# Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

## TL;DR

This paper theoretically examines how pairing fluctuations and harmonic trapping influence the local spin susceptibility in an ultracold Fermi gas across the BCS-BEC crossover, revealing non-monotonic temperature behavior and methods to isolate intrinsic effects.

## Contribution

It introduces a theoretical framework combining extended T-matrix approximation and local density approximation to analyze spin susceptibility in trapped Fermi gases, accounting for pairing fluctuations and trap effects.

## Key findings

- Pairing fluctuations cause non-monotonic temperature dependence of spin susceptibility.
- Trap effects influence the observed spin-gap phenomenon, requiring correction methods.
- Results aid in interpreting experimental data on preformed pairs in cold atom systems.

## Abstract

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $\chi_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $\chi_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a {\it uniform} Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from $\chi_{\rm t}(r,T)$, to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.