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

M Asano,L Yang,K Y Bliokh,T Yamamoto,Y S Kivshar,Ş.K Özdemir,A G Kofman,Y P Bliokh,R Ikuta,F Nori,N Imoto

doi:10.1038/ncomms13488

Abstract

Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos–Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale.

Highlights

Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves
We show that in such near-zero scattering, the wave packet experiences an anomalously large time delay and a large frequency shift
Assuming that the spectral width of the wave packet is much smaller than the linewidth of the resonance, the typical time delay is estimated as the inverse linewidth, that is, the time the pulse is trapped in the resonator[9]

Summary

Introduction

Wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. We show that in such near-zero scattering, the wave packet experiences an anomalously large time delay (either positive or negative) and a large frequency shift. Using the extended theory of quantum weak measurements[14,29], we derive simple expressions that accurately describe the anomalous (but finite) time and frequency shifts for near-zero scattering.

Results

Conclusion