Universality of the unitary Fermi gas

a few-body perspective

Jesper Levinsen, Pietro Massignan, Shimpei Endo, Meera M Parish

Research output: Contribution to journalReview ArticleResearchpeer-review

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 ≤ 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 → ∞.

Original languageEnglish
Article number072001
Number of pages11
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Volume50
Issue number7
DOIs
Publication statusPublished - 16 Mar 2017

Keywords

  • degenerate Fermi gas
  • few-body physics
  • strongly correlated systems
  • ultracold atomic gases

Cite this

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title = "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 ≤ 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 → ∞.",
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Universality of the unitary Fermi gas : a few-body perspective. / Levinsen, Jesper; Massignan, Pietro; Endo, Shimpei; Parish, Meera M.

In: Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 50, No. 7, 072001, 16.03.2017.

Research output: Contribution to journalReview ArticleResearchpeer-review

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