Coupled cavities beyond standard coupled mode theory

The phenomenon of evanescent coupling between adjacent optical cavities has been exploited for a diverse array of technologies both existing and emerging, from coupled-resonator optical waveguides to photonics-based analog quantum simulators. Coupled mode theory (CMT) has long served as an invaluable heuristic model for understanding the various effects which arise in these systems such as mode splitting and supermode formation, but it lacks predictive power and broad applicability beyond weak coupling. In this work, we present a first-principles theoretical description of coupled cavities with semi-analytical predictivity beyond the scope of CMT without introducing phenomenological parameters. We demonstrate that coupled cavity modes are most appropriately described by oscillators which are coupled not only through their coordinates, but also their momenta, in contrast with CMT which considers only the former. Upon quantization, we show that this dual coupling significantly enhances the influence of counter-rotating interaction terms, suggesting the possibility for phenomena typically associated with the ultrastrong coupling regime, such as virtual excitations in the ground state, in more modest parameter regimes.