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

Abstract

We revisit the properties of the two-component Fermi gas with short-range\ninteractions in three dimensions, in the limit where the s-wave scattering\nlength diverges. Such a unitary Fermi gas possesses universal thermodynamic and\ndynamical observables that are independent of any interaction length scale.\nFocusing on trapped systems of N fermions, where N$\\leq10$, we investigate how\nwell we can determine the zero-temperature behavior of the many-body system\nfrom published few-body data on the ground-state energy and the contact. For\nthe unpolarized case, we find that the Bertsch parameters extracted from\ntrapped few-body systems all lie within 15% of the established value.\nFurthermore, the few-body values for the contact are well within the range of\nvalues determined in the literature for the many-body system. In the limit of\nlarge spin polarization, we obtain a similar accuracy for the polaron energy,\nand we estimate the polaron's effective mass from the dependence of its energy\non N. We also compute an upper bound for the squared wave-function overlap\nbetween the unitary Fermi system and the non-interacting ground state, both for\nthe trapped and uniform cases. This allows us to prove that the trapped\nunpolarised ground state at unitarity has zero overlap with its non-interacting\ncounterpart in the many-body limit N$\\to \\infty$.\n