Chiral Polaritonics: Analytical Solutions, Intuition, and Use

Preferential selection of a given enantiomer over its chiral counterpart has become increasingly relevant in the advent of the next era of medical drug design. In parallel, cavity quantum electrodynamics has grown into a solid framework to control energy transfer and chemical reactivity, the latter requiring strong coupling. In this work, we derive an analytical solution to a system of many chiral emitters interacting with a chiral cavity similar to the widely used Tavis-Cummings and Hopfield models of quantum optics. We are able to estimate the discriminating strength of chiral polaritonics, discuss possible future development directions and exciting applications such as elucidating homochirality, and deliver much needed intuition to foster the newly flourishing field of chiral polaritonics

Toward Molecular Chiral Polaritons

Coupling between light and material excitations underliesa widerange of optical phenomena. Polaritons are eigenstates of a coupledsystem with a hybridized wave function. Owing to their hybrid composition,polaritons exhibit at the same time properties typical for photonicand electronic excitations, thus offering new ways for controllingelectronic transport and even chemical kinetics. While most theoreticaland experimental efforts have been focused on polaritons with electric-dipolecoupling between light and matter, in chiral quantum emitters, electronictransitions are characterized by simultaneously nonzero electric andmagnetic dipole moments. Thus, it is natural to wonder what kindsof novel effects chirality may enable in the realm of strong light-mattercoupling. Right now, this field located at the intersection of nanophotonics,quantum optics, and chemistry is in its infancy. In this Perspective,we offer our view toward chiral polaritons. We review basic physicalconcepts underlying chirality of matter and electromagnetic field,discuss the main theoretical and experimental challenges that needto be solved, and consider novel effects that could be enabled bystrong coupling between chiral light and matter

Dielectric resonances of ordered passive arrays

The electrical and optical properties of ordered passive arrays, constituted of inductive and capacitive components, are usually deduced from Kirchhoff's rules. Under the assumption of periodic boundary conditions, comparable results may be obtained via an approach employing transfer matrices. In particular, resonances in the dielectric spectrum are demonstrated to occur if all eigenvalues of the transfer matrix of the entire array are unity. The latter condition, which is shown to be equivalent to the habitual definition of a resonance in impedance for an array between electrodes, allows for a convenient and accurate determination of the resonance frequencies, and may thus be used as a tool for the design of materials with a specific dielectric response. For the opposite case of linear arrays in a large network, where periodic boundary condition do not apply, several asymptotic properties are derived. Throughout the article, the derived analytic results are compared to numerical models, based on either Exact Numerical Renormalisation or the spectral method.Comment: 12 pages, 12 figure

Spectral gap of the totally asymmetric exclusion process at arbitrary filling

We calculate the spectral gap of the Markov matrix of the totally asymmetric simple exclusion process (TASEP) on a ring of L sites with N particles. Our derivation is simple and self-contained and extends a previous calculation that was valid only for half-filling. We use a special property of the Bethe equations for TASEP to reformulate them as a one-body problem. Our method is closely related to the one used to derive exact large deviation functions of the TASEP

Fiber-optical analogue of the event horizon

The physics at the event horizon resembles the behavior of waves in moving media. Horizons are formed where the local speed of the medium exceeds the wave velocity. We use ultrashort pulses in microstructured optical fibers to demonstrate the formation of an artificial event horizon in optics. We observed a classical optical effect, the blue-shifting of light at a white-hole horizon. We also show by theoretical calculations that such a system is capable of probing the quantum effects of horizons, in particular Hawking radiation.Comment: MEDIA EMBARGO. This paper is subject to the media embargo of Scienc

POPLMark reloaded: Mechanizing proofs by logical relations

We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks