Stimulated Emission in Absorption Imaging

Question

A laser passing through a cloud of ultra cold atoms drives the atomic ensemble to a steady state solution of the optical Bloch equations (OBE). The resulting state is a statistical mixture (rather than a pure state) and depends on detuning $\delta$, the Rabi frequency $\Omega$, and the rate of emission $\Gamma$. In particular, the steady state has the occupations $$\rho_{ee}=\frac{\Omega^2/4}{\Gamma^2/4+\delta^2+\Omega^2/2}\,\,\,,\,\,\, \rho_{gg}=1-\rho_{ee}.$$ The scattering rate is of the ensemble is then given by $\Gamma_s=N\rho_{22}\Gamma$ where $N$ is the number of atoms in the cloud. My question is as follows:

In absorption imaging, a photon is "lost" by spontaneous emission but also from an imbalance between absorption and stimulated emission. Naively, I would expect the effect on the absorption image to contain the scattering rate and the imbalance between absorption and stimulated emission. However, in literature one commonly characterizes the process only by the photon scattering rate of the ensemble. Does this mean that one disregards the stimulated emission's contribution to the absorption image?

Answer 1

The forward intensity, which reduces the contrast of the shadow of the atoms in absorption imaging needs to be considered. There is a publication by Reinaudi et al. (http://arxiv.org/abs/0707.2930) that considers intensity dependent corrections in a "mysterious" factor $\alpha$. Vibel et al. (http://arxiv.org/abs/2402.06514) go into more detail about this factor.

TL;DR: People consider this effect, but it is generally hard to distinguish it from other scattering processes. By introducing some correction, that has to be calibrated in the experiment, it is taken care of.