2026/07/27 by Luis Alberto Medina Dozal, Alejandro R. Urzua, Carlos Andres Gonzalez-Gutierrez +1
paper · doi:10.1088/1402-4896/ae913b
Abstract We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes–Cummings framework. While the single-mode model is exactly solvable due to its conserved excitation number, yielding finite-dimensional invariant subspaces, the two-mode model extension presents a fundamental challenge: although the total excitation number remains conserved, each invariant subspace is infinite-dimensional, preventing a closed-form analytical solution. Our scheme separates the dynamics into a dominant, exactly solvable semiclassical component—the atom interacting with the mean fields of both modes—and treats the remaining quantum fluctuations through a sequence of unitary transformations that preserve essential quantum features. We validate our approach through direct comparison with numerical solutions, focusing on the non-resonant regime where multiple detunings give rise to rich interference effects and multi-timescale dynamics inaccessible to standard approximations. The method accurately reproduces atomic inversion, field observables, and fidelity over relevant timescales, while remaining computationally efficient.