Confinement-Induced Resonances in Ultracold Atom-Ion Systems

We investigate confinement-induced resonances in a system composed by a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region -- from the "long-wavelength" limit to the opposite case when the typical length scale of the atom-ion polarisation potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the "long-wavelength and zero-energy" limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semi-analytic formula for the resonance position in the "long-wavelength and zero-energy" limit and we investigate numerically how the position of the resonance is affected by a finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi one dimensional atomic quantum gas.