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Title

Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

Author(s)

Sykes, Andrew G.;  Drummond, P. D.;  Davis, Matthew J.

Abstract

The exactly solvable Lieb-Liniger model of interacting bosons in one dimension has attracted renewed interest as current experiments with ultracold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to 20 particles for attractive interactions. We discuss the features of the solutions, and how they deviate from the well-known string solutions at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive one-dimensional Bose gas on a ring.

Publication type

Journal article

Source

Physical Review A, Vol. 76, no. 6 (2007), article no. 063620

Publication year

2007

FOR Code(s)

0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics;  0204 Condensed Matter Physics;  0205 Optical Physics

Keyword(s)

Bethe ansatz solution;  Boson systems;  Bound states;  Circular waveguides;  Excitation energy;  Excitation spectrum;  Excited states;  Finite densities;  Hamiltonians;  Many-body problems;  One dimensional;  Phase transformations;  Phase transitions;  Quantum theory;  Wave functions

Publisher

American Physical Society

ISSN

1050-2947

Publisher URL

http://dx.doi.org/10.1103/PhysRevA.76.063620

Copyright

Copyright © 2007 The American Physical Society. Published version of this paper reproduced here in accordance with the copyright policy of the publisher.

Full text

Peer reviewed