Cavity-QED Simulation of a Maser beyond the Mean-Field Approximation

Based on the well-known Tavis-Cummings (TC) model of cavity quantum electrodynamics (QED), we introduce a method for quantum-mechanically simulating the dynamics of experimental masers beyond the mean-field approximation (MFA) that takes into account the spatial variation of the a.c. magnetic field of the maser's amplified microwave mode across its gain medium. The distribution in the coupling between the amplified mode and the medium's very large number typically $10¹⁷$ of spatially distributed quantum emitters can be determined straightforwardly for a given geometry and composition using an electromagnetic-field solver. Upon discretising this distribution as a histogram over a small finite number of bins, we assign - as an approximation - the same coupling to all emitters that fall within the same bin, where the value of this coupling equals the center value of the bin's range. With our approximate Hamiltonian arranged as a weighted sum over these bins, we generate expressions for expectation values of operators in the Heisenberg picture to second order in cumulant expansion, using the publicly available QuantumCumulants.jl package in Julia. For ten evenly spaced bins, our model, which can be run on a laptop computer, is used to simulate the recorded output from an experimental maser with a pentacene-doped para-terphenyl gain medium. We find that it replicates the quantum-mechanical features of the measured maser's dynamics, in particular its damped collective Rabi oscillations, more closely than the standard TC model under the MFA can, with an R² value of 0.774, as opposed to 0.265. Our model should thus aid the quantitative engineering of improved, optimised maser designs.