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

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.

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• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• Unconventional pairing in few-fermion systems at finite temperature
• Few-body perspective on fermionic pairing in one spatial dimension
• Few-to-many-particle crossover of pair excitations in a superfluid
• Unconventional pairing in few-fermion systems tuned by external confinement