Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

Abstract

We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas $\delta$-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

39 pages, 10 figures; Restored overall phase factor in Eq. (66), references added

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Cited by in corpus (17)

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• Emergence of a sharp quantum collective mode in a one-dimensional Fermi polaron
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• Nature of polaron-molecule transition in Fermi polarons
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Mobile impurities interacting with a few one-dimensional lattice bosons
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Mobile impurity in a one-dimensional gas at finite temperatures
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• Local spectral density of an interacting one-dimensional Bose gas with an impurity
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• Efficient variational approach to the Fermi polaron problem in two dimensions, both in and out of equilibrium
• Impurity in a zero-temperature three-dimensional Fermi gas
• Testing eigenstate decoherence hypothesis in a model of collisional decoherence