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arXiv:1408.3312 · Physical Review A

Fate of a gray soliton in a quenched Bose-Einstein condensate

Oleksandr Gamayun, Yulia V. Bezvershenko, Vadim Cheianov

Published Mar 25, 2015• 21 citations
arXivHTMLPDF

Abstract

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the nonlinearity parameter. The outcome of the quench is found to depend dramatically on the ratio $\ensuremath{\eta}$ of the final and initial values of the speed of sound. For integer $\ensuremath{\eta}$ the soliton splits into exactly $2\ensuremath{\eta}\ensuremath{-}1$ solitons. For noninteger $\ensuremath{\eta}$ the soliton decays into multiple solitons and Bogoliubov modes. The case of integer $\ensuremath{\eta}$ is analyzed in detail. The parameters of solitons in the out state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for similar quenches in any classical integrable system.

DOI
10.1103/physreva.91.031605

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We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the nonlinearity parameter. The outcome of the quench is found to depend dramatically on the ratio \ensuremathη\ensuremath{\eta}\ensuremathη of the final and initial values of the speed of sound. For integer \ensuremathη\ensuremath{\eta}\ensuremathη the soliton splits into exactly 2\ensuremathη\ensuremath−12\ensuremath{\eta}\ensuremath{-}12\ensuremathη\ensuremath−1 solitons. For noninteger \ensuremathη\ensuremath{\eta}\ensuremathη the soliton decays into multiple solitons and Bogoliubov modes. The case of integer \ensuremathη\ensuremath{\eta}\ensuremathη is analyzed in detail. The parameters of solitons in the out state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for similar quenches in any classical integrable system.
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The excitations of a two-dimensional (2D) Bose-Einstein condensate in the presence of a soliton are studied by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. The excitation spectrum is found to contain states which are localized near the soliton and have a dispersion law similar to the one of the stable branch of transverse oscillations of a 1D gray soliton in a 2D condensate. By using the stabilization method we show that these localized excitations behave as resonant states coupled to the continuum of free excitations of the condensate.
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We investigate the dynamics of pulses in a cigar-shaped Bose-Einstein condensate with repulsive atom-atom interactions without using Thomas-Fermi approximation. In the linear level our results give the Bogoliubov excitation spectrum for sound propagation with speed c = c 0 /(2) 1/2 , where c 0 is the speed for the case without a trap. We develop a Korteweg-de Vries (KdV) description for dark soliton propagation in the system and show that it is the quantum pressure that contributes the dispersion necessary for the formation of the dark solitons.
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.