Pairing in a system of a few attractive fermions in a harmonic trap

TL;DR

This paper provides an exact analysis of a few attractive fermions in a harmonic trap, revealing how strong attraction leads to correlated pairs with universal temperature dependence, advancing understanding of strongly correlated quantum systems.

Contribution

It offers an exact diagonalization study of few-fermion systems, showing universal pairing behavior analogous to superconductivity, valid in strong attraction regimes.

Findings

Correlated pairs emerge under strong attraction.

Pair fraction depends universally on temperature.

Predictions are exact and applicable in strong coupling.

Abstract

We study a strongly attractive system of a few spin-1/2 fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one-- and two--particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.