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Title: Correlation Functions of the One-Dimensional Attractive Bose Gas

Abstract

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the Moessbauer effect.

Authors:
 [1];  [2]
  1. Dipartimento di Fisica dell'Universita di Pisa and INFN, Pisa (Italy)
  2. Institute for Theoretical Physics, Universiteit van Amsterdam, 1018 XE Amsterdam (Netherlands)
Publication Date:
OSTI Identifier:
20951224
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevLett.98.150403; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN GAS; CORRELATION FUNCTIONS; DELTA FUNCTION; INTERACTIONS; MOESSBAUER EFFECT; ONE-DIMENSIONAL CALCULATIONS

Citation Formats

Calabrese, Pasquale, and Caux, Jean-Sebastien. Correlation Functions of the One-Dimensional Attractive Bose Gas. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.150403.
Calabrese, Pasquale, & Caux, Jean-Sebastien. Correlation Functions of the One-Dimensional Attractive Bose Gas. United States. doi:10.1103/PHYSREVLETT.98.150403.
Calabrese, Pasquale, and Caux, Jean-Sebastien. Fri . "Correlation Functions of the One-Dimensional Attractive Bose Gas". United States. doi:10.1103/PHYSREVLETT.98.150403.
@article{osti_20951224,
title = {Correlation Functions of the One-Dimensional Attractive Bose Gas},
author = {Calabrese, Pasquale and Caux, Jean-Sebastien},
abstractNote = {The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the Moessbauer effect.},
doi = {10.1103/PHYSREVLETT.98.150403},
journal = {Physical Review Letters},
number = 15,
volume = 98,
place = {United States},
year = {Fri Apr 13 00:00:00 EDT 2007},
month = {Fri Apr 13 00:00:00 EDT 2007}
}
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  • The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.
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  • 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 andmore » 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.« less