Anomalous time delays and quantum weak measurements in optical   micro-resonators
  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. 
M. Asano, K.Y. Bliokh, Y.P. Bliokh, A.G. Kofman, R. Ikuta, T.   Yamamoto, Y.S. Kivshar, L. Yang, N. Imoto, S.K. Ozdemir, and...
physics.optics quant-ph