Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value $a$ of the $s$-wave scattering length of the two-body potential. For $a>0$ and $a$ smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length $a_m=0.6a$. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.

Figure 1

Energy per particle in the BEC-BCS crossover. Solid symbols refer to results obtained with the trial wave function ${\psi }_{\mathrm{B}\mathrm{C}\mathrm{S}}$; open symbols refer to the ones obtained with ${\psi }_{\mathrm{J}\mathrm{S}}$. The dot-dashed line is the expansion (6) holding in the BCS region and the dotted line corresponds to the binding energy ${ϵ}_b/2$. Inset: finite-size effects in the unitary limit $-1/k_{F}a=0$.

Figure 2

Energy per particle in the BEC-BCS crossover with the binding energy subtracted from $E/N$. Solid symbols: results with ${\psi }_{\mathrm{B}\mathrm{C}\mathrm{S}}$; open symbols: results with ${\psi }_{\mathrm{J}\mathrm{S}}$. The dot-dashed line is as in Fig. 1 and the dashed line corresponds to the expansion (7) holding in the BEC regime. Inset: enlarged view of the BEC regime $-1/k_{F}a\le -1$. The solid line corresponds to the mean-field energy [first term in the expansion (7)]; the dashed line includes the beyond mean-field correction [Eq. (7)].

Figure 3

Pair correlation function of parallel, $g_2^{\uparrow \uparrow }(r)$, and (inset) of antiparallel spins, $g_2^{\uparrow \downarrow }(r)$, for $-1/k_{F}a=0$ (unitary limit), $-1/k_{F}a=-4$ (BEC regime), $-1/k_{F}a=4$ (BCS regime) and for a noninteracting Fermi gas (FG). The dot-dashed line corresponds to the pair correlation function of a Bose gas with $a_m=0.6a$ and $-1/k_{F}a=-4$ calculated using the Bogoliubov approximation.