Quasi-one- and quasi-two-dimensional Bose-Fermi mixtures from weak coupling to unitarity

TL;DR

This paper develops and validates reduced-dimensional models for ultracold Bose-Fermi mixtures across the weak-coupling to unitarity crossover, incorporating beyond-mean-field effects, and compares these models with full 3D numerical solutions.

Contribution

It introduces simplified quasi-1D and quasi-2D models for Bose-Fermi mixtures that include beyond-mean-field interactions and validates them against full 3D simulations.

Findings

Reduced models accurately reproduce 3D ground states.

Models incorporate Lee-Huang-Yang interactions and unitarity effects.

Validation confirms applicability in various confinement regimes.

Abstract

We study ultracold superfluid Bose-Fermi mixtures in three dimensions, with stronger confinement along one or two directions, using a non-perturbative beyond-mean-field model for bulk chemical potential valid along the weak-coupling to unitarity crossover. Although bosons are considered to be in a superfluid state, we consider two possibilities for the fermions -- spin-polarized degenerate state and superfluid state. Simplified reduced analytic lower-dimensional models are derived along the weak-coupling to unitarity crossover in quasi-one-dimensional (quasi-1D) and quasi-two-dimensional (quasi-2D) settings. The only parameters in these models are the constants of the beyond-mean-field Bose-Bose and Fermi-Fermi Lee-Huang-Yang interactions and the respective universal Bertsch parameter at unitarity. In addition to the numerical results for a fully-trapped system, we also present results for quasi-2D Bose-Fermi mixtures where one of the components is untrapped but localized due to the interaction mediated by the other component. We demonstrate the validity of the reduced quasi-1D and quasi-2D models via a comparison of the numerical solutions for the ground states obtained from the reduced models and the full three-dimensional (3D) model.