|
Résumé |
The resonant Fermi gas, i.e. two-component fermions in 3D interacting by a short-range
potential of large scattering length a2 , is a textbook model describing cold atoms near
a Feshbach resonance.
A key quantity is the 2-body contact C2 , which determines e.g. the number of nearby
fermion pairs, the tail of the single-particle momentum distribution, the derivative of the
energy with respect to a2 , or the 2-body loss rate [1,2] .
Based on the non-trivial power-law scaling of the 3-body wavefunction at short distances,
we introduce the three-body contact C3 , in terms of which we express e.g. the number
of nearby fermion triplets, or the large-momentum tail of the two-particle momentum
distribution. The formation rate of deeply bound dimers by three-body recombination is
expressed in terms of C3 and a parameter a3 defined through the asymptotic behavior
of the zero-energy 3-body wavefunction at distances between the range and |a2| [3].
We compute C3 to leading order in the non-degenerate limit for the homogeneous gas,
using the exact 3-body wavefunction at the unitary limit a2 = infinite; , and a diagrammatic
approach at negative a2 . In the Feynman diagram technique, the three-body short-
distance power-law scaling comes from a large-wavevector tail of the 3-body T-matrix [4].
We propose a procedure to experimentally determine C3 in the degenerate regime, whose
computation is an open theoretical challenge.
[1] S. Tan, Ann. Phys. 323, 2952 (2008); ibid. 323, 2971 (2008)
[2] E. Braaten and L. Platter, Phys. Rev. Lett. 100, 205301 (2008)
[3] FW and X. Leyronas, Comptes Rendus Physique 25, 179 (2024)
[4] X. Leyronas and FW, in preparation |
