Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time

TL;DR

This paper uses the functional renormalization group to analyze a mobile impurity in a Fermi sea, calculating ground state energies, Tan's contact, and quasiparticle properties, including spectral functions, across the polaron-molecule transition.

Contribution

It introduces a real-time method to go beyond derivative expansion, providing detailed quasiparticle properties and effects of mass imbalance in the impurity problem.

Findings

Calculated ground state energy and Tan's contact across the transition

Obtained spectral functions, effective mass, and quasiparticle weight

Clarified the impact of mass imbalance on impurity quasiparticles

Abstract

Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polaron, the effective mass and quasiparticle weight of attractive and repulsive polarons, and clarify how they are affected by mass imbalances.