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Physics of Wave Phenomena

Scattering of two-dimensional dark quasi-solitons by smooth inhomogeneities in a Bose-Einstein condensate

V. A. Mironov, Lev A. Smirnov

Published Jan 1, 2013• 4 citations
Publisher

Abstract

It is theoretically shown that creation of artificial inhomogeneities allows one to control dynamics of two-dimensional dark quasi-solitons in a Bose-Einstein condensate. A method to calculate trajectories of these quasi-solitons is proposed. It allows control parameters to be selected for the potentials responsible for formation of the Bose gas density distributions required for the scattering through the given angle.

DOI
10.3103/s1541308x13010123

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It is theoretically shown that creation of artificial inhomogeneities allows one to control dynamics of two-dimensional dark quasi-solitons in a Bose-Einstein condensate. A method to calculate trajectories of these quasi-solitons is proposed. It allows control parameters to be selected for the potentials responsible for formation of the Bose gas density distributions required for the scattering through the given angle.
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Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.
We investigate dark-bright vector solitary wave solutions to the coupled nonlinear Schrödinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in nonlinear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effect of controllably different interparticle scattering lengths is examined, and stability against three-dimensional deformations is considered.
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We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a ΛΛΛ-coupled three-level system. Numerical simulations of the corresponding two-component system reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. However, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in, which happens after a few tens of milliseconds after the quench of the optical fields.