Pseudopotential model of ultracold atomic collisions in quasi-one- and two-dimensional traps

We describe a model for s-wave collisions between ground-state atoms in optical lattices, considering especially the limits of quasi-one- and two-dimensional axisymmetric harmonic confinement. When the atomic interactions are modeled by an s-wave Fermi pseudopotential, the relative motion energy eigenvalues can easily be obtained. The results show that except for a bound state, the trap eigenvalues are consistent with one- and two-dimensional scattering with renormalized scattering amplitudes. For absolute scattering lengths large compared with the tightest trap width, our model predicts a bound state of low energy and nearly-isotropic wave function extending on the order of the tightest trap width.