# Local Photoemission Spectra and Effects of Spatial Inhomogeneity in the BCS-BEC Crossover Regime of a Trapped Ultracold Fermi Gas

## TL;DR

This paper theoretically analyzes local photoemission spectra in a trapped ultracold Fermi gas across the BCS-BEC crossover, comparing with experiments and discussing implications for understanding pseudogap phenomena and quantum simulation.

## Contribution

It introduces a theoretical framework incorporating strong pairing fluctuations and trap effects to interpret local photoemission spectra in ultracold Fermi gases.

## Key findings

- Theoretical results agree with recent JILA experiments under current conditions.
- Current spectroscopy methods have limitations in detecting the pseudogap.
- Results aid in applying trapped gases as quantum simulators for homogeneous systems.

## Abstract

We theoretically investigate single particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-Condensation) crossover regime of an ultracold Fermi gas. Including strong pairing fluctuations within a $T$-matrix approximation, as well as effects of a harmonic trap potential in the local density approximation, we calculate the local photoemission spectrum in the normal state. Recently, JILA group has measured this quantity in a $^{40}$K Fermi gas, in order to examine homogeneous single-particle properties of this system. Comparing our results with this experiment, we show that, this attempt indeed succeeds under the JILA's experimental condition. However, we also find that the current local photoemission spectroscopy still has room for improvement, in order to examine the pseudogap phenomenon predicted in the BCS-BEC crossover region. Since ultracold Fermi gases are always in a trap, our results would be useful in applying this system to various homogeneous Fermi systems, as a quantum simulator.