Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps

We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional (1D) trapping potentials, allowing for two different atom species. As a consequence, the centre-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.