Quantum theory of bright matter-wave solitons in harmonic confinement

Holdaway, D.I.H.; Weiss, C.; Gardiner, S.A.

Abstract

This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.

Citation

Holdaway, D., Weiss, C., & Gardiner, S. (2012). Quantum theory of bright matter-wave solitons in harmonic confinement. Physical Review A, 85(5), Article 053618. https://doi.org/10.1103/physreva.85.053618

• Journal Article Type: Article
• Publication Date: May 15, 2012
• Deposit Date: May 21, 2012
• Publicly Available Date: Feb 5, 2014
• Journal: Physical Review A - Atomic, Molecular, and Optical Physics
• Print ISSN: 1050-2947
• Electronic ISSN: 1094-1622
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Issue: 5
• Article Number: 053618
• DOI: https://doi.org/10.1103/physreva.85.053618
• Public URL: https://durham-repository.worktribe.com/output/1475809