Theoretical treatment of a closed-loop excitation scheme for phase-sensitive RF E-field sensing using Rydberg atom-based sensors

In this talk, we present theoretical work aimed at understanding radio frequency phase measurement using all-optical, atom-based electric field sensors. Atom-based radio frequency field sensors have a number of applications in communications, radar and test and measurement. All of these applications benefit from being able to detect phase, but Rydberg atom-based sensors in the steady state are square law detectors. To obtain an analytic expression for phase detection, we investigate closed-loop excitations in cesium that preserve phase information in a probe laser signal transmission amplitude coupled to one transition of the loop. Insight into the mechanisms that enable phase determination is gained by analyzing the closed-loop processes. In the 5-level excitation scheme, we find the highest sensitivity region by looking at the absorption contrast. It turns out that the sensitivity maximizes when the atomic vapor is weakly probed. Furthermore, we apply the weak probe approximation to the Lindblad-master equation and find an analytic expression for the absorption coefficient. With this expression, we gain a deeper understanding of the multi-photon interference and how this applies to phase readout in the atom-based radio frequency sensors.