### 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 language | English |
---|---|

Article number | 072001 |

Number of pages | 11 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 50 |

Issue number | 7 |

DOIs | |

Publication status | Published - 16 Mar 2017 |

### Keywords

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

### Cite this

*Journal of Physics B: Atomic, Molecular and Optical Physics*,

*50*(7), [072001]. https://doi.org/10.1088/1361-6455/aa5a1e

}

*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 50, no. 7, 072001. https://doi.org/10.1088/1361-6455/aa5a1e

**Universality of the unitary Fermi gas : a few-body perspective.** / Levinsen, Jesper; Massignan, Pietro; Endo, Shimpei; Parish, Meera M.

Research output: Contribution to journal › Review Article › Research › peer-review

TY - JOUR

T1 - Universality of the unitary Fermi gas

T2 - a few-body perspective

AU - Levinsen, Jesper

AU - Massignan, Pietro

AU - Endo, Shimpei

AU - Parish, Meera M

PY - 2017/3/16

Y1 - 2017/3/16

N2 - 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 → ∞.

AB - 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 → ∞.

KW - degenerate Fermi gas

KW - few-body physics

KW - strongly correlated systems

KW - ultracold atomic gases

UR - http://www.scopus.com/inward/record.url?scp=85016159071&partnerID=8YFLogxK

U2 - 10.1088/1361-6455/aa5a1e

DO - 10.1088/1361-6455/aa5a1e

M3 - Review Article

VL - 50

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 7

M1 - 072001

ER -