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.

arXiv comment39 pages, 10 figures; Restored overall phase factor in Eq. (66), references added

References in corpus (37)

• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations
• On the Numerical Evaluation of Fredholm Determinants
• Normal state of highly polarized Fermi gases: simple many-body approaches
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Quantum dynamics of ultracold Bose polarons
• Tan relations in one dimension
• Bloch oscillations in the absence of a lattice
• Form factor approach to dynamical correlation functions in critical models
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Radio frequency spectroscopy of polarons in ultracold Bose gases
• Quantum flutter of supersonic particles in one-dimensional quantum liquids
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Quantum Flutter: Signatures and Robustness
• Exact calculation of spectral properties of a particle interacting with a one dimensional fermionic system
• Polaronic mass renormalization of impurities in BEC: correlated Gaussian wavefunction approach
• Momentum relaxation of a mobile impurity in a one-dimensional quantum gas
• Highly polarized Fermi gases: One-dimensional case
• Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Impurity Green's function of a one-dimensional Fermi-gas
• Temperature correlators in the two-component one-dimensional gas
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
• Dissipative correlated dynamics of a moving impurity immersed in a Bose-Einstein Condensate
• Energy and contact of the one-dimensional Fermi polaron at zero and finite temperature
• Mean-field construction for spectrum of one-dimensional Bose polaron
• Spin-charge separation in a strongly correlated spin-polarized chain
• Quantum Boltzmann equation for a mobile impurity in a degenerate Tonks-Girardeau gas
• Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant
• Microscopic approach to a class of 1D quantum critical models
• Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• From hardcore Bosons to free Fermions with Painlev{é} V

Cited by in corpus (18)

• Quantum speed limit for thermal states
• Emergence of a sharp quantum collective mode in a one-dimensional Fermi polaron
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• 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
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
• Efficient variational approach to the Fermi polaron problem in two dimensions, both in and out of equilibrium
• Testing eigenstate decoherence hypothesis in a model of collisional decoherence
• Quench dynamics and quantum flutter properties of one-dimensional attractive single-spin flipped Fermi gases
• Impurity in a zero-temperature three-dimensional Fermi gas