Effective Pair Potential for the Ground-State Ideal Fermi Gas

Sergei V. Traven

Walter Greiner, Ludwig Neise, Horst Stöcker B

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.

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.

Ravinder Rupchand Puri

Silvio R. A. Salinas