Analytic approximations to the strengths of near-threshold optical Feshbach resonances

TL;DR

This paper derives analytic formulas for the strength of near-threshold optical Feshbach resonances, linking them to physical parameters, and extends their application to atom pairing in optical lattices.

Contribution

It provides the first fully analytic approximations for optical Feshbach resonance strengths near threshold, applicable to specific molecular states and useful for ultracold atom experiments.

Findings

Analytic expressions for optical length near threshold.

Relation between Rabi frequency and optical length in optical lattices.

Applicability to resonant-dipole and van der Waals interactions.

Abstract

Optical Feshbach resonances (OFRs) allow one to control cold atomic scattering, produce ultracold molecules and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold s-wave collisions the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, excited state binding energy, the s-wave scattering length and the Condon point. Additionally, we extend the utility of the optical length to associative STIRAP in 3D optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.