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The recent realization of mixed-dimensional systems of cold atoms hasattracted much attention from both experimentalists and theorists. Differenteffective interactions and novel correlated quantum many-body phases may beengineered in these systems, with the different phases being tunable viaexternal parameters. In this article we investigate a two-species Fermi atommixture: one species of atom exists in two hyperfine states and is confined tomove in a two-leg ladder, interacting with an on-site interaction, and theother moves freely in a two dimensional square lattice that contains thetwo-leg ladder. The two species of atoms interact via an on-site interaction onthe ladder. In the limit of weak inter-species interactions, thetwo-dimensional gas can be integrated out, leading to an effective long-rangemediated interaction in the ladder, generated by to the on-site inter-speciesinteraction. We show that the form of the mediated interaction can becontrolled by the density of the two-dimensional gas and that it enhances thecharge density wave instability in the two-leg ladder after the renormalizationgroup transformation. Parameterizing the phase diagram with variousexperimentally controllable quantities, we discuss the possible tuning of themacroscopic quantum many-body phases of the two-leg ladder in thismixed-dimensional fermionic cold atom system.

Possible quantum phase-manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms