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Physical Review E

Taming rogue waves in vector Bose-Einstein condensates

P. S. Vinayagam, Ramaswamy Radha, Kuppuswamy Porsezian

Published Oct 11, 2013• 50 citations
Publisher

Abstract

Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons.

DOI
10.1103/physreve.88.042906

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Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons.
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We consider two coupled Gross—Pitaevskii equations describing a two-component Bose—Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.
We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.
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.
We investigate bright, dark and two rogue waves in two-component Bose—Einstein condensates. It is found that one rogue wave of a new structure that contains two humps and two valleys around one center in the temporal-spatial distribution interacts with the conventional rogue wave. We present an effective way to obtain long-lived rogue waves through managing the nonlinear interaction with modulating trapping frequency and interchange atoms between thermal clouds and condensates. The results provide many possibilities to manipulate rogue waves experimentally in the condensate system.