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We give explicit connections of quantum one-hole excited states to classicalsolitons for the one-dimensional Bose gas with repulsive short-rangeinteractions. We call the quantum states connected to classical solitons thequantum soliton states. We show that the matrix element of the canonical fieldoperator between quantum soliton states with $N-1$ and $N$ particles is givenby a dark soliton of the Gross-Pitaevskii equation in the weak coupling case.We suggest that the matrix element corresponds to the order parameter of BEC inthe quantum soliton state. The result should be useful in the study ofmany-body effects in Bose-Einstein condensation and superfluids. For instance,we derive the superfluid velocity for a quantum soliton state.

Quantum dark solitons in the 1D Bose gas and the superfluid velocity