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Chinese Physics

The stability of Bose–Einstein condensates in a two-dimensional shallow trap

Zhou Xiao-Yan, Mu Ai-Xia, Xue Ju-Kui

Published Nov 1, 2007• 4 citations
Publisher

Abstract

The stability of Bose–Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.

DOI
10.1088/1009-1963/16/11/009

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The stability of Bose–Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.
Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity) we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially-screened radially-symmetric harmonic potential well in two and three dimensions. We also consider an axially-symmetric configuration with zero axial trap and a exponentially-screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillation of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.
We have studied the dynamics of two-dimensional (2D) trapped and untrapped Bose–Einstein condensates (BECs) with a rapid periodic modulation of the scattering length via a Feshbach resonance technique, a → a 0 + a 1 sin (Ω t ) with an attractive (negative) mean value and the large constants a 0 , a 1 and Ω. Applying a variation approximation (VA), the critical threshold for the collapse of the 2D trapped vortex BEC is predicted and the collapse is prevented by causing the scattering length oscillating rapidly. On the other hand, with analytical calculation, we prove that the stabilization of a bright soliton in a 2D untrapped BEC is impossible for enough large interaction intensity and the upper limit of the intensity for the soliton stabilization is derived.
The stability of the ground state of two-component Bose–Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross–Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.
We have studied the dynamics of two-dimensional (2D) trapped and untrapped Bose-Einstein condensates (BECs)with a rapid periodic modulation of the scattering length via a Feshbach resonance technique, α→α0 +α1 sin(Ωt)with an attractive (negative) mean value and the large constants α0, α1 and Ω. Applying a variation approximation(VA), the critical threshold for the collapse of the 2D trapped vortex BEC is predicted and the collapse is prevented by causing the scattering length oscillating rapidly. On the other hand, with analytical calculation, we prove that the stabilization of a bright soliton in a 2D untrapped BEC is impossible for enough large interaction intensity and the upper limit of the intensity for the soliton stabilization is derived.
We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear equations of motion for the widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. We conduct both linear and nonlinear stability analyses for the equations of motion and find qualitative agreement, thus concluding that the stability of two equilibrium widths of a BEC might be inverted by parametric excitation.