We show that a purely s-wave interaction in three dimensions (3D) can induce
higher partial-wave resonances in mixed dimensions. We develop two-body
scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and
determine the positions of higher partial-wave resonances in terms of the 3D
s-wave scattering length assuming a harmonic confinement potential. We also
compute the low-energy scattering parameters in the p-wave channel (scattering
volume and effective momentum) that are necessary for the low-energy effective
theory of the p-wave resonance. We point out that some of the resonances
observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)]
can be interpreted as the p-wave resonances in the 2D-3D mixed dimensions. Our
study paves the way for a variety of physics, such as Anderson localization of
matter waves under p-wave resonant scatterers.Comment: 19 pages, 8 figures; published versio
