Highly polarized Fermi gases in two dimensions

TL;DR

This paper explores the phase diagram of highly polarized two-dimensional Fermi gases, revealing conditions for polaron, dimer, and trimer formation, and identifying a superfluid-normal transition at zero temperature.

Contribution

It provides a comprehensive variational analysis of impurity states in 2D Fermi gases, including bounds on the polaron-dimer transition and the existence of trimer states.

Findings

Trimer states exist for certain mass ratios, similar to 3D.

Finite momentum dimers suggest FFLO superfluid states.

Polaron energy matches experimental data.

Abstract

We investigate the highly polarized limit of a two-dimensional (2D) Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio M/m and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer or even larger clusters. Similarly to 3D, we find that the Fermi sea favors the trimer state so that it exists for M/m less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario which corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (M=m), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.