Non-secular polariton leakage and dark-state protection in hybrid plasmonic cavities

TL;DR

The paper tackles radiative and absorption losses in hybrid plasmonic cavities by formulating a time-local, completely positive master equation that preserves non-secular cross-damping between upper and lower polaritons. By combining a Hopfield diagonalization with a Dyson self-energy approach, it connects the microscopic material response to a GKSL framework, and introduces a design rule based on the ratio $\Delta/\gamma_{\mathrm{D}}$ to predict when bath-induced coherence and dark-polariton protection emerge. It demonstrates, through both analytical construction and numerics in a truncated two-polariton space, that non-secular leakage can sustain dark-state populations and generate bath-induced coherence in the unresolved regime, while converging to secular behavior when $\Delta\gg\gamma_{\mathrm{D}}$. The results offer a practically accessible route to engineer plasmonic-cavity devices with enhanced lifetimes and controllable polariton dynamics, and suggest extensions to more complex reservoirs, output fields, and non-Markovian regimes.

Abstract

A major issue in exploiting plasmonic cavities as key components in nanotechnology is the effect of radiative and absorption losses on their electrodynamic behavior. Treating them as open-systems, we derive a time-local, completely positive master equation that retains non-secular interference between decay pathways and reduces to the standard secular description when the environment resolves polariton splitting. When it does not, the theory predicts order-one deviations from secular leakage dynamics, including bath-induced coherences and stabilization of dark polaritons, and provides a simple design criterion based on the ratio of polariton splitting to reservoir linewidth. A time-resolved leakage measurement, such as transmission, reflectivity, or photoluminescence, can be used to observe these effects.

Figures (4)

• Figure 1: Schematic representation of EC–SPP hybridization and dispersion of eigenfrequencies $\omega_\pm$. The cavity is illuminated from below and supports an EC mode at $\omega_\mathrm{c}$. SPPs with frequency $\omega_\mathrm{pl}$ are excited by a metasurface (e.g., a periodic lattice of nanoparticles) on the illuminated face of the cavity and propagate along the dielectric/reflector interface, which is assumed to be a medium-low loss material. The dispersion $\omega_\pm$ is calculated as in 2025Vallone_NPJ for $\omega_\mathrm{c} = 1$ eV, plasma frequency $\Omega_\mathrm{pl} \approx 8.5$ eV, dimensionless EC–SPP coupling constant $\xi = 0.02$, and zero losses.
• Figure 2: Time evolution under the two-stage drive protocol of the single-excitation bright and dark populations, $\langle \hat{P}_{\mathrm{b}}(t)\rangle$ and $\langle \hat{P}_{\mathrm{d}}(t)\rangle$. Solid lines: full non-secular common-bath leakage; dashed lines: secular approximation (diagonal Kossakowski matrix). Parameters: $T=300$ K, $\gamma_\mathrm{D}=0.04$ ps$^{-1}$, $\Gamma_{\mathrm{pl}}=2\gamma_\mathrm{D}$, $\gamma_{\downarrow}=10^{-3}$ ps$^{-1}$ (with $\gamma_{\uparrow}$ fixed by detailed balance), $\gamma_{\phi}=5\times10^{-4}$ ps$^{-1}$, and drive amplitude $f=0.01$ ps$^{-1}$. The bright drive is applied for $0\le t<t_\mathrm{sw}$ with $t_\mathrm{sw}=1000$ ps, while for $t_\mathrm{sw}\le t<t_\mathrm{off}$ (with $t_\mathrm{off}=3000$ ps) the illumination is switched to the dark drive and a Raman-like coupling $\mathcal{R}_\mathrm{UP\!-\!LP}=0.01$ ps$^{-1}$ is turned on. Panels (a,b): $\Delta=0.015$ ps$^{-1}$; panels (c,d): $\Delta=0.15$ ps$^{-1}$.
• Figure 3: (Color online) Stage-2 maximum deviation $D_{\max}^{(X)}(\Delta,\gamma_\mathrm{D})$, \ref{['eq:Dmax_def']}, between the non-secular common-bath leakage model and its secular approximation, for $X=\langle\hat{P}_\mathrm{b}\rangle$ (a), $\langle\hat{P}_\mathrm{d}\rangle$ (b), and $|\rho_\mathrm{c}|$ (c), evaluated over the stage-2 time window of Fig. \ref{['f:fig_2']} while scanning $\Delta$ and $\gamma_\mathrm{D}$. The bath spectrum is Lorentzian, \ref{['eq:J_Lorentz']}, with FWHM $\gamma_\mathrm{D}$ and peak rate $\Gamma_\mathrm{pl}\equiv J(\omega_\mathrm{pl})=2\gamma_\mathrm{D}$. Weak coherent couplings: $f=\mathcal{R}_\mathrm{UP\!-\!LP}=0.01~\mathrm{ps}^{-1}$.
• Figure 4: (Color online) Same as Fig. \ref{['f:fig_3']}, but for stronger coherent couplings $f=\mathcal{R}_\mathrm{UP\!-\!LP}=0.1~\mathrm{ps}^{-1}$.