Two level system in a thermal noise electric field

Hello! I have a 2 level system with a dipole moment d. I want to simulate numerically the evolution of the system under an external sinusoidal electric field (far off resonant). This is straightforward using SE. However I also have on top of that another electric field, created by a coupling of the 2 level system (ion) to a resonant circuit (not necessarily relevant but in this case I have an ion inside a Penning trap inducing image charges to a resonant RLC circuit). I'm interested in the case when the ion is in thermal equilibrium with the rlc circuit. I assume that the noise from the circuit will induce further population transfer between the 2 levels of the system. However I'm not sure how to model this thermal noise-like electric field, as an extra off diagonal term in my Hamiltonian. Can someone advice me about it? Thank you!

This is niche research stuff. Time to do a literature review