Numerical Study of Interactions between Multiple Atoms and Electromagnetic Fields in a Lossy Cavity without Markovian Approximation

Quantization of lossy electromagnetic (EM) systems is a challenging task since the standard (eigen)mode decomposition approach [1], [2] is no longer available. The use of eigenmodes from non-Hermitian systems does not preserve the equal-time commutators; consequently, the Heisenberg uncertainty principle breaks down. Recently, we have proposed the so-called BAMA formulation [3] to account for the radiation and medium loss effects in the quantization of electromagnetic fields based on the fluctuation-dissipation theorem and Green's function approach [4]. In this presentation, we show how to incorporate the BAMA formulation into the multimode Jaynes-Cummings model to describe the dynamics of two-level systems placed inside a lossy cavity from the first principle, i.e., without the master equation based on the Markovian approximation. s