Disorder-Induced Spectral Splitting versus Rabi Splitting under Strong Light-Matter Coupling

TL;DR

This work challenges the conventional association of spectral splitting with polariton formation by showing that strong disorder can produce disorder-induced spectral splitting that mimics Rabi splitting in steady-state absorption. By developing a non-perturbative collective-mode framework that includes bright and dark molecular modes and validating it with three classical-electrodynamics–based approaches (homogeneous/isotropic, Monte Carlo, and collective-mode EOM) plus FDTD simulations for a plasmonic nanodisk, the authors derive a splitting scale of $\hbar\Omega_\pm = \hbar\Omega_v \pm \sqrt{N(|u_0|^2+\sigma_u^2)}$ and demonstrate that both bright-mode and dark-mode contributions can yield similar spectra. The results show that disorder-induced splitting can occur even when $|u_0|=0$, and that steady-state absorption alone cannot discriminate between polaritons and dark-state–driven splitting, especially in realistic plasmonic geometries where disorder is inherent. These findings motivate using time-resolved or off-resonant techniques to differentiate the underlying mechanisms and have implications for interpreting experiments in disordered light-matter systems.

Abstract

The notion of strong light-matter coupling is typically associated with the observation of Rabi splitting, corresponding to the formation of the hybrid light-matter states known as polaritons. However, this relationship is derived based on the assumption that disorder can be ignored or acts as a perturbative effect. Contrary to conventional treatment of disorder effects, we investigate the impact of strong disorder on the absorption spectrum by developing a non-perturbative effective model combined with classical electrodynamics simulation. Intriguingly, we find that strong disorder leads to an enhanced spectral splitting that closely resembles Rabi splitting, yet originates from a fundamentally different mechanism as induced by the dark modes. Specifically, we examine a disordered molecular ensemble in proximity to a plasmonic nanodisk and demonstrate disorder-induced spectral splitting in the absorption spectrum. This conclusion raises a controversial issue, suggesting that both polaritons (dominate in the strong coupling regime) and dark modes (dominate in the strong disorder regime) can lead to spectral splitting, and one cannot distinguish them solely based on the steady-state absorption spectrum.

Figures (3)

• Figure 1: Left: The phase diagram in terms of $\sqrt{N}|u_0|/\gamma_p$ and $\sqrt{N}\sigma_u/\gamma_p$. The dashed line depicts the criterion $N(|u_0|^2+\sigma_u^2)=\gamma_p^2$ and the shaded area indicates the parameter regime where the two peaks cannot be resolved. The orientation disorder is swept through $\theta_\text{max}= 0, \frac{1}{4}\pi, \frac{1}{2}\pi, \frac{3}{4}\pi, \pi$, labeled by (a)--(e) for the LWA cases ($\Delta{W}=0$, blue circles) and the non-uniform field cases ($\Delta{W}=1.1$, red diamonds). Right: The corresponding absorption spectra $P(\omega)/\omega$ are plotted for the LWA (blue dashed lines) and the non-uniform field (red solid lines) cases. Note that, while (e) indicates completely disordered photon-molecule coupling (i.e. $|u_0|=0$), we can resolve two absorption peaks when the coupling disorder is large. More importantly, although blue (a) and red (e) arise from different mechanisms, they exhibit nearly identical absorption spectra.
• Figure 2: The absorption spectrum ($P(\omega)/\omega$) of a disordered molecular ensemble as obtained by solving the collective mode EOM. We choose $\sqrt{N}\sigma_u \gg g_p$ and fix $\sqrt{N}\sigma_u$ and $\sqrt{N}\sigma_g$ and vary the correlation parameter $\xi=|\xi|e^{i\phi}$. (a) For $\phi=0$, $P(\omega)/\omega$ exhibit a single peak at $\omega=\omega_p$ for the uncorrelated case ($|\xi|=0$) and two peaks at $\omega=\Omega_\pm$ for the fully correlated case ($|\xi|=1$). (b) For $|\xi|=0.5$, the spectra with varying relative phase $\phi=0,0.5\pi,\pi,1.5\pi$ shows that the as induced by the interference between $a_p$ and $D_g$ modes.
• Figure 3: The steady-state absorption spectrum $P(\omega)/\omega$ of molecular ensemble near a plasmonic nanodisk (as shown in the schematic figure) is calculated by (I) homogeneous and isotropic approximation (dashed line), (II) Monte Carlo method (red error bar), (III) the collective-mode EOM (blue shaded area). Here $g_p$ is chosen to real-valued and positive and the plasmon resonance frequency is $\omega_p=6196~\text{cm}^{-1}$ and $\gamma_p = 130~\text{meV}$. The amplitude of the molecular transition dipole moment is chosen to be $\mu = 1.0 [\text{Debye}]$. For (II) and (III), the distribution of $\{g_j\}$ and $\{u_j\}$ based on the sampled molecules are plotted in a complex plane in (b) and (c). Note that both distributions are centered at the origin, implying that $g_0=0$ and $u_0=0$. The correlation between $\{g_j\}$ and $\{u_j\}$ are plotted in (c), showing that the molecule-field coupling and the molecule-plasmon coupling are partially correlated with $|\xi|\approx0.5$.