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Title: Dynamic response of one-dimensional bosons in a trap

Abstract

We calculate the dynamic structure factor S(q,{omega}) of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the (1D) motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation in the gas density around the trap center leads to softening of the singular behavior of S(q,{omega}) at the first Lieb excitation mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response S(q,{omega}) remains a nonanalytic function of q and {omega} at the first Lieb excitation mode in the limit of weak trap confinement. The exponent of the power-law nonanalyticity is modified due to the inhomogeneity in a universal way and thus bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semicircular peak in S(q,{omega}) centered at the on-site repulsion energy, {omega}=U. Similar peaks of smaller amplitudes exist at multiples of U as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recentlymore » by Clement et al. [Phys. Rev. Lett. 102, 155301 (2009)], based on an f-sum rule for the Bose-Hubbard model.« less

Authors:
 [1];  [2];  [3]
  1. Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universitaet, 80333 Munich (Germany)
  2. Laboratoire de Physique et de Modelisation des Milieux Condenses, C.N.R.S., Universite Joseph Fourier, BP 166, 38042 Grenoble (France)
  3. Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)
Publication Date:
OSTI Identifier:
21316448
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 80; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.80.043611; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BOSE-EINSTEIN GAS; BOSONS; EXCITATION; INTERACTIONS; ONE-DIMENSIONAL CALCULATIONS; STRUCTURE FACTORS; SUM RULES; TRAPS

Citation Formats

Golovach, Vitaly N., Minguzzi, Anna, and Glazman, Leonid I.. Dynamic response of one-dimensional bosons in a trap. United States: N. p., 2009. Web. doi:10.1103/PHYSREVA.80.043611.
Golovach, Vitaly N., Minguzzi, Anna, & Glazman, Leonid I.. Dynamic response of one-dimensional bosons in a trap. United States. doi:10.1103/PHYSREVA.80.043611.
Golovach, Vitaly N., Minguzzi, Anna, and Glazman, Leonid I.. 2009. "Dynamic response of one-dimensional bosons in a trap". United States. doi:10.1103/PHYSREVA.80.043611.
@article{osti_21316448,
title = {Dynamic response of one-dimensional bosons in a trap},
author = {Golovach, Vitaly N. and Minguzzi, Anna and Glazman, Leonid I.},
abstractNote = {We calculate the dynamic structure factor S(q,{omega}) of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the (1D) motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation in the gas density around the trap center leads to softening of the singular behavior of S(q,{omega}) at the first Lieb excitation mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response S(q,{omega}) remains a nonanalytic function of q and {omega} at the first Lieb excitation mode in the limit of weak trap confinement. The exponent of the power-law nonanalyticity is modified due to the inhomogeneity in a universal way and thus bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semicircular peak in S(q,{omega}) centered at the on-site repulsion energy, {omega}=U. Similar peaks of smaller amplitudes exist at multiples of U as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recently by Clement et al. [Phys. Rev. Lett. 102, 155301 (2009)], based on an f-sum rule for the Bose-Hubbard model.},
doi = {10.1103/PHYSREVA.80.043611},
journal = {Physical Review. A},
number = 4,
volume = 80,
place = {United States},
year = 2009,
month =
}
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