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We present a new method to study the semiclassical dynamics of theJaynes-Cummings dimer model, describing two coupled cavities each containing atwo-level system (qubit). We develop a Fock space WKB approach in the polaritonbasis where each site is treated exactly while the intersite polariton hoppingis treated semiclassically. We show that the self-trapped states can be viewedas Fock space localized states. We find that this picture yields the correctcritical value of interaction strength at which the delocalization-localizationtransition occurs. Moreover, the validity of our WKB approach is supported byshowing that the quantum spectrum can be derived from a set of Bohr-Sommerfeldquantization conditions and by confirming that the quantum eigenstates areconsistent with the classical orbital motion in the polariton band picture. Theunderlying idea of our method is quite general and can be applied to otherinteracting spin-boson models.

Fock space localization of polaritons in the Jaynes-Cummings dimer model