Reliable equation of state for composite bosons in the 2D BCS-BEC crossover

TL;DR

This paper develops a reliable equation of state for 2D composite bosons in the BCS-BEC crossover by applying quantum-field-theory formalism and dimensional regularization to account for fluctuations.

Contribution

It introduces a novel approach to accurately describe the 2D BCS-BEC crossover using quantum-field theory and regularization techniques.

Findings

Derived a consistent equation of state for 2D systems at low temperatures.

Validated the formalism with experimental observations.

Provided insights into collective excitations in 2D Fermi gases.

Abstract

We briefly discuss recent experiments on the BCS-BEC crossover with ultracold alkali-metal atoms both in three-dimensional configurations and two-dimensional ones. Then we analyze the quantum-field-theory formalism used to describe an attractive $D$-dimensional Fermi gas taking into account Gaussian fluctuations. Finally, we apply this formalism to obtain a reliable equation of state of the 2D system at low temperaratures in the BEC regime of the crossover by performing a meaningful dimensional regularization of the divergent zero-point energy of collective bosonic excitations.