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

Abstract

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. Different effective interactions and novel correlated quantum many-body phases may be engineered in these systems, with the different phases being tunable via external parameters. 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 inter-species interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by to the on-site inter-species 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. Parameterizing 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.

Unconventional superconducting phases for the two-dimensional extended Hubbard model on a square lattice

“…Another possible way to manifest a mediated attraction is through another species of fermions in a Fermi-Fermi atom mixture. 44 By introducing an interspecies interaction in Fermi-Fermi mixtures, an effective interaction for one species of fermions can be obtained by tracing out the other species. This can be justified, for example, if one of the species has a much smaller effective mass than the other.…”

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

“…We also note that a 3 He - 4 He solution provides effectively mixed-dimensional Fermi gases [28]. Theoretical works on mixed-dimensional systems predict phenomena such as Efimov effects [29,30], mediated pairing [31][32][33][34][35], or a topological superfluid [36,37].…”

“…A further increase of the 2D filling leads to spin-triplet pairing (TS) and then eventually the mediated interaction becomes too weak. We consider the TS region to be reminiscent of the d-wave pairing in a two-leg ladder with mediated interactions [32].…”