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Chinese Physics Letters

Bogoliubov Quasiparticles Carried by Dark Solitonic Excitations in Nonuniform Bose-Einstein Condensates

Tao Hong, Yuzhu Wang, Yunsheng Huo

Published Aug 1, 1998• 31 citations
Publisher

Abstract

We consider the noncondensate part of the Bose gas in presence of dark solitons. We get a stationary equation of Bogoliubov quasiparticles and find that these Bogoliubov quasiparticles are confined by a dark soliton and carried to propagate with it. This model of the compound structure of the soliton and Bogoliubov quasiparticles provides more precise description of localized sound excitations in Bose-Einstein condensates.

DOI
10.1088/0256-307x/15/8/002

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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 develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg--de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.
We consider a dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing an expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals a good agreement even if the strength of disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on the quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of disorder. The Anderson-localized soliton may decay due to quasiparticle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than the condensate lifetime in a typical experiment.
Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large-amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.
Quantum fluctuations of coupled dark solitons in a trapped BosendashndashndashEinstein condensate