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

TL;DR

This paper explores how mixed-dimensional fermionic cold atom systems can be used to manipulate quantum phases in a two-leg ladder, revealing tunable long-range interactions and phase transitions driven by experimental parameters.

Contribution

It introduces a method to control quantum phases in a two-leg ladder via mediated interactions from a two-dimensional gas in a mixed-dimensional cold atom setup.

Findings

Mediated interactions can be tuned by the 2D gas density.

Enhanced charge density wave instability observed.

Phase diagram parameterized by experimental controls.

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.