# Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations

## TL;DR

This paper presents ab initio Monte Carlo calculations of the pairing gap, spectral function, and structure factors in a 2D Fermi gas, offering detailed insights into the BEC-BCS crossover relevant for experiments.

## Contribution

The study introduces first-principles numerical methods to compute dynamical properties of the 2D Fermi gas, enabling direct experimental comparison.

## Key findings

- Computed pairing gap across the BEC-BCS crossover
- Obtained spectral functions using analytic continuation
- Visualized density and spin structure factors

## Abstract

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-art analytic continuation techniques, we obtain the spectral function, and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.