Exact and efficient method for Doppler averaging of atomic systems

Calculating Doppler broadening due to thermal atomic motion is important in many spectroscopy and sensing experiments. In general, analytic solutions are not possible, which necessitates sampling and numerically solving the density matrix for many velocity classes and averaging over the Maxwell-Boltzmann distribution. This process is inexact and inefficient, adding an overhead of several orders of magnitude to computational time and memory. Here, we present an exact and efficient numerical method that calculates Doppler broadening in one dimension at steady state for any atomic system. The method requires a single diagonalization of the system, without velocity sampling, and is applicable to any time-independent or periodic Hamiltonian. As an example, we demonstrate how to calculate the Doppler-averaged signals exactly in electromagnetically induced transparency (EIT) experiments with Rydberg atoms in warm vapor cells.

Refs:

O. Nagib & T. G. Walker, Exact steady state of perturbed open quantum systems, Physical Review Research 7, 033076 (2025) [arXiv:2501.06134]

O. Nagib & T. G. Walker, Fast and Accurate Method for Doppler Averaging of Rydberg EIT Signals, 2025 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM), Boulder, CO, USA, 2025, pp. 8-9 (2025) [arXiv:2501.02141]