Quantum theory of bright matter-wave solitons in harmonic confinement

David I. H. Holdaway, Christoph Weiss, and Simon A. Gardiner
Phys. Rev. A 85, 053618 – Published 15 May 2012

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.

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  • Received 27 March 2012

DOI:https://doi.org/10.1103/PhysRevA.85.053618

©2012 American Physical Society

Authors & Affiliations

David I. H. Holdaway*, Christoph Weiss, and Simon A. Gardiner

  • Department of Physics, Durham University, Durham DH1 3LE, United Kingdom

  • *d.i.h.holdaway@dur.ac.uk

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Vol. 85, Iss. 5 — May 2012

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