Coupled eigenmodes in a two-component Bose-Einstein condensate

We have studied the elementary excitations in a two-component Bose-Einstein condensate. We concentrate on the breathing modes and find the elementary excitations to possess avoided crossings and regions of coalescing oscillations where both components of the condensates oscillate with same frequency. For large repulsive interactions between the condensates, their oscillational modes tend to decouple due to decreased overlap. A thorough investigation of the eigenmodes near the avoided crossings is presented.Comment: Replacement, 17 pages, 9 figure

Entanglement of distant optomechanical systems

We theoretically investigate the possibility to generate non-classical states of optical and mechanical modes of optical cavities, distant from each other. A setup comprised of two identical cavities, each with one fixed and one movable mirror and coupled by an optical fiber, is studied in detail. We show that with such a setup there is potential to generate entanglement between the distant cavities, involving both optical and mechanical modes. The scheme is robust with respect to dissipation, and nonlocal correlations are found to exist in the steady state at finite temperatures.Comment: 12 pages (published with minor modifications

Fourier transforming a trapped Bose-Einstein condensate by waiting a quarter of the trap period: simulation and applications

We investigate the property of isotropic harmonic traps to Fourier transform a weakly interacting Bose–Einstein condensate (BEC) every quarter of a trap period. We solve the Gross–Pitaevskii equation numerically to investigate the time evolution of interacting BECs in the context of the Fourier transform, and we suggest potential applications

Excitation spectrum and instability of a two-species Bose-Einstein condensate

We numerically calculate the density profile and excitation spectrum of a two-species Bose-Einstein condensate for the parameters of recent experiments. We find that the ground state density profile of this system becomes unstable in certain parameter regimes, which leads to a phase transition to a new stable state. This state displays spontaneously broken cylindrical symmetry. This behavior is reflected in the excitation spectrum: as we approach the phase transition point, the lowest excitation frequency goes to zero, indicating the onset of instability in the density profile. Following the phase transition, this frequency rises again.Comment: 8 pages, 5 figures, uses REVTe

Boundary of two mixed Bose-Einstein condensates

The boundary of two mixed Bose-Einstein condensates interacting repulsively was considered in the case of spatial separation at zero temperature. Analytical expressions for density distribution of condensates were obtained by solving two coupled nonlinear Gross-Pitaevskii equations in cases corresponding weak and strong separation. These expressions allow to consider excitation spectrum of a particle confined in the vicinity of the boundary as well as surface waves associated with surface tension.Comment: 6 pages, 3 figures, submitted to Phys.Rev.

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

Macroscopic quantum tunneling of two-component Bose-Einstein condensates

We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.Comment: 11 pages, 10 figures, revtex

Binary Bose-Einstein Condensate Mixtures in Weakly and Strongly Segregated Phases

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a `penetration depth' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.Comment: minor change

Critical velocity in cylindrical Bose-Einstein condensates

We describe a dramatic decrease of the critical velocity in elongated cylindrical Bose-Einstein condensates which originates from the non-uniform character of the radial density profile. We discuss this mechanism with respect to recent measurements at MIT.Comment: 3 pages, 2 eps figures, revised according to referee's comment

Painlev\'{e} test of coupled Gross-Pitaevskii equations

Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied. Computer algebra is applied to evaluate j=4 compatibility condition for admissible external potentials. Appearance of an arbitrary real potential embedded in the external potentials is shown to be the consequence of the coupling. Connection with recent experiments related to stability of two-component Bose-Einstein condensates of Rb atoms is discussed.Comment: 13 pages, no figure