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Journal of Tsinghua University(Science and Technology)

Collective oscillations of a Bose-Einstein condensate stimulated by growth

Lixian Liu

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The collective oscillations of the trapped Bose Einstein Condensate (BEC) are studied using the computational model of the Gross Pitaevskii Equation, the nonlinear Schroedinger equation describing the BEC dynamics. Typical examples of the 3 dimensional BEC for both spherical and axial symmetry showed that the collective BEC oscillations can be stimulated by its growth. A frequency analysis of the oscillations is presented. The numerical simulation showed that the collective BEC oscillations are damped by the interaction of the BEC and the noncondensate Bose gas at a nonzero temperature.

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The collective oscillations of the trapped Bose Einstein Condensate (BEC) are studied using the computational model of the Gross Pitaevskii Equation, the nonlinear Schroedinger equation describing the BEC dynamics. Typical examples of the 3 dimensional BEC for both spherical and axial symmetry showed that the collective BEC oscillations can be stimulated by its growth. A frequency analysis of the oscillations is presented. The numerical simulation showed that the collective BEC oscillations are damped by the interaction of the BEC and the noncondensate Bose gas at a nonzero temperature.
We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized Gross-Pitaevskii equation, which is coupled to a thermal cloud modeled by a Monte Carlo algorithm. This allows us to include the collective dynamics of both the condensed and noncondensed components self-consistently. We simulate quadrupolar excitations, and measure the damping rate and frequency as a function of temperature. We also observe revivals in condensate oscillations at high temperatures, and in the thermal cloud at low temperature. Extensions of the model to include nonequilibrium effects and describe more complex phenomena are discussed.
Using the explicit numerical solution of the axially symmetric Gross–Pitaevskii equation, we study the oscillation of the Bose–Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a . When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC.
Using the explicit numerical solution of the axially symmetric Gross–Pitaevskii equation, we study the oscillation of the Bose–Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a. When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC. 1.
We analytically and numerically study nonlinear dynamics in Bose–Einstein condensates (BECs) induced either by a harmonic modulation of the interaction or by the geometry of the trapping potential. To analytically describe BEC dynamics, we use a perturbative expansion based on the Poincaré–Lindstedt analysis of a Gaussian variational ansatz, whereas in the numerical approach we use numerical solutions of both a variational system of equations and the full time-dependent Gross–Pitaevskii equation. The harmonic modulation of the atomic s-wave scattering length of a BEC of 7 Li was achieved recently via Feshbach resonance, and such a modulation leads to a number of nonlinear effects, which we describe within our approach: mode coupling, higher harmonics generation and significant shifts in the frequencies of collective modes. In addition to the strength of atomic interactions, the geometry of the trapping potential is another key factor for the dynamics of the condensate, as well as for its collective modes. The asymmetry of the confining potential leads to important nonlinear effects, including resonances in the frequencies of collective modes of the condensate. We study in detail such geometric resonances and derive explicit analytic results for frequency shifts for the case of an axially symmetric condensate with two- and three-body interactions. Analytically obtained results are verified by extensive numerical simulations.
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