An impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

TL;DR

This study investigates the effects of a narrow Feshbach resonance on an impurity in a Fermi sea, analyzing polaronic and dimeronic states using a variational approach and identifying phase transitions and analytical limits.

Contribution

The paper introduces a variational method limited to one particle-hole pair to analyze impurity states in a narrow Feshbach resonance, providing new phase diagrams and analytical insights.

Findings

Mapped phase diagram including stable, unstable, and complex energy regions.

Determined the closed channel population relevant for experiments.

Identified a weakly attractive limit with analytical solutions.

Abstract

We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length $R_*$ naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed channel population which is experimentally accessible. Finally we identify a non-trivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.