Pairing in a system of a few attractive fermions in a harmonic trap
1 Institute of Physics of the Polish Academy of Sciences - Al. Lotników 32/46, 02-668 Warszawa, Poland
2 Center for Theoretical Physics of the Polish Academy of Sciences - Al. Lotników 32/46, 02-668 Warszawa, Poland
Received: 5 September 2014
Accepted: 12 January 2015
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.
PACS: 67.85.Lm – Degenerate Fermi gases
© EPLA, 2015