Effective Mass in Dissipative Coupled Polaritons

TL;DR

The paper develops and analyzes a non-Hermitian polariton model incorporating both coherent and dissipative light–matter coupling. By deriving exact complex polariton branches and their Hopfield weights, it maps how dissipation, dissipative coupling, and detuning reshape level attraction, exceptional points, and the effective mass, including the emergence of bound states in the continuum only when both non-Hermitian channels are present. The study links full quantum descriptions to a classical mean-field limit via coherent states, showing consistent short-time signatures of negative mass and dynamical attractor/repulsor behavior tied to the imaginary parts of the eigenvalues. Overall, it provides a parametric roadmap for engineering non-Hermitian phenomena in polariton systems with potential implications for topological control, sensing, and non-reciprocal light–matter devices.

Abstract

Dissipative coupling refers to the effect where two systems interact with each other mediated by dissipation channels. Recent advances in controlling light-matter systems have opened new avenues to explore non-Hermitian effects arising from dissipative coupling, such as level attraction and anomalous dispersions. In this work, we perform a parametric study of these effects in a polariton system, i.e., a light-matter superposition, under both dissipative and coherent coupling. We characterize the effects of different sources of non-Hermitian behavior and analytically identify the conditions for the emergence of negative effective mass, exceptional points, and bound states in the continuum as a function of the light-matter detuning, the coherent-to-dissipative coupling ratio, and the relative decay rate of the non-interacting subsystems. We also analyze the classical limit of the polariton system within a non-Hermitian framework, employing coherent states.

Figures (5)

• Figure 1: (a) Real and (b) imaginary parts of the exciton-polariton energy as a function of detuning, and (c) and (d) as a function of momentum. In panels (a)–(d), different colors represent curves corresponding to different values of $\gamma_{x}/2\Omega=0.2$, $0.3$, $0.5$, $1.0$, and where the EPs occur. The orange color corresponds to the bare exciton and photon. In the third row, we show the density map of the effective mass $m^{*}$ as a function of detuning $\delta$ and the relative dissipation $\Delta\gamma$ for the (e) upper and (f) lower polariton branches. In panels (e) and (f), the solid black lines indicate the points where the effective mass vanishes. Throughout all panels, we have fixed $\gamma_{c}/2\Omega=0.1$.
• Figure 2: In panels (a)-(d) we show the same as Fig. \ref{['fig:1']} (a)-(d), but for different values of the $\tilde{\Omega}=\Omega_{\text{Im}}/\Omega=0.1$, $0.5$, $1.0$, and $3.0$. In the third row, we show the density map of the effective mass $m^{*}$ as a function of detuning $\delta$ and the dissipative coupling $\Omega_{\text{Im}}$ for the (e) upper and (f) lower polariton branches. In panels (e) and (f), the solid black lines indicate the points where the effective mass vanishes. Throughout all panels, we have fixed $\gamma_{c}/2\Omega=0.1$.
• Figure 3: In panels (a)-(d) we show the same as Fig. \ref{['fig:1']} (a)-(d), but for different values of the $\gamma_x/2\Omega=0.1,0.3,0.5$ and $1$, with $\gamma_{c}/2\Omega=0.1$ and $\Omega=\Omega_{\text{Im}}$. In panels (e) and (f), we show the same as in Fig. \ref{['fig:1']} (e) and (f), where we have taken $\gamma_{x}=0.5(2\Omega)$. The BIC condition is plotted as a white curve.
• Figure 4: Parametric solution for BIC as a function of (a) detuning and (b) momentum for $\Omega_{\text{Im}}/\Omega=0.2$, $0.5$, and $1.0$ as indicated in the figure.
• Figure 5: Temporal evolution of the classical polariton quadrature $q_{\sigma\mathbf{k}}(t)$ for the (top row) upper and (bottom row) lower polaritons at $\Omega_{\text{Im}}=\Omega$ and different values of relative dissipation $\Delta\gamma$ and $k$ as indicated in (a).