Quantum dark solitons in the one-dimensional Bose gas

Dark and gray soliton-like states are shown to emerge from numerically constructed superpositions of translationally invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a density depression with ballistic spreading that is absent in classical solitons. A simple theory based on finite-size bound states of holes with quantum-mechanical center-of-mass motion quantitatively explains the time-evolution and predicts quantum effects that could be observed in ultracold gas experiments. The soliton phase step is found relevant for explaining finite-size effects in numerical simulations. An invariant fundamental soliton width is shown to deviate from the Gross-Pitaevskii predictions in the interacting regime and vanishes in the Tonks-Girardeau limit.