Equation of state of cold atoms: A lowest-order-constrained variational study of systems with large non-s-wave scattering lengths

Abstract

Dilute Fermi systems with large $s$-wave scattering length ${a}_{s}$ exhibit universal properties if the interparticle spacing ${r}_{0}$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, ${r}_{0}$ is the only relevant length scale and observables such as the energy per particle depend only on ${r}_{0}$ (or, equivalently, the energy ${E}_{\mathrm{FG}}$ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum $l$ using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an $l$-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite $l$. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.