# Single-particle Excitations and Effects of Hetero-pairing Fluctuations in a Bose-Fermi Mixture with a Feshbach Resonance

## TL;DR

This paper theoretically explores the effects of hetero-pairing fluctuations on the single-particle excitations and spectral properties of a Bose-Fermi mixture near a Feshbach resonance, revealing unique coupling phenomena and spectral features.

## Contribution

It introduces an improved T-matrix approximation to analyze hetero-pairing fluctuations and uncovers novel spectral behaviors in a Bose-Fermi mixture at unitarity.

## Key findings

- Hetero-pairing fluctuations couple Fermi and molecular excitations.
- A pseudo-gap does not appear in the density of states at unitarity.
- A spectral peak along molecular dispersion emerges in the spectral weight.

## Abstract

We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green's function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature $T_{\rm BEC}$. In the unitary regime at $T_{\rm BEC}$, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight.We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas.