Three-body contact for fermions. I. General relations
We consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables. Within the zero-range model, the number of nearby fermion t...
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Académie des sciences
2024-04-01
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| Series: | Comptes Rendus. Physique |
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| author | Werner, Félix Leyronas, Xavier |
| author_facet | Werner, Félix Leyronas, Xavier |
| author_sort | Werner, Félix |
| collection | DOAJ |
| description | We consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables. Within the zero-range model, the number of nearby fermion triplets, the large-momentum tail of the center-of-mass momentum distribution of nearby fermion pairs, as well as the large-momentum tail of the two-particle momentum distribution, are expressed in terms of the three-body contact. For a small finite interaction range, the formation rate of deeply bound dimers by three-body recombination, as well as the three-body contribution to the finite-range correction to the energy, are expressed in terms of the three-body contact and of a three-body parameter. This three-body parameter, which vanishes in the zero-range limit, is defined through the asymptotic behavior of the zero-energy scattering state at distances intermediate between the range and the two-body scattering length. In general, the three-body contact has different contributions labeled by spin and angular momentum indices, and the three-body parameter can depend on those indices. We also include the generalization to unequal masses for $\uparrow $ and $\downarrow $ particles. With respect to the relation between three-body loss rate and number of nearby triplets stated in [Petrov, Salomon and Shlyapnikov, PRL 93, 090404 (2004)], the present work adds a derivation, expresses the proportionality factor in terms of the three-body parameter, and includes the general case where there are several contributions to the three-body contact and several three-body parameters. |
| format | Article |
| id | doaj-art-5b21cbfadac94e4fa68a35147a61ba84 |
| institution | Kabale University |
| issn | 1878-1535 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj-art-5b21cbfadac94e4fa68a35147a61ba842025-02-07T13:53:46ZengAcadémie des sciencesComptes Rendus. Physique1878-15352024-04-0125G117921810.5802/crphys.18110.5802/crphys.181Three-body contact for fermions. I. General relationsWerner, Félix0https://orcid.org/0000-0002-5631-9024Leyronas, Xavier1https://orcid.org/0000-0002-9499-6800Laboratoire Kastler Brossel, Ecole Normale Supérieure - Université PSL, CNRS, Collège de France, Sorbonne Université, 75005 Paris, FranceLaboratoire de Physique de l’Ecole Normale Supérieure, ENS - Université PSL, Sorbonne Université, Université Paris Cité, CNRS, 75005 Paris, FranceWe consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables. Within the zero-range model, the number of nearby fermion triplets, the large-momentum tail of the center-of-mass momentum distribution of nearby fermion pairs, as well as the large-momentum tail of the two-particle momentum distribution, are expressed in terms of the three-body contact. For a small finite interaction range, the formation rate of deeply bound dimers by three-body recombination, as well as the three-body contribution to the finite-range correction to the energy, are expressed in terms of the three-body contact and of a three-body parameter. This three-body parameter, which vanishes in the zero-range limit, is defined through the asymptotic behavior of the zero-energy scattering state at distances intermediate between the range and the two-body scattering length. In general, the three-body contact has different contributions labeled by spin and angular momentum indices, and the three-body parameter can depend on those indices. We also include the generalization to unequal masses for $\uparrow $ and $\downarrow $ particles. With respect to the relation between three-body loss rate and number of nearby triplets stated in [Petrov, Salomon and Shlyapnikov, PRL 93, 090404 (2004)], the present work adds a derivation, expresses the proportionality factor in terms of the three-body parameter, and includes the general case where there are several contributions to the three-body contact and several three-body parameters.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.181/Unitary gasfermionscold atoms |
| spellingShingle | Werner, Félix Leyronas, Xavier Three-body contact for fermions. I. General relations Comptes Rendus. Physique Unitary gas fermions cold atoms |
| title | Three-body contact for fermions. I. General relations |
| title_full | Three-body contact for fermions. I. General relations |
| title_fullStr | Three-body contact for fermions. I. General relations |
| title_full_unstemmed | Three-body contact for fermions. I. General relations |
| title_short | Three-body contact for fermions. I. General relations |
| title_sort | three body contact for fermions i general relations |
| topic | Unitary gas fermions cold atoms |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.181/ |
| work_keys_str_mv | AT wernerfelix threebodycontactforfermionsigeneralrelations AT leyronasxavier threebodycontactforfermionsigeneralrelations |