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

TL;DR

This paper investigates the universal properties of the unitary Fermi gas using few-body data, demonstrating that small systems can accurately reflect many-body behavior and establishing bounds on wave-function overlaps.

Contribution

It shows that few-body calculations can reliably estimate many-body properties of the unitary Fermi gas, including energy and contact, and proves the zero overlap in the many-body limit.

Findings

Few-body energies closely match known many-body values.

Contact values from few-body systems agree with literature.

Proves zero wave-function overlap in the thermodynamic limit.

Abstract

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 possesses universal thermodynamic and dynamical observables that are independent of any interaction length scale. Focusing on trapped systems of N fermions, where N$\leq10$, 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 unpolarised ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N$\to \infty$.