94 research outputs found
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
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