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

Abstract

The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.

arXiv comment4 pp., 2 figures, revtex4; error in Eq.(6) corrected and derivation simplified

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• Suppression and enhancement of impurity scattering in a Bose-Einstein condensate
• Many-body solitons in a one-dimensional condensate of hard core bosons
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
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• Comment on "Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons [Phys. Rev. A 79, 033610 (2009)]"
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