Abstract
We consider a high-Q microresonator with $\chi^{(2)}$ nonlinearity under conditions when the coupling rates between the sidebands around the pump and second harmonic exceed the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator approach we demonstrate that this regime leads to the dominance of the Hermitian part of the operator driving the side-band dynamics over its non-Hermitian part responsible for the parametric gain. This has allowed us to introduce and apply the cross-area concept of the polariton quasi-particles and define their effective masses in the context of $\chi^{(2)}$ ring-microresonators. We further use polaritons to predict the modified spectral response of the resonator to a weak probe field, and to reveal splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Polariton basis also allows deriving a discrete sequence of the parametric thresholds for the generation of sidebands of different orders.
Highlights
Strong coupling (SC) between photons and matter is at the heart of modern cavity quantum electrodynamics [1]
The μ-specific instability domains are arranged as a sequence of the 4-beam stars shifted along the δo, but nearly coinciding along the δe, direction
We have proposed and formalised a concept of the polariton quasiparticles, photon-photon polaritons, in the context of multimode high-Q χ (2) microring resonators
Summary
Strong coupling (SC) between photons and matter is at the heart of modern cavity quantum electrodynamics [1]. A combination of these two factors favors considering if a multimode χ (2) microresonator could go beyond modifying the light-matter interaction by reducing the density of states, i.e., the Purcell regime, available for photon transitions and to cross into SC, where new families of states (dressed states and associated energy levels) are created. We parametrize the energies of the dressed, i.e., hybrid ordinary-extraordinary, states with their momenta, and define the microresonator polaritonic quasiparticles—photon-photon polaritons. They are different from the above-mentioned families of the exciton-polaritons in planar [3,4,5,6,7,8,9] and ring [45] semiconductor microresonators, and from other polaritons.
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