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SPLITTING AND RECOMBINATION OF 2D MATTER-WAVE SOLITONS IN A TRANSIENT TRAP

VR Sanal Kumar, Lin Wen, R. Radha, WM Liu

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

We propose a novel and an alternative approach to manipulate two-dimensional bright matter-wave solitons by tuning the frequency of the transient trap unlike Feshbach resonance management. The bright soliton solutions for the two-dimensional Gross-Pitaevskii (GP) equation in a time-dependent trap are constructed analytically and their dynamics shows no collapse while modulating the trap frequency. The two-soliton dynamics exhibits an interesting splitting and recombination phenomenon which generates an interference pattern in the process. This type of behavior 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.

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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.

Chinese Physics Letters•Jan 1, 2005•0 citations
We propose a novel and an alternative approach to manipulate two-dimensional bright matter-wave solitons by tuning the frequency of the transient trap unlike Feshbach resonance management. The bright soliton solutions for the two-dimensional Gross-Pitaevskii (GP) equation in a time-dependent trap are constructed analytically and their dynamics shows no collapse while modulating the trap frequency. The two-soliton dynamics exhibits an interesting splitting and recombination phenomenon which generates an interference pattern in the process. This type of behavior 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.
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.
The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose–Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross–Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.
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 present three families of one-soliton solutions for (2+1)-dimensional Gross—Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose—Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.
We present three families of one-soliton solutions for (2+l)-dimensional Gross-Pitaevskii equation withboth time-dependent scattering length and gain or loss in a harmonic trap.Then we investigate the dynamics of thesesolitons in Bose-Einstein condensates (BECs) by some selected control functions.Our results show that the intensitiesof these solitons first increase rapidly to the condensation peak,then decay very slowly to the background;thus thelifetime of a bright soliton,a train of bright solitons and a dark soliton in BECs can be all greatly extended.Our resultsoffer a useful method for observing matter-wave solitons in BECs in future experiments.
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.