# Thermal crossover, transition, and coexistence in Fermi polaronic spectroscopies

## TL;DR

This paper studies how RF spectra of a spin-imbalanced Fermi gas evolve with temperature, revealing a transition from Fermi polarons to classical gases, with a focus on the effects of strong correlations near unitarity.

## Contribution

It introduces a self-consistent diagrammatic approach to analyze RF spectra across different temperature regimes in strongly interacting Fermi gases.

## Key findings

- Identification of a thermal crossover shifted to a sharp transition near unitarity.
- Observation of double-peak coexistence of attractive and repulsive branches in strong coupling.
- Semiquantitative agreement with recent experimental RF spectroscopy data.

## Abstract

We investigate thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using a self-consistent framework of strong-coupling diagrammatic approaches, both of the ejection and reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan {\it et al}., arXiv:1811.00481v1] and demonstrate that the RF spectroscopy is an essential probe to examine effects of strong correlations and finite temperature.