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

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$\le 10$, 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 unpolarised ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N$\to \infty$.

12 pages, 6 figures

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• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• Quench dynamics of mass-imbalanced three-body fermionic systems in a spherical trap
• Bose polaron in spherically symmetric trap potentials: Ground states with zero and lower angular momenta
• Polaritons for testing the universality of an impurity in a Bose-Einstein condensate
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Effects of Efimov states on quench dynamics in a three-boson trapped system
• When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases
• The normal state of attractive Fermi gases from coupled-cluster theory
• Arbitrary interaction quench phenomena in harmonically trapped two-body systems
• Observation of Universal Expansion Anisotropy from Cold Atoms to Hot Quark-Gluon Plasma
• Equivalence of dissipative and dissipationless dynamics of interacting quantum systems with its application to the unitary Fermi gas
• Emergence of Fermi's Golden Rule in the Probing of a Quantum Many-Body System