Relaxation breakdown and resonant tunneling in ultrastrong-coupling cavity QED

We study the open relaxation dynamics of an asymmetric dipole that is ultrastrongly coupled to a single electromagnetic cavity mode. By using a thermalizing master equation for the whole interacting system we derive a phase diagram of the Liouvillian gap. It emerges that the ultrastrong coupling inhibits the system's relaxation toward the equilibrium state due to an exponential suppression of the dipole tunneling rate. However, we find that polaronic multiphoton resonances restore fast relaxation by a cavity-mediated dipole resonant tunneling process. Aside from the numerical evidence, we develop a fully analytical description by diagonalizing the Rabi model through a generalized rotating-wave approximation, valid in the so-called polaron frame. The relaxation physics of such ultrastrong-coupling systems is then reduced to a multiphoton polaron version of the standard textbook dressed states picture. At the end we discuss an extension to a multiwell dipole that can set the basis of a cascaded resonant tunneling setup in the ultrastrong coupling regime.