We find a dependence on the chirp direction, and also quantify the role of gravitation.Comment: 4 pages, Late

Probing dipolar effects with condensate shape oscillation

We discuss the low energy shape oscillations of a magnetic trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g. as for $^{85}$Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley {\it et al.}, Nature {\bf 412}, 295 (2001)].Comment: revised version, submitte

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp