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Title: Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices

Abstract

We propose a Pfaffian-like ansatz for the ground state of bosons subject to three-body infinite repulsive interactions in a one-dimensional (1D) lattice. Our ansatz consists of symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized. Our findings may open the way for the creation of non-Abelian anyons in 1D systems.

Authors:
 [1];  [2]; ;  [3]
  1. Institut fuer Physik, Johannes Gutenberg-Universitaet, Staudingerweg 7, D-55099 Mainz (Germany)
  2. (Germany)
  3. Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Strasse 1, Garching, D-85748 (Germany)
Publication Date:
OSTI Identifier:
20982571
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.053611; (c) 2007 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; ANYONS; ATOMS; BOSONS; GASES; GROUND STATES; INTERACTIONS; MOLECULES; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS; THREE-BODY PROBLEM

Citation Formats

Paredes, B., Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Strasse 1, Garching, D-85748, Keilmann, T., and Cirac, J. I. Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.053611.
Paredes, B., Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Strasse 1, Garching, D-85748, Keilmann, T., & Cirac, J. I. Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices. United States. doi:10.1103/PHYSREVA.75.053611.
Paredes, B., Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Strasse 1, Garching, D-85748, Keilmann, T., and Cirac, J. I. Tue . "Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices". United States. doi:10.1103/PHYSREVA.75.053611.
@article{osti_20982571,
title = {Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices},
author = {Paredes, B. and Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Strasse 1, Garching, D-85748 and Keilmann, T. and Cirac, J. I.},
abstractNote = {We propose a Pfaffian-like ansatz for the ground state of bosons subject to three-body infinite repulsive interactions in a one-dimensional (1D) lattice. Our ansatz consists of symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized. Our findings may open the way for the creation of non-Abelian anyons in 1D systems.},
doi = {10.1103/PHYSREVA.75.053611},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.
  • We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Ourmore » results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.« less
  • The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.
  • With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one-dimensional periodic potential. The analysis of these ground states shows that when the number of bosons N is commensurate with the number of wells M in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when N is not commensurate with M, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in termsmore » of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.« less
  • Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation {lambda}{sub {eta}} of the natural orbitals for large-{eta} at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.