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The low-lying eigenstates of a one-dimensional (1D) system of manyimpenetrable point bosons and one moving impurity particle with repulsivezero-range impurity-boson interaction are found for all values of theimpurity-boson mass ratio and coupling constant. The moving entity is apolaron-like composite object consisting of the impurity clothed by a co-movinggray soliton. The special case with impurity-boson interaction of pointhard-core form and impurity-boson mass ratio $m_i/m$ unity is first solvedexactly as a special case of a previous Fermi-Bose (FB) mapping treatment ofsoluble 1D Bose-Fermi mixture problems. Then a more general treatment is givenusing second quantization for the bosons and the second-quantized form of theFB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pinescanonical transformation. This yields the exact solution for arbitrary $m_i/m$and impurity-boson interaction strength.

Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons