Disordered ensembles of strongly coupled single-molecule plasmonic picocavities as nonlinear optical metamaterials

Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities

Experiments have demonstrated that the strong light-matter coupling in polaritonic microcavities significantly enhances transport. Motivated by these experiments, we have solved the disordered multimode Tavis-Cummings model in the thermodynamic limit and used this solution to analyze its dispersion and localization properties. The solution implies that wave-vector-resolved spectroscopic quantities can be described by single-mode models, but spatially resolved quantities require the multimode solution. Nondiagonal elements of the Green's function decay exponentially with distance, which defines the coherence length. The coherent length is strongly correlated with the photon weight and exhibits inverse scaling with respect to the Rabi frequency and an unusual dependence on disorder. For energies away from the average molecular energy E_{M} and above the confinement energy E_{C}, the coherence length rapidly diverges such that it exceeds the photon resonance wavelength λ_{0}. The rapid divergence allows us to differentiate the localized and delocalized regimes and identify the transition from diffusive to ballistic transport.

Exact Results for the Tavis-Cummings and Hückel Hamiltonians with Diagonal Disorder

We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that in cases where the disorder has a Cauchy distribution, the disorder averaged one particle Green's function can be calculated directly, using a deterministic, complex (non-Hermitian) Hamiltonian. For this we use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solution for the case of N molecules with site disorder, confined to a microcavity, for any value of N. Our analysis shows that the width of the polaritonic states as a function of N depends on the nature of disorder, and hence it can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for Hückel type Hamiltonians with on-site Cauchy disorder and demonstrate its use.

Picocavities: a Primer

Picocavities are sub-nanometer-scale optical cavities recently found to trap light, which are formed by single-atom defects on metallic facets. Here, we develop simple picocavity models and discuss what is known and unknown about this new domain of atom-scale optics, as well as the challenges for developing comprehensive theories. We provide simple analytic expressions for many of their key properties and discuss a range of applications from molecular electronics to photocatalysis where picocavities are important.