Experimental validation of a recursive density matrix expansion for four-wave mixing: Propagation and suppression effects in dense rubidium vapor
Phys. Rev. A 114, 013522 – Published 29 July, 2026
DOI: https://doi.org/10.1103/yy3x-mbkq
Abstract
We present a combined experimental and theoretical study of degenerate four-wave mixing (FWM) in a thermal rubidium vapor on the line. The experiment employs a forward phase-matched geometry with a single laser, where the atomic density—and thus the optical depth—is controlled via the cell temperature. We measure the generated FWM signal across a wide range of densities, observing a characteristic suppression and saturation at high optical depths. To explain these phenomena, we develop a theoretical model based on a semiclassical treatment of the atomic response that includes nonlinear propagation effects. The model's core is a recursive Liouville equation derived from a systematic expansion of the system's density matrix, which provides an analytical solution for the optical coherence and the generated field in a closed four-level excitation loop. This theoretical framework shows excellent agreement with the experimental data across all densities. By confronting theory and experiment, we demonstrate that our model simultaneously captures the roles of absorption, propagation, and interference in shaping the nonlinear optical response, showing that the observed suppression of the FWM signal at high atomic density arises from the combined action of these competing mechanisms.
