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Chinese Physics Letters

Stabilizations of Two-Dimensional Trapped and Untrapped Matter Waves via a Feshbach Resonance Technique

罗小兵, 海文华

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

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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 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.
We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of two-dimensional (2D) and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.
Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.
By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an optical lattice (OL) whose amplitude is subjected to periodic time modulation (the modulation frequency $\ensuremath{\omega}$ may be in the range of several kHz). Regions of stability of the solitons against the collapse and decay are identified in the space of the model's parameters. A noteworthy result is that the stability limit may reach the largest (100%) modulation depth, and the collapse threshold may exceed its classical value in the static lattice (which corresponds to the norm of Townes soliton). The minimum norm Nmin{N}_{\text{min}}Nmin​ necessary for the stability of the solitons is identified too. It features a strong dependence on $\ensuremath{\omega}$ at low frequencies, due to a resonant decay of the soliton. Predictions of the VA are reasonably close to results of the simulations. In particular, the VA helps understand salient resonant features in the shape of the stability boundaries observed with the variation of $\ensuremath{\omega}$.
We propose a novel approach to manipulate two-dimensional bright matter-wave solitons by tuning the frequency of the trap which is different from Feshbach resonance technique. The exact bright soliton solutions for two-dimensional Gross-Pitaevskii (GP) equation with attractive interaction strength in a time-dependent trap are constructed analytically and its dynamics show no collapse while modulating the trap frequency. The two-soliton dynamics exhibits an interesting splitting and recombination phenomenon which generates interference pattern in the process. This type of behaviour in two-dimensional BECs has wider ramifications and our approach opens new avenues in stabilizing bright solitons in higher dimensional regime. We have also explored the experimental realization of this novel phenomenon.