Effective Pair Potential for the Ground-State Ideal Fermi Gas

Sergei V. Traven

Ravinder Rupchand Puri

Valdir C. Aguilera-Navarro, Mauricio Fortes, MANUEL DE LLANO

A Bethe–Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea" produces unstable CPs if holes are not ignored. Stable CPs with damping emerge when the BCS ground state replaces the IFG, and are positive-energy, finite-lifetime resonances for nonzero center-of-mass momentum with a linear dispersion leading term. Bose–Einstein condensation of such pairs may thus occur in exactly two dimensions as it cannot with quadratic dispersion.

Silvio R. A. Salinas

Lars Schonenberg, G. J. Conduit

A Fermi gas of cold atoms allows precise control over the dimensionless effective range, ${k}_{\mathrm{F}}{R}_{\mathrm{eff}}$, of the Feshbach resonance. Our pseudopotential formalism allows us to create smooth potentials with effective range, $\ensuremath{-}2\ensuremath{\le}{k}_{\mathrm{F}}{R}_{\mathrm{eff}}\ensuremath{\le}2$, which we use for a variational and diffusion Monte Carlo study of the ground state of a unitary Fermi gas. We report values for the universal constants of $\ensuremath{\xi}=0.388(1)$ and $\ensuremath{\zeta}=0.087(1)$, and compute the condensate fraction, momentum distribution, and pair correlations functions. Finally, we show that a gas with ${k}_{\mathrm{F}}{R}_{\mathrm{eff}}\ensuremath{\gtrsim}1.9$ is thermodynamically unstable.

David Mitrouskas, Peter Pickl

We study the dynamics of a small number of impurity particles coupled to the ideal Fermi gas in a $d$-dimensional box. The impurities interact with the fermions via a two-body potential $λv(x)$ where $λ$ is a coupling constant and $v(x)$ for instance a screened Coulomb potential. After taking the large-volume limit at positive Fermi momentum $k_F$ we consider the regime of high density of the fermions, that is, $k_F$ large compared to one. For coupling constants that scale like $λ^2 \sim k_F^{(2-d)}$ we show that the impurity particles effectively decouple from the fermions but evolve with an attractive pair interaction among each other which is induced by fluctuations in the Fermi gas.