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

Journal Article · Sun Oct 15 00:00:00 EDT 2006 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2005.11.017· OSTI ID:20845931

Imambekov, Adilet ^[1]; Demler, Eugene ^[1]

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1. Department of Physics, Harvard University, Cambridge, MA 02138 (United States)

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.

• OSTI ID: 20845931
• Journal Information: Annals of Physics (New York), Vol. 321, 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); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

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