Interference-induced cavity resonances and imaginary Rabi splitting

TL;DR

The paper develops a general framework for polaritons in structured electromagnetic environments by introducing interference-induced resonances as effective non-Hermitian modes that couple to quantum emitters. Using a few-mode quantization, the authors map complex spectral densities $J_{\mathrm{EM}}(\omega)$ onto a small set of modes and derive how these resonances hybridize with emitters to form polaritons with imaginary Rabi splitting, even when single-mode strong coupling is not satisfied. They extend the theory to ensembles, showing collective coupling can yield long-lived polaritons that outlive dark excitonic states, with two distinct mechanisms for coupling multiple emitters to the antiresonance. Numerical simulations in a realistic hybrid metallodielectric platform confirm the predictions and demonstrate robustness to disorder, highlighting a new regime for engineering light–matter interactions via non-Hermitian spectral features.

Abstract

Polaritons are usually described within single-mode cavity QED models. However, nanophotonic environments typically involve several modes that spectrally overlap and interfere, giving rise to sharp dip features such as Fano profiles in the electromagnetic spectral density. Here, we identify these features as interference-induced resonances, effective electromagnetic modes with complex, non-Hermitian couplings to quantum emitters. We show that these modes hybridize with emitters to form polaritons even when the system parameters do not satisfy the single-mode strong-coupling criterion. Moreover, the resulting polaritons differ in their decay rates, a phenomenon we term imaginary Rabi splitting. Extending the analysis to ensembles, we find that coupling to interference-induced resonances produces long-lived polaritons that can outlast excitonic dark states. Numerical simulations of a realistic hybrid metallodielectric platform confirm these predictions and demonstrate their robustness against disorder and loss. Our results reveal a new polaritonic regime beyond the single-mode description, offering new opportunities for controlling light-matter interactions in complex electromagnetic environments.

Figures (4)

• Figure 1: The coupling of a two-level emitter to (a) a single-mode resonance with a Lorentzian spectral density, and (b) a two-mode cavity with a more complex spectral density. The latter can be described as the sum of a background plus an interference-induced resonance. The vertical dashed lines represent the emitter frequency. In panel (a), the QE frequency coincides with maximum of the Lorentzian-shaped ${\rm J}(\omega)$, whereas in panel (b), ${\rm J}(\omega_e)$ is the minimum of the spectral density.
• Figure 2: (a) Scheme of a hybrid cavity consisting of a Fabry-Perot cavity and multiple metal nanoparticles, each interacting with a different QE. (b) The diagonal entries of the spectral density, J$_{\alpha\alpha}(\omega)$, and the cross ones, J$_{\alpha\beta}(\omega)$, for the QE ensemble in panel (a). ${\rm J}_ \mathrm{ar}(\omega)={\rm J}_ \mathrm{ir}(\omega)$ is the spectral density of the antiresonance formed in this setup, and J$_{\alpha\alpha}^{bg}(\omega)$ and J$_{\alpha\beta}^{bg}(\omega)$ are the spectral densities obtained when subtracting J$_ \mathrm{ar}(\omega)$ from J$_{\alpha\alpha}(\omega)$ and J$_{\alpha\beta}(\omega)$, respectively.
• Figure 3: Decay rates of the eigenstates resulting from the QE-antiresonance coupling in the setup shown in \ref{['fig:2']}(a) as a function of: (a) $g$ when $d\sqrt{N}=\kappa_p/10$, and (b) $d$ when $g=\kappa_p/20$. Blue and black/gray lines correspond to polariton states, while the orange line renders the dark exciton states that do not interact with the antiresonance. Solid lines were obtained from full calculations, while dashed (adiabatic elimination of the plasmonic modes) and dotted (coupling to the antiresonance with the EM background treated in a Markovian manner) lines plot approximate calculations. (c) Steady state populations for the system in (a) under coherent driving of the cavity mode, normalized by the total population at the first excited manifold. (d) Same as (c) but for the system in (b). The insets in (c-d) demonstrate the conditions for almost-complete population of the narrow eigenstate.
• Figure 4: Decay rate of the eigenstates in the system in \ref{['fig:2']}(a) as a function of: (a) the detuning between the QE frequencies and the antiresonance (no disorder); (b) disorder in the QE frequencies; (c) disorder in the plasmon frequencies; (d) disorder in the plasmon linewidths; (e) disorder in the plasmon-emitter couplings; and (f) disorder in the plasmon-cavity couplings. The color code is the same as in \ref{['fig:3']}. In (b)-(f), $\delta X$ denotes the standard deviation of a Gaussian distribution with mean $\overline{X}$, and the shaded regions span one standard deviation above and below the geometric mean of the decay rates (solid lines).