Universality of the unitary Fermi gas: A few-body perspective

We revisit the properties of the two-component Fermi gas with short-range interactions in three dimensions, in the limit where the s -wave scattering length diverges. Such a unitary Fermi gas pos- sesses universal thermodynamic and dynamical observables that are independent of any interaction length scale. Focusing on trapped systems of N fermions, where N = 10, we investigate how well we can determine the zero-temperature behavior of the many-body system from published few-body data on the ground-state energy and the contact. For the unpolarized case, we find that the Bertsch parameters extracted from trapped few-body systems all lie within 15% of the established value. Furthermore, the few-body values for the contact are well within the range of values determined in the literature for the many-body system. In the limit of large spin polarization, we obtain a similar accuracy for the polaron energy, and we estimate the polaron’s effective mass from the dependence of its energy on N . We also compute an upper bound for the squared wave-function overlap between the unitary Fermi system and the non-interacting ground state, both for the trapped and uniform cases. This allows us to prove that the trapped unpolarized ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N ¿8Peer Reviewe