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Springer series in optical sciences/SPringer series in optical sciences

Weak Coupling, Strong Coupling, Critical Coupling and Fano Resonances: A Unifying Vision

Simone Zanotto

Published Jan 1, 2018• 3 citations
Publisher
DOI
10.1007/978-3-319-99731-5_23

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A critical aspect of quantum mechanics is the nonlocal nature of the wavefunction, a characteristic that may yield unexpected coupling of nominally isolated systems. The capacity to detect this coupling can be vital in many situations, especially those in which its strength is weak. In this work we demonstrate an approach to such detection by making use of one of the most ubiquitous of wave-interference phenomena, namely the Fano resonance. The focus of this joint experimental and theoretical work is on demonstrating a novel form of \textit{nonequilibrium} Fano resonance, that is very different in nature to the usual (quasi-equilibrium) implementations of this phenomenon. The essential idea of our approach is to exploit the strong sensitivity of the Fano resonance to the presence of additional transmission pathways, as a means to identify the coupling of some host system to an \textit{intruder}. Crucially, our nonequilibrium scheme allows us to detect the presence of \textit{hidden} components within some system, even while they remain \textit{invisible} in near-equilibrium transport. For a proof-of-concept demonstration of this phenomenon, we implement an electron-wave interferometer from mesoscopic quantum point contacts. The wave-based origins of the Fano resonance imply, however, that our scheme should be widely realizable across a variety of physical platforms.
Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.
N\mathcal{N}N emitters collectively coupled to a quantized cavity mode are described by the Tavis-Cummings model. We present a complete analytical solution of the model in the presence of inhomogeneous couplings and energetic disorder. We derive the exact expressions for the bright and the dark sectors that decouple the disordered model and find that, in the thermodynamic limit, the energetic disorder transforms the bright sector to Fano's model that can be easily solved. We thoroughly explore the effects of energetic disorder assuming a Gaussian distribution of emitter transition energies. We compare the Fano resonances in optical absorption and inelastic electron scattering in both the weak and the strong coupling regimes. We study the evolution of the optical absorption with an increase in the disorder strength and find that it changes the lower and upper polaritons to their broadened resonances that finally transform to a single resonance at the bare cavity photon energy, thus taking the system from the strong to the weak coupling regime. Interestingly, we learn that Rabi splitting can exist even in the weak coupling regime, while the polaritonic peaks in the strong coupling regime can represent almost excitonic states at intermediate disorder strengths. We also calculate the photon Green's function to see the effect of cavity leakage and nonradiative emitter losses and find that the polariton line width exhibits a minimum as a function of detuning when the cavity leakage is comparable to the Fano broadening.