Ultracold collisions in tight harmonic traps: Quantum defect model and application to metastable helium atoms

Abstract

We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (GP) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schrödinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with those computed self-consistently using the generalized self-consistent method.

11 pages,REVTEX, text substantially revised, title modified

References in corpus (4)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Bose-Einstein Condensation of Metastable Helium
• Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps
• Ionization rates in a Bose-Einstein condensate of metastable Helium

Cited by in corpus (9)

• Few-body physics with ultracold atomic and molecular systems in traps
• Generalized Pseudopotentials for Higher Partial Wave Scattering
• Trap-induced resonances in controlled collisions of cesium atoms
• A quasi-Hermitian pseudopotential for higher partial wave scattering
• Spin-dipole induced lifetime of the least-bound quintet sigma state of He(2S)+He(2S)
• Ultracold atomic collisions in tight harmonic traps: Perturbation theory, ionization losses and application to metastable helium atoms
• Autoionization of spin-polarized metastable helium in tight anisotropic harmonic traps
• Ultracold homonuclear and heteronuclear collisions in metastable helium
• A model study on atom-atom interactions with large scattering length in quasi-two dimensional traps