Fitting line shapes in photoassociation spectroscopy of ultracold atoms: A useful approximation

Abstract

Line shapes observed in photoassociation spectroscopy of ultracold $(T<1\mathrm{mK})$ atoms are asymmetric and the peak of the line is shifted by a temperature-dependent amount from the zero-temperature threshold. In principle, calculating the line shape requires a full knowledge of both the ground- and excited-state potentials. We demonstrate here that an approximation based on the Wigner threshold law for scattering yields a relatively simple expression which allows one to extract line positions and linewidths directly from the data. The formula contains a few parameters (threshold frequency, linewidth, temperature, height) and does not require a detailed knowledge of the molecular potentials involved. We illustrate the utility of this approach with examples for Na photoassociation at 500 \ensuremath{\mu}K and also discuss the limitations of the approach.