Ground-State Properties of Fermi Gases in the Strongly Interacting Regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green’s function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.

Figure 1

The trial, mixed, and extrapolated $g_{\uparrow \uparrow }(r)$ with the LOCV ${\Psi }_T(\mathbf{R})$ are compared with the trial $g_{\uparrow \uparrow }(r)$ with the ${\Psi }_{\mathrm{optim}}(\mathbf{R})$. Note that the mixed and trial pair distributions are the same for ${\Psi }_{\mathrm{optim}}(\mathbf{R})$. $r_0$ is given by $4\pi r_0^3\rho =3$.

Figure 2

Optimized $f_{\uparrow \uparrow }(r)$ for different values of $a{k}_F$.

Figure 3

Optimized $f_{\uparrow \downarrow }(r)$ (dashed line) and LOCV $f_{\uparrow \downarrow }(r)$ (continuous line) for different values of $a{k}_F$.

Figure 4

Comparison of the pair distribution function $g_{\uparrow \downarrow }(r)$ with the radial probability distribution of the molecule in the $a>0$ regime.