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We study quantum dynamics of a dark soliton in a one-dimensional Bose gas inan optical lattice within the truncated Wigner approximation. A previous workhas revealed that in the absence of quantum fluctuations, dynamical stabilityof the dark soliton significantly depends on whether its phase kink is locatedat a lattice site or a link of two neighboring sites. It has also shown thatthe dark soliton is unstable in a regime of strong quantum fluctuationsregardless of the phase-kink position. To bridge the gap between the classicaland strongly quantum regimes, we investigate the dynamical stability of thedark soliton in a regime of weak quantum fluctuations. We find that theposition dependence of the dynamical stability gradually diminishes andeventually vanishes as the strength of quantum fluctuations increases. Thisclassical-to-quantum crossover of the soliton stability remains even in thepresence of a parabolic trapping potential. We suggest that the crossoverbehavior can be used for experimentally diagnosing whether the instability of adark soliton is due to quantum fluctuations or classical dynamical instability.

Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice