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Quantum theory of bright matter-wave solitons in harmonic confinement

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

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D.I.H. Holdaway

C. Weiss


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.


Holdaway, D., Weiss, C., & Gardiner, S. (2012). Quantum theory of bright matter-wave solitons in harmonic confinement. Physical Review A, 85(5), Article 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
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 85
Issue 5
Article Number 053618


Published Journal Article (681 Kb)

Copyright Statement
© 2012 American Physical Society

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