# Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover

## TL;DR

This paper develops a low-energy effective field theory describing Goldstone and Higgs modes in the BCS-BEC crossover, analyzing their coupled dynamics and comparing theoretical predictions with experimental data in two dimensions.

## Contribution

It introduces a microscopic derivation of the coupled Goldstone-Higgs effective theory and explores pair fluctuation effects beyond mean-field in the BCS-BEC crossover.

## Key findings

- Gaussian theory aligns with experimental data in 2D ultracold Fermi superfluids.
- Pair fluctuations significantly influence the collective mode dynamics.
- The effective field theory captures key features of the BCS-BEC crossover in different dimensions.

## Abstract

We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS-BEC crossover is compared with available experimental data of the two-dimensional ultracold Fermi superfluid.