Polaritons and excitons: Hamiltonian design for enhanced coherence

Abstract

The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian—connections between sites (or molecules) made by electronic coupling—is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.

Disorder enhanced vibrational entanglement and dynamics in polaritonic chemistry

“…The observation of large-scale entanglement entropy build-up on very short femtosecond timescales suggests that quantum effects can play an important role in polaritonic chemistry experiments on timescales faster then the cavity-decay for experimentally feasible cavities with low Q factors (Q ∼ 1000). Our work highlights the general importance of disorder for understanding polaritonic chemistry [53][54][55].…”

Long-range interactions boost singlet exciton diffusion in nanofibers of $\pi$-extended polymer chains

“…As a matter of fact, our excitonic Hamiltonian retaining the full range of interactions is intermediate between the nearest-neighbor one-dimensional model for charge transport and the star-like graph pertaining to polaritons, with the latter providing ensemble properties that are more robust to disorder than the former (i.e. more prompt to exciton delocalization thanks to reduced von Neumann entropy) [32]. Exciton delocalization along polymer chains somehow "redistributes" the total excitonic interactions among shortand long-range intermolecular contributions in a way that is favorable to energy migration between chains, the weak distance dependence of the excitonic interactions in the -extended polymer chains offering multiple efficient pathways for long-distance energy migration.…”

Catalysis by Dark States in Vibropolaritonic Chemistry

“…Disorder, despite its ubiquity in molecular systems, has often been ignored when modeling molecules under strong light-matter coupling. Only recently has it been shown that the strong coupling of disordered chromophores to an optical cavity mode can produce dark states which are delocalized on multiple molecules [40,41] (hereafter, referred as semilocalized). This semilocalization is predicted to improve or even enable coherent energy transport [40,42].…”

“…Next, we examine the delocalization of the dark modes. For the purpose of studying chemical reactions, it is useful to compute the molecular participation ratio (PR) [41,44]. This measure, defined as…”