Confinement-induced resonance from the generalized Gross-Pitaevskii equations

Abstract

The confinement-induced resonances for trapped bosons in the cigar-shaped and pancake geometries are studied within the generalized Gross-Pitaevskii equations, which are a simplified version of the Hartree-Fock-Bogoliubov approximation. Although the Hartree-Fock-Bogoliubov method is considered applicable only for small interparticle interactions, the resonance denominators for the chemical potential are obtained in both quasi-one and quasi-two dimensions. A useful integral representation of the one-particle Green's function are found for the cylindrical confinement. We find the position of a smoothed resonance for the chemical potential in the pancake geometry at positive scattering length.

9 pages, 1 figure

References in corpus (9)

• Quantum depletion of a homogeneous Bose-Einstein condensate
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Suppression of Quantum Scattering in Strongly Confined Systems
• Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
• Effective-range description of a Bose gas under strong one- or two-dimensional confinement
• Confinement-induced resonance in quasi-one-dimensional systems under transversely anisotropic confinement
• Reactive collisions in confined geometries
• Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
• Two ultracold atoms in a completely anisotropic trap