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arXiv:0909.2621 · Physical Review Letters

Quantum and Thermal Effects of Dark Solitons in a One-Dimensional Bose Gas

Andrew D. Martin, Janne Ruostekoski

Published May 12, 2010• 72 citations
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Abstract

We numerically study the imprinting and dynamics of dark solitons in a bosonic atomic gas in a tightly confined one-dimensional harmonic trap both with and without an optical lattice. Quantum and thermal fluctuations are synthesized within the truncated Wigner approximation in the quasicondensate description. We track the soliton coordinates and calculate position and velocity uncertainties. We find that the phase fluctuations lower the classically predicted soliton speed and seed instabilities. Individual runs show interactions of solitons with sound waves, splitting, and disappearing solitons.

DOI
10.1103/physrevlett.104.194102

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The motion of a dark soliton is investigated in a one-dimensional dilute Bose–Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the perturbing optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilization of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realized by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.
The motion of a dark soliton is investigated in a one-dimensional dilute Bose-Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the perturbing optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilization of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realized by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.
We discuss stochastic phase-space methods within the truncated Wigner approximation and show explicitly that they can be used to solve non-equilibrium dynamics of bosonic atoms in one-dimensional traps. We consider systems both with and without an optical lattice, and address different approximations in the stochastic synthesization of quantum statistical correlations of the initial atomic field. We also present a numerically efficient projection method for analyzing correlation functions of the simulation results, and demonstrate physical examples of non-equilibrium quantum dynamics of solitons and atom number squeezing in optical lattices.
We study, within the framework of the classical-field approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results [A. Perrin et al., Nat. Phys. 8, 195 (2012)]. We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above-mentioned experiment with the elongated system. Although the system was much larger than that studied here, we believe that the behavior of the density correlation function found there is quite generic. Our theoretical study indicates also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the presence of spontaneous dark solitons in the elongated gas at thermal equilibrium.