David I. H. Holdaway, Christoph Weiss, Simon A. Gardiner
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 wavefunction and use this to create a variational technique based on energy minimization of this wavefunction 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.
View original:
http://arxiv.org/abs/1203.6006
No comments:
Post a Comment