Coherent state of a weakly interacting ultracold Fermi gas

TL;DR

This paper explores the theoretical description of a macroscopic coherent state in a weakly interacting ultracold Fermi gas, using fermionic coherent states and Grassmann algebra to analyze its properties.

Contribution

It introduces a fermionic coherent state framework for ultracold Fermi gases and derives key properties like the thermodynamic limit, symmetry breaking, and quasi-particle spectrum.

Findings

Fermionic coherent states can describe macroscopic coherence in Fermi gases.

Derived the thermodynamic limit and spontaneous symmetry breaking for the system.

Analyzed the quasi-particle spectrum using Grassmann algebra.

Abstract

We examine the weakly interacting atoms in an ultracold Fermi gas leading to a state of macroscopic coherence, from a theoretical perspective. It has been shown that this state can be described as a fermionic coherent state. These coherent states are the eigenstates of fermionic annihilation operators, the eigenvalues being anti-commuting numbers or Grassmann numbers. By exploiting the simple rules of Grassmann algebra and a close kinship between relations evaluated for more familiar bosonic fields and those for fermionic fields, we derive the thermodynamic limit, the spontaneous symmetry breaking and the quasi-particle spectrum of the fermionic system.