Photon-assisted confinement-induced resonances for ultracold atoms

We solve the two-particle s-wave scattering for an ultracold atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included in terms of Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. We use the Floquet approach to show that additional photon-assisted resonant scattering channels open up due to the harmonic modulation. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Schr\"odinger equation which is universal at low energies. The binding energies and the effective one-dimensional scattering length can be controlled by the external driving.