Anomalous time delays and quantum weak measurements in optical micro-resonators

TL;DR

This paper investigates how near-zero scattering in optical micro-resonators causes large time delays and frequency shifts, revealing a link to weak measurements and demonstrating these effects experimentally.

Contribution

It introduces a novel analysis of anomalous time delays and shifts in optical micro-resonators, connecting non-Hermitian physics with weak measurement amplification in a scalar wave system.

Findings

Large time delays observed near zero scattering points

Experimental verification of weak-measurement amplification

Generic applicability to quantum and classical scattering systems

Abstract

We study inelastic resonant scattering of a Gaussian wave packet with the parameters close to a zero of the complex scattering coefficient. We demonstrate, both theoretically and experimentally, that such near-zero scattering can result in anomalously-large time delays and frequency shifts of the scattered wave packet. Furthermore, we reveal a close analogy of these anomalous shifts with the spatial and angular Goos-H\"anchen optical beam shifts, which are amplified via quantum weak measurements. However, in contrast to other beam-shift and weak-measurement systems, we deal with a one-dimensional scalar wave without any intrinsic degrees of freedom. It is the non-Hermitian nature of the system that produces its rich and non-trivial behaviour. Our results are generic for any scattering problem, either quantum or classical. As an example, we consider the transmission of an optical pulse through a nano-fiber with a side-coupled toroidal micro-resonator. The zero of the transmission coefficient corresponds to the critical coupling conditions. Experimental measurements of the time delays near the critical-coupling parameters verify our weak-measurement theory and demonstrate amplification of the time delay from the typical inverse resonator linewidth scale to the pulse duration scale.