Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

Abstract

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of ${}^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schrödinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.

9 pages

References in corpus (12)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• The cold atom Hubbard toolbox
• Observation of Bose-Einstein Condensation of Molecules
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Repulsively bound atom pairs in an optical lattice
• Confinement induced molecules in a 1D Fermi gas
• Pure Gas of Optically Trapped Molecules Created from Fermionic Atoms
• Formation of Quantum-Degenerate Sodium Molecules
• Feshbach resonances in an optical lattice
• Quantum logic via optimal control in holographic dipole traps
• Resonant Feshbach scattering of fermions in one-dimensional optical lattices
• Trap-induced resonances in controlled collisions of cesium atoms

Cited by in corpus (1)

• The rotating Morse potential model for diatomic molecules in the J-matrix representation: II. The S-matrix approach