Excitations of a Bose-condensed gas in anisotropic traps

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.Comment: 7 pages Revtex, 9 Postscript figure

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.Comment: revtex, 9 pages, 5 figure

Collective excitations of a two-dimensional interacting Bose gas in anti-trap and linear external potentials

We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special form $u(x,y)=\mu -u \cosh^2 x/l$, where $\mu$ is the chemical potential. The eigenvalue problem is solved analytically for an artificial model allowing the unbounded density of the particles. The spectra of collective modes are calculated numerically for the stripe, the rare density valley and the edge geometry and compared with the analytical results. It is shown that the energies of the modes localized at the rare density region and at the edge are well approximated by the analytical expressions. We discuss Bose-Einstein condensation (BEC) in the systems under investigations at $T\ne 0$ and find that in case of a finite number of the particles the regime of BEC can be realized, whereas the condensate disappears in the thermodynamic limit.Comment: 10 pages, 2 figures include

Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.Comment: 6 pages, 3 figures small typos fixe

Elementary excitations of trapped Bose gas in the large-gas-parameter regime

We study the effect of going beyond the Gross-Pitaevskii theory on the frequencies of collective oscillations of a trapped Bose gas in the large gas parameter regime. We go beyond the Gross-Pitaevskii regime by including a higher-order term in the interatomic correlation energy. To calculate the frequencies we employ the sum-rule approach of many-body response theory coupled with a variational method for the determination of ground-state properties. We show that going beyond the Gross-Pitaevskii approximation introduces significant corrections to the collective frequencies of the compressional mode.Comment: 17 pages with 4 figures. To be published in Phys. Rev.

Generalized coherent state representation of Bose-Einstein condensates

We show that the quantum many-body state of Bose-Einstein condensates (BEC) consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state (GCS). At zero temerature, the non-condensate density and the anomalous non-condensate correlation are not independent, allowing us to elimiate one of the three variables in the TDHFB.Comment: Submitted to Phys. Rev. A. No figures. Revised version fixes several minor typos, and adds to some discussions; no change to the conclusio

Mechanical response functions of finite temperature Bose-Einstein Condensates

Using the Liouville space framework developed in nonlinear optics we calculate the linear response functions and susceptibilities of Bose-Einstein condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures of the dynamics of finite temperature BEC are obtained by solving the Hartree-Fock-Bogoliubov theory. Numerical simulations of the position dependent linear response functions of one dimensional trapped BEC in the time and the frequency domains are presented.Comment: 9 figures. Submitted to Phys. Rev.