Finite-range effects in dilute Fermi gases at unitarity

Abstract

We develop a theoretical method going beyond the contact-interaction approximation frequently used in mean-field theories of many-fermion systems, based on the low-energy T matrix of the pair potential to rigorously define the effective radius of the interaction. One of the main consequences of our approach is the possibility to investigate finite-density effects, which are outside the range of validity of approximations based on δ-like potentials. We apply our method to the calculation of density-dependent properties of an ultracold gas of 6Li atoms at unitarity, whose two-body interaction potential is calculated using ab initio quantum chemistry methods. We find that density effects will be significant in ultracold gases with densities 1 order of magnitude higher than those attained in current experiments

Effective-range dependence of resonantly interacting fermions

“…To extract the unitary parameters thus requires an extrapolation to zero effective range. Range effects in the ufg are also discussed in [14] (large r e ), [4] (Fixed-Node qmc (fnqmc)), and in [15,16] (Bogoliubov-de Gennes (bdg) approximation).…”

Collective excitations of a trapped Fermi gas at finite temperature

“…Hence we neglect the Hartree energy but observe that this has also the positive side effect that it shows more clearly the effect of interactions eventually introduced by the GRPA for quasiparticle excitations in the normal state. Notice that the problems with the Hartree shift ultimately derive from the attempt to describe interactions through the two-body scattering T matrix instead of the bare atom-atom interaction [29]. These problems do not manifest for example in density-functional theories which, when used in the atomic gas context, do not separate the Hartree and exchange-correlation energies [30,31].…”

A scattering view of the Bogoliubov-de Gennes equations

“…The potential energy curves have been obtained from ab initio quantum chemical calculations using Configuration Interaction with single and double excitations from the reference Hartree-Fock ground state by expanding molecular orbitals in a cc-pVQZ basis set of atomic-centered Gaussians. The singlet and triplet potentials have been used to calculate the interaction as a function of the external magnetic field, taking into account fine and hyperfine structure terms [23].…”

“…We now show how the BdG equation can be rewritten as a function of the T -matrix, and we apply this scheme to investigate an homogeneous system of strongly interacting 6 Li atoms at unitarity [23]. The solution for ultracold atoms at unitarity using FCI requires a nontrivial renormalisation procedure [4].…”

“…We will show that our approach naturally introduces finite-range effects in the system through the dependence of T on the interaction radius of the pair potential, enabling us to discuss the density dependence of the principal thermodynamical observables (gap, chemical potential, transition temperature) [23].…”