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arXiv:1108.2330

Controlled Split-Recombination of 2D Matter-Wave Solitons in Time-Dependent Trap

Vaduganathan Ramesh Kumar, Lin Wen, R. Radha, W. M. Liu

Published Aug 11, 2011• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1108.2330

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•Jan 1, 2021•0 citations
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.
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 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 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.
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.
Using the Feshbach resonance (FR) one can change a scattering length of two-body interactions and thus affect nonlinear dynamics of excitations in a Bose-Einstein condensate. The phenomenon is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity. In this work we discuss the effect of variation of the nonlinearity on excitations in a BEC placed in an optical lattice. More specifically, we describe reductions of a three-dimensional (3D) GP equation to a 1D perturbed nonlinear Schrödinger (NLS) equation for different relations among parameters; discuss periodic solutions of the NLS equation; carry out numerical study of the dynamics of the NLS equation with a periodic and parabolic trap potentials. Special attention is paid to the process of generation of trains of bright and dark matter solitons from initially periodic waves.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.