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

TL;DR

This paper introduces a Fock space WKB method to analyze polariton localization in the Jaynes-Cummings dimer, accurately predicting the localization transition and connecting quantum spectra with classical dynamics.

Contribution

The paper develops a novel semiclassical Fock space WKB approach for the Jaynes-Cummings dimer, enabling precise analysis of polariton localization and transition phenomena.

Findings

Correct critical interaction strength for localization transition

Quantum spectrum derived from Bohr-Sommerfeld quantization

Quantum eigenstates match classical orbital motion

Abstract

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.