Phase Equilibrium of Binary Mixtures in Mixed Dimensions

TL;DR

This paper investigates the phase behavior of a mixed-dimensional Bose-Fermi system in coupled 1D tubes, revealing that the nature of phase transitions depends on interspecies interactions and fermion mobility, with implications for experimental systems.

Contribution

It provides an exact analysis of phase transitions in mixed-dimensional Bose-Fermi systems using Bethe ansatz, highlighting the conditions for first or second order transitions.

Findings

Transitions between pure fermion and finite boson density phases are always first order.

The transition from pure boson to mixed phase can be second or first order depending on fermion hopping.

Results have implications for experiments with 174Yb-6Li and other mixed-dimensional atomic systems.

Abstract

We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) "tubes", where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the 174Yb-6Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on 174Yb-6Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed dimensional optical lattice system.