Adiabatic transfer of light in a double cavity and the optical Landau-Zener problem

We analyze the evolution of an electromagnetic field inside a double cavity when the difference in length between the two cavities is changed, e.g., by translating the common mirror. We find that this allows photons to be moved deterministically from one cavity to the other. We are able to obtain the conditions for adiabatic transfer by first mapping the Maxwell wave equation for the electric field onto a Schrödinger-like wave equation and then using the Landau-Zener result for the transition probability at an avoided crossing. Our analysis reveals that this mapping only rigorously holds when the two cavities are weakly coupled (i.e., in the regime of a highly reflective common mirror) and that, generally speaking, care is required when attempting a Hamiltonian description of cavity electrodynamics with time-dependent boundary conditions.