  We present a new method to study the semiclassical dynamics of the
Jaynes-Cummings dimer model, describing two coupled cavities each containing a
two-level system (qubit). We develop a Fock space WKB approach in the polariton
basis where each site is treated exactly while the intersite polariton hopping
is treated semiclassically. We show that the self-trapped states can be viewed
as Fock space localized states. We find that this picture yields the correct
critical value of interaction strength at which the delocalization-localization
transition occurs. Moreover, the validity of our WKB approach is supported by
showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld
quantization conditions and by confirming that the quantum eigenstates are
consistent with the classical orbital motion in the polariton band picture. The
underlying idea of our method is quite general and can be applied to other
interacting spin-boson models.
