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arXiv:1001.3385 · New Journal of Physics

Nonequilibrium quantum dynamics of atomic dark solitons

Andrew D. Martin, Janne Ruostekoski

Published May 28, 2010• 43 citations
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Abstract

We study quantum dynamics of bosonic atoms that are excited to form a phase kink, or several kinks, by an imprinting potential in a one-dimensional trap. We calculate dissipation due to quantum and thermal fluctuations in soliton trajectories, collisions and the core structure. Single-shot runs show weak filling of a soliton core, typically deeper solitons in the case of stronger fluctuations and spreading/disappearing solitons due to collisions. We also analyze a soliton system in an optical lattice that shows especially strong fluctuation-induced phenomena.

DOI
10.1088/1367-2630/12/5/055018

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We study quantum dynamics of bosonic atoms that are excited to form a phase kink, or several kinks, by an imprinting potential in a one-dimensional trap. We calculate dissipation due to quantum and thermal fluctuations in soliton trajectories, collisions and the core structure. Single-shot runs show weak filling of a soliton core, typically deeper solitons in the case of stronger fluctuations and spreading/disappearing solitons due to collisions. We also analyze a soliton system in an optical lattice that shows especially strong fluctuation-induced phenomena.
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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.
Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of noninteracting fermions but the wave functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.
Mean-field dynamics of strongly interacting bosons described by hard-core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii type (GP type) where the condensate fraction remains dark, and a non-Gross-Pitaevskii type (non-GP type) characterized by brightening of the condensate fraction. Here we study the effects of quantum fluctuations on these solitons using the adaptive time-dependent density matrix renormalization group method, which takes into account the effect of strong correlations. We use local observables as the density, condensate density, and correlation functions as well as the entanglement entropy to characterize the stability of the initial states. We find both species of solitons to be stable under quantum evolution for a finite duration, their tolerance to quantum fluctuations being enhanced as the width of the soliton increases. We describe possible experimental realizations in atomic Bose-Einstein condensates, polarized degenerate Fermi gases, and in systems of polar molecules on optical lattices.