UC Riverside

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two-dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak interspecies interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by the on-site interspecies interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge-density wave instability in the two-leg ladder after the renormalization-group transformation. Parametrizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system. © 2013 American Physical Society.