Determine the origin of the finite imaging offset parameter

Identify the physical origin of the finite reduced offset parameter \(\tilde{c}_2\) in the detection of the cesium \(\ket{2}\) population during state-resolved imaging, after excluding the Cs\(\ket{1}\)\(\leftrightarrow\)Cs\(\ket{2}\) transfer, optical pumping, closed-transition imaging light, and camera-related artifacts.

Background

The experiment determines the transferred fraction between the two lowest cesium hyperfine states by imaging Cs$\ket{1}$ directly and transferring Cs$\ket{2}$ into Cs$\ket{1}$ for a second imaging sequence. The detected Cs$\ket{2}$ population is modeled heuristically as $N_{2,\mathrm{det}}=c_1N_2+c_2$, where the offset $c_2=\tilde{c}_2\overline{N}$ scales with the total cesium atom number. Calibration yields $c_1=0.85(3)$ and $\tilde{c}_2=0.059(0.012)$.

The authors report that the finite value of the offset parameter cannot be explained by the state-transfer or optical-pumping procedures, nor by the imaging transition light or camera artifacts. Consequently, the physical source of this systematic offset remains unresolved and limits the interpretation and calibration of state-resolved cesium imaging.