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Chinese Physics Letters

The Interference Effect of a Bose—Einstein Condensate in a Ring-Shaped Trap

Li-Juan Cao, Shujuan Liu, Baolong Lü

Published May 1, 2012• 4 citations
Publisher

Abstract

We have studied the interference effect of a Bose—Einstein condensate expanding in a ring-shaped trap. The dynamic process of the condensate is analyzed based on the Gross—Pitaevskii equation. Our numerical results show that a petal-like interference pattern is formed during expansion within the ring-shaped trap. The petal number depends on the evolution time, which can be well explained by the interference of two flows of the condensate.

DOI
10.1088/0256-307x/29/5/050305

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We have studied the interference effect of a Bose—Einstein condensate expanding in a ring-shaped trap. The dynamic process of the condensate is analyzed based on the Gross—Pitaevskii equation. Our numerical results show that a petal-like interference pattern is formed during expansion within the ring-shaped trap. The petal number depends on the evolution time, which can be well explained by the interference of two flows of the condensate.
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We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.
In this paper, we derive equations for the dynamics of ring dark solitons in an expanding cloud of a two-dimensional Bose-Einstein condensate. Assuming that the soliton's width is much smaller than its radius, we obtain the Hamilton equations for its evolution. Then they are transformed into the Newton equation, which is more convenient for applications. The general theory is illustrated by the solution of the Newton equation for the case of the axially symmetric condensate cloud, which expands after switching off a harmonic trap. The validity of our approximate analytical approach is confirmed by comparison with the results of numerical simulations of the Gross-Pitaevskii equation.
This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied the dynamics of a BEC after release from a toroidal trap potential by solving the three-dimensional Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated by imprinting a linear azimuthal phase on the initial condensate wave function. The simulated TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring-shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.