When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases

TL;DR

This study investigates how pairing in two-dimensional trapped mesoscopic Fermi gases evolves with particle number, revealing the emergence of a Fermi sea that suppresses pairing at low momenta as the system size increases.

Contribution

It provides detailed theoretical analysis of pairing behavior in small versus larger mesoscopic Fermi systems, highlighting the transition to Fermi sea formation.

Findings

Pairing is maximized below the Fermi surface for up to six fermions.

In larger systems, pairing peaks at the Fermi surface, indicating Fermi sea emergence.

Transition from six to twelve particles shows the development of Fermi sea effects.

Abstract

Pairing lies at the heart of superfluidity in fermionic systems. Motivated by recent experiments in mesoscopic Fermi gases, we study up to six fermionic atoms with equal masses and equal populations in two different spin states, confined in a quasi-two-dimensional harmonic trap. We couple a stochastic variational approach with the use of an explicitly correlated Gaussian basis set, which enables us to obtain highly accurate energies and structural properties. Utilising two-dimensional two-body scattering theory with a finite-range Gaussian interaction potential, we tune the effective range to model realistic quasi-two-dimensional scattering. We calculate the excitation spectrum, pair correlation function, and number of pairs as a function of increasing attractive interaction strength. For up to six fermions in the ground state, we find that opposite spin and momentum pairing is maximised well below the Fermi surface in momentum space. By contrast, corresponding experiments on twelve fermions have found that pairing is maximal at the Fermi surface and strongly suppressed beneath [M. Holten et al., Nature 606, 287-291 (2022)]. This suggests that the Fermi sea $-$ which acts to suppress pairing at low momenta via Pauli blocking $-$ emerges in the transition from six to twelve particles.