The transition from the classical to the quantum regime for rubidium-87 (87Rb) vapor in terms of the second virial coefficient and the scattering length

Abstract

This work focuses on two major properties of 87Rb gas for a very broad temperature range of ∼nK–3000 K. The first is the second virial coefficient B, encompassing both classical ( Bcl) and quantum ( Bq) regimes as well as, in between, the classical coefficient plus the first quantum correction ( Bqcl). The transition from the classical to the quantum regime in this system is explored. The second property is the s-wave scattering length a0 for both singlet [[Formula: see text]] and triplet [[Formula: see text]] states. The medium is incorporated into the picture via the Galitskii–Migdal–Feynman formalism. Its main output is the medium phase shifts for the system, using the “best” available interatomic potential. These are plugged into the Beth–Uhlenbeck formula to give Bq, whereas Bc l and Bqcl are readily calculated from standard expressions, the only input needed being the binary potential. Our results show that Bq exhibits clear demarcation from Bcl, especially at nK temperatures where Bose–Einstein condensation (BEC) manifests itself. Comparison to other calculations in the literature is made only for Bcl; Bq for this gas is computed here for the first time, as are [Formula: see text] and [Formula: see text] for the medium. It turns out that these scattering lengths are larger than their vacuum counterparts at BEC temperatures.