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

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