Strong coupling between two-dimensional transition metal dichalcogenides and plasmonic-optical hybrid resonators

In the past decade, strong coupling of two-dimensional transition metal dichalcogenides (TMDs) with plasmonic and optical resonators has become an attractive field in cavity quantum electrodynamics. On one hand, how to enhance the Rabi splitting in such a system is important for applications. On the other hand, the underlying strong-coupling mechanism is not clear yet, especially for the complicated coupling case related to multiple photonic quasiparticles. Here we propose a plasmonic-optical hybrid resonator composed of a Au nanoantenna and photonic crystal cavity. When monolayer $\mathrm{Mo}{\mathrm{S}}_2$ is coupled with this hybrid resonator, we demonstrate a large Rabi splitting up to 460 meV, which is better than ever reported in similar systems. More importantly, we provide a deeper understanding of complicated coupling mechanisms in such a hybrid system, paving the way for studying strong light–matter interactions with multiple photonic quasiparticles in TMD materials coupled with different plasmonic-optical hybrid resonators.

Figure 1

(a) Schematic of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ coupled with a Au NA-PC cavity hybrid resonator. (b) Schematic of the 2D PC cavity. (c) Oscillator model of the hybrid system.

Figure 2

(a) Absorption spectrum of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ coupled with Au NAs. The solid black line is the anticrossing curve fitted by the coupled oscillator model. (b) Absorption spectrum as a function of $f_x$ when $r_{\mathrm{Au}}=40\mathrm{nm}$. Red, green, and yellow squares correspond to three absorption peaks when $f_x=0.3$. (c) Absorption curves of LSP mode, Ex mode, ENZ mode, and their coupled mode when $r_{\mathrm{Au}}=40\mathrm{nm}$. The inset shows the schematic of the coupled structure. (d) Electric field distributions on the y-z plane for three absorption peaks in (b).

Figure 3

(a) $\mathrm{Re}\left({\varepsilon }_{\mathrm{eff}}\right)$ and (b) $\mathrm{Im}\left({\varepsilon }_{\mathrm{eff}}\right)$ as a function of $f_x$. The insets in (a) and (b) show the $\mathrm{Re}\left({\varepsilon }_{\mathrm{Au}}\right)$ and $\mathrm{Im}\left({\varepsilon }_{\mathrm{Au}}\right)$, respectively. (c) ${\varepsilon }_{{\mathrm{MoS}}_2}$ as a function of wavelength when $f_x=0.3$. (d) A mode intensity distribution of the ENZ mode at 567 nm along the $z$ direction. The inset shows the electric filed distribution in the center of the $\mathrm{Mo}{\mathrm{S}}_2$ layer. (e), (f) $\mathrm{Re}\left(n_{\mathrm{eff}}\right)$ and $\mathrm{Im}\left(n_{\mathrm{eff}}\right)$ of the ENZ mode as a function of $f_x$.

Figure 4

(a) Absorption curves of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ coupled with a Au NA-PC cavity hybrid resonator for different values of $r_{\mathrm{Au}}$. (b) Absorption spectrum of the coupled system. Dashed lines represent the uncoupled photon, LSP, Ex, and ENZ modes, respectively. The solid black line is the anticrossing curve fitted by the coupled oscillator model. (c) Linewidth as a function of $r_{\mathrm{Au}}$ for four uncoupled modes and four branches in (a). (d) The mixing coefficients of four uncoupled modes as function of $r_{\mathrm{Au}}$. (d) Energy-state map of the coupled system.