Fast and Accurate Method for Doppler Averaging of Rydberg EIT Signals

Modeling the effect of Doppler broadening due to the thermal atomic motion of Rydberg sensors typically relies on sampling a large velocity class, solving the equations of motion for each velocity, and then averaging the atomic density matrix over that velocity class. This process is inexact, slow, and presents a bottleneck in simulating Rydberg sensors. We present an approach that allows for fast, exact velocity averaging just by solving the equations of motion twice. We find the "propagator" that acts on the zero-velocity solution to generate the velocity-dependent atomic state for all velocities. By averaging this propagator over the Maxwell-Boltzmann velocity distribution of the atoms, we obtain an explicit, analytic formula that generates the averaged atomic state. This method is expected to save memory and time computational resources by one to several orders of magnitude, compared to traditional sampling approaches.