Interaction beween polarons and analogous effects in polarized Fermi gases

TL;DR

This paper investigates the interactions between polarons in strongly interacting imbalanced ultracold Fermi gases, revealing additional interaction terms beyond the non-interacting approximation and comparing results with Monte-Carlo simulations.

Contribution

It introduces and calculates interaction terms between polarons proportional to x^2 and x^{7/3}, extending the polaron energy expansion in polarized Fermi gases.

Findings

Interaction terms due to polaron cloud overlap and energy modification are identified.

At unitarity, the dominant interaction term disagrees with Monte-Carlo results.

The study provides insights into polaron interactions across different interaction strengths.

Abstract

We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density $x=n\ds /n\us$ is usually considered as a gas of non interacting polarons. This allows to calculate, in the expansion of the total energy of the system in powers of $x$, the terms proportional to $x$ (corresponding to the binding energy of the polaron) and to $x^{5/3}$ (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to $x^2$ and $x^{7/3}$. We find three such terms. A first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the non-zero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte-Carlo results. The possible origins of this discrepancy are discussed.