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Title: Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes

Abstract

We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size.more » We investigate numerically two strong singularities of the momentum distribution for fermions at k {sub f} and k {sub f} + 2k {sub b}. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature {approx}E {sub f}/{gamma} << E {sub f}, where E {sub f} = ({pi}hn){sup 2}/(2m), n is the total density and {gamma} = mg/(h {sup 2} n) >> 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures.« less

Authors:
 [1];  [1]
  1. Department of Physics, Harvard University, Cambridge, MA 02138 (United States)
Publication Date:
OSTI Identifier:
20845931
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 321; Journal Issue: 10; Other Information: DOI: 10.1016/j.aop.2005.11.017; PII: S0003-4916(05)00268-X; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSE-EINSTEIN GAS; BOSONS; BOUNDARY CONDITIONS; COLLECTIVE MODEL; CORRELATION FUNCTIONS; EXACT SOLUTIONS; FERMI GAS; FERMI INTERACTIONS; FERMIONS; FOURIER TRANSFORMATION; GROUND STATES; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; POLYNOMIALS; SINGULARITY; TEMPERATURE DEPENDENCE; TIME-OF-FLIGHT METHOD; WAVE FUNCTIONS

Citation Formats

Imambekov, Adilet, and Demler, Eugene. Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes. United States: N. p., 2006. Web. doi:10.1016/j.aop.2005.11.017.
Imambekov, Adilet, & Demler, Eugene. Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes. United States. https://doi.org/10.1016/j.aop.2005.11.017
Imambekov, Adilet, and Demler, Eugene. Sun . "Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes". United States. https://doi.org/10.1016/j.aop.2005.11.017.
@article{osti_20845931,
title = {Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes},
author = {Imambekov, Adilet and Demler, Eugene},
abstractNote = {We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size. We investigate numerically two strong singularities of the momentum distribution for fermions at k {sub f} and k {sub f} + 2k {sub b}. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature {approx}E {sub f}/{gamma} << E {sub f}, where E {sub f} = ({pi}hn){sup 2}/(2m), n is the total density and {gamma} = mg/(h {sup 2} n) >> 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures.},
doi = {10.1016/j.aop.2005.11.017},
url = {https://www.osti.gov/biblio/20845931}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 10,
volume = 321,
place = {United States},
year = {2006},
month = {10}
}