Abstract
We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark soliton significantly depends on whether its phase kink is located at a lattice site or a link of two neighboring sites. It has also shown that the dark soliton is unstable in a regime of strong quantum fluctuations regardless of the phase-kink position. To bridge the gap between the classical and strongly quantum regimes, we investigate the dynamical stability of the dark soliton in a regime of weak quantum fluctuations. We find that the position dependence of the dynamical stability gradually diminishes and eventually vanishes as the strength of quantum fluctuations increases. This classical-to-quantum crossover of the soliton stability remains even in the presence of a parabolic trapping potential. We suggest that the crossover behavior can be used for experimentally diagnosing whether the instability of a dark soliton is due to quantum fluctuations or classical dynamical instability.
Highlights
Solitons are robust nonlinear waves, which are localized and collide elastically with one another like particles
To bridge the gap between the classical and strongly quantum regimes, we investigate the dynamical stability of the dark soliton in a regime of weak quantum fluctuations
We study the dynamical stability of the dark soliton of a 1D lattice Bose gas in a regime of weak quantum fluctuations
Summary
Solitons are robust nonlinear waves, which are localized and collide elastically with one another like particles. Soliton solutions in classical systems are described as analytical solutions of integrable nonlinear equations, including the Korteweg–de Vries equation [1], the sine-Gordon equation [2], and nonlinear Schrödinger equations [3]. Experiments with ultracold atoms are suited for studying dynamical processes of BECs in an ideal situation because the system is well isolated from environment and the relaxation time is sufficiently longer than the typical timescale of interesting dynamical phenomena. Taking these advantages, previous experiments have extensively investigated dynamical properties of solitons in atomic BECs [5,6,7,8,9,10].
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