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

Journal Article · Sat Dec 15 04:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.063620· OSTI ID:21140692

Sykes, Andrew G; Drummond, Peter D; Davis, Matthew J ^[1]

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1. ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072 (Australia)

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 [Thacker, Rev. Mod. Phys. 53, 253 (1981)] 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.

• OSTI ID: 21140692
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSE-EINSTEIN GAS
BOSONS
BOUND STATE
COMPARATIVE EVALUATIONS
EXACT SOLUTIONS
EXCITATION
EXCITED STATES
HAMILTONIANS
INTERACTING BOSON MODEL
MANY-BODY PROBLEM
MEAN-FIELD THEORY
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARTICLES
PHASE TRANSFORMATIONS
STRONG INTERACTIONS
TEMPERATURE RANGE 0000-0013 K
WAVE FUNCTIONS
WAVEGUIDES