At the nanoscale, the strong interaction between the emitter and optical cavity has been considered to be a pivotal factor propelling the advancement and application of quantum devices^[1]. In the strong coupling regime, the coherent and incoherent exchange of photon energy collectively contributes to radiation coupling. This not only modifies the energetics of the coupled system but also dominates its dynamics by altering the radiative damping of hybrid modes, resulting in sub- and super-radiant phenomena^[2,3]. For instance, polaritons formed through coherent energy exchange in strong coupling systems provide an excellent platform for achieving Bose–Einstein condensation^[4,5], low-threshold lasing^[6], quantum information processing and storage^[7], and the realization of photonic logic gate structures^[8]. The coupling strength, defined as $g=\sqrt{N}\mu |E_{\mathrm{vac}}|\propto \mu \sqrt{N/V}$, can be enhanced by reducing the mode volume ($V$) of the optical cavity and increasing the transition dipole moment ($\mu$) of the emitter^[9]. In this regard, plasmonic nanostructures have been extensively employed to achieve strong coupling under ambient conditions^[10], leveraging the advantage of strong local field enhancement^[11], thereby enhancing the rate of coherent energy exchange. The coherent energy exchange in strongly coupled systems, consisting of metal nanostructures and various emitters such as quantum dots^[12], dye molecules^[13], and J-aggregates^[14], has resulted in mode splitting in the spectral domain and ultrafast coherent energy oscillation in the time domain. The coherent plasmon and exciton interaction is of central importance for various applications, including all-optical ultrafast plasmonic circuits^[13], nanoscale optical modulators, and quantum gates^[12]. However, the coherent coupling is influenced by the photostability of these organic molecules or quantum dots, as well as the heterogeneous and disordered assembly of excitons.

Monolayer transition metal dichalcogenides (TMDs) are direct bandgap semiconductor materials characterized by significant transition dipole moments, relative inertness, optical stability, and large exciton binding energy^[15–17]. Recently, the plasmon–exciton coherent coupling has been extensively investigated in monolayer TMDs integrated with a variety of plasmonic structures, including single metallic nanoparticles^[18], particle-on-mirror (PoM) nanocavities^[10,19], and metallic nanostructure arrays^[20,21]. As an example, in the hybrid structure composed of the monolayer ${\mathrm{WS}}_2$ and PoM nanocavity, neutral excitons can coherently couple with magnetic plasmon mode, leading to a Rabi splitting energy of 200 meV^[22]. Of note, besides the coherent coupling, the hybrid system also has an incoherent damping channel. In this channel, the spontaneously emitted photon decays to a continuum reservoir and is subsequently reabsorbed by the other subsystem without conserving any phase relationship^[3,22,23]. Consequently, this channel inevitably degrades the coherence of the coupling process^[24] and hinders the potential applications in quantum computing and communication^[25]. Current studies reveal that the incoherent coupling strength of hybrid systems can be significantly mitigated by suppressing the photon exchange between the two subsystems through the continuum reservoir^[23,26]. This is achieved by aligning the net electric dipole moment (${\mu }_{\text{pl}}$) perpendicular to the exciton transition dipole moment (${\mu }_{\text{ex}}$) and minimizing the nonradiative decay of the exciton^[24]. However, to achieve a strong coupling, the electric dipole moment of the plasmonic mode is commonly required to be parallel with the dominated in-plane exciton of TMDs^[20,27], which simultaneously introduces large decoherence to the coupled system. On the other hand, for monolayer TMDs, the underlying substrate inevitably introduces the nonradiative recombination losses caused by charged impurities, optical phonons, and surface roughness^[28,29], resulting in the broadening of the exciton linewidth^[24,30]. These two factors pose substantial obstacles in suppressing incoherent damping during strong coupling.

To address these challenges, we propose a strong coupling system by integrating monolayer ${\mathrm{WS}}_2/\text{graphene}$ van der Waals heterostructures (${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs) with an Au nanocube (Au NC). Growing monolayer ${\mathrm{WS}}_2$ on Gr, featured by defect-free lattices and smooth surfaces, effectively suppresses nonradiative pathways of neutral excitons^[31], leading to a narrower photoluminescence (PL) linewidth^[32,33]. Additionally, a tilted plasmonic dipole is employed to achieve strong coupling with the in-plane exciton in ${\mathrm{WS}}_2$, while simultaneously maintaining high coherence by suppressing the photon exchange between the two subsystems. These two advantages afford us to observe a plasmon–exciton strong coupling, characterized by a Rabi splitting up to 120 meV and a remarkably low incoherent coupling strength of 1 meV. Remarkably, this incoherent coupling strength is three times smaller than the optimal results reported in current plasmon–exciton hybrid systems.

The scattering spectra of the coupled systems were calculated using the finite-element method (FEM), with experimental counterparts as models. The permittivity values for gold, graphene, and monolayer ${\mathrm{WS}}_2$ were determined based on the experimental data^[34–36], while those of ${\mathrm{Al}}_2{\mathrm{O}}_3$ and CTAB were set to 1.5 and 1.435, respectively. The scattering field is calculated through a two-step method, wherein the background field originating from the plane wave incident on the bare substrate serves as the excitation in the presence of Au NC.

The coupled system consists of an Au NC positioned on a monolayer ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs, as shown in Fig. 1(a). The bright-field image of the coupled system is presented in Fig. 1(b), where the monolayer ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs flakes, with a dimension over 20 µm, are indicated by the white dashed box. In Fig. 1(c), we present the scanning electronic microscope (SEM) image of the coupled system, wherein the constituent Au NC, denoted by a white dashed circle, exhibits an edge length of 87 nm as shown in Fig. 1(d). The monolayer ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs is characterized by the Raman spectrum depicted by the blue solid lines of Fig. 1(e), where the peak positions at 351.6, 356.3, and $418.1{\mathrm{cm}}^{-1}$ are identified as 2LA, ${\mathrm{E}}_{2g}^1$, and ${\mathrm{A}}_{1g}$ modes, respectively. The frequency difference of $61.8{\mathrm{cm}}^{-1}$ between ${\mathrm{A}}_{1g}$ and ${\mathrm{E}}_{2g}^1$ modes, along with a peak intensity ratio of 6.2 for $I(2\mathrm{LA})/I({\mathrm{A}}_{1g})$, confirms the monolayer thickness of the as-grown ${\mathrm{WS}}_2$ flakes^[37,38]. The Raman spectrum of Gr [Fig. 1(e)] shows an $I(G)/I({\mathrm{Si}}_G)$ peak area intensity ratio of 0.32, suggesting that the graphene primarily consists of regions with 4 layers^[39].

The scattering spectrum of the Au NC ($L=87\mathrm{nm}$) under $p$-polarized illumination at an incident angle of 60° is shown in Fig. 2(a). It exhibits a prominent plasmon resonance at 584 nm with a linewidth of 210 meV (${\mathrm{\Gamma }}_{\text{pl}}=2{\gamma }_{\text{pl}}$). The collaboration of the simulated charge map enables us to identify this plasmonic mode originating from a tilt-oriented electric dipole, as depicted in the inset of Fig. 2(a). This configuration can achieve a balance between the plasmon–exciton strong coupling and the suppression of incoherent coupling strength. The plasmonic mode exhibits a maximum enhancement factor of 13 for the in-plane electric field, as shown in Fig. 2(b), making it suitable for strong coupling with the in-plane neutral exciton of ${\mathrm{WS}}_2$. Compared to the PoM nanocavity^[19], the out-of-plane component of the electric field is relatively weak, which allows us to disregard the contribution of dark excitons to the scattering spectrum in this experiment. Figure 2(c) depicts the PL spectra of monolayer ${\mathrm{WS}}_2$ and ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs. Compared with monolayer ${\mathrm{WS}}_2$, the neutral exciton emission from the vdWhs exhibits a redshift of 4 meV due to the decreased tensile stress in ${\mathrm{WS}}_2$ grown on Gr^[32,40,41]. Notably, the ${\mathrm{WS}}_2$ in the vdWhs region demonstrates fewer defects and charged impurities^[32], which effectively suppresses nonradiative pathways of neutral excitons^[28,29,32], resulting in a narrower PL linewidth (${\mathrm{\Gamma }}_{\text{ex}}=2{\gamma }_{\text{ex}}=20\mathrm{meV}$) compared with the monolayer ${\mathrm{WS}}_2$ (64 meV). The lower panel of Fig. 2(a) shows a typical dark-field scattering spectrum of the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC coupled system, revealing a pronounced dip near the position of the neutral exciton. This observation indicates significant coupling arising from the interaction between the plasmonic dipole mode and neutral excitons. Figure 2(d) shows the mode volume of two coupled systems, i.e., ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC and ${\mathrm{WS}}_2\text{-}\mathrm{Au}$ NC, as a function of wavelength. As seen, owing to the semimetallic nature of Gr, the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC exhibits a smaller mode volume of ${10}^3{\mathrm{nm}}^3$, which is comparable to the state-of-the-art results achieved with individual nanoparticles such as gold bipyramids^[27] and ultra-small gold nanorods^[42]. Similar to the PoM nanocavity, the plasmonic mode of the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC coupled system has the potential to enhance PL emission^[19]. More importantly, this tightly confined electric field is highly favorable for reducing the number of excitons involved in the strong coupling.

According to the Maxwell–Garnett theory, the plasmon resonance wavelength strongly depends on the local dielectric environment^[43]; therefore, a dynamically adjustable coupling system can be achieved by changing the dielectric screening effect through successively depositing alumina layers onto the sample using atomic layer deposition^[44]. For an Au NC on the ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate, the dipolar plasmonic resonance can be redshifted from 584 to 644 nm by increasing the coating thickness from 0 to 15.4 nm (see Fig. 3). Consequently, this spectral tunability ensures plasmon resonance frequency ${\omega }_{\text{pl}}$ shifts across that of exciton ${\omega }_{\text{ex}}$, as illustrated by the dots in Fig. 4(a). It is observed that the scattering spectra of the coupled system at room temperature consistently exhibit a dip near the position of the exciton at different detunings, demonstrating an evident anticrossing behavior. The excitonic behavior of TMDs remains relatively stable at room temperature, thereby mitigating the effects of temperature-induced dephasing on excitonic states and minimizing the reduction in exciton coherence, which may consequently influence plasmon–exciton coupling^[45]. Moreover, the simulated scattering spectra are consistent with the anticrossing behavior of the coupled system, as shown in Fig. 4(b). It is worth noting that an enhanced exciton oscillation strength results in a simulated coupling strength in the scattering spectra that surpasses the experimental value^[44,45].

To explore the coupling effect between the excitons and the dipolar mode, we fitted the scattering spectra with a Fano-like line shape $S(\omega )={|s(\omega )|}^2$ with the scattering coefficient $s(\omega )$ defined as^[23]$$s(\omega )=a_b+\sum _{k=\mathrm{UPB},\mathrm{LPB}}\frac{b_k{\gamma }_k{e}^{i{\varphi }_k}}{\omega -{\omega }_k+i{\gamma }_k},$$(1)where $a_b$ denotes the background amplitude, ${\varphi }_k$ represents the spectral phase of the hybrid states, and $b_k$ is the amplitude. The fitted spectra shown as solid lines in Fig. 4(a) are in good agreement with the experiment results. However, due to the low radiation efficiency of these higher-order modes around 550 nm, they appear comparatively weak in the experimental scattering spectrum. Consequently, our theoretical model mainly focused on investigating the coupling between tilt-oriented electric dipoles and neutral excitons. This discrepancy between the fitted and simulated scattering spectra arises as a result.

Figures 5(a) and 5(e) present two spectral maxima (${\omega }_k$) and their corresponding spectral full width at half-maximum (FWHM, denoted by ${\mathrm{\Gamma }}_k=2{\gamma }_k$), which are extracted from the measured scattering spectra using Eq. (1). To further analyze the coherent and incoherent coupling process of a coupled system, we employ the coupled-oscillator model (COM)^[45] with a non-Hermitian Hamiltonian to describe the eigenvalue problem^[14,23]: $$(\left[\begin{array}{cc}{\overline{\omega }}_{\text{pl}}& {\mathrm{\Omega }}_R\\ {\mathrm{\Omega }}_R& {\overline{\omega }}_{\mathrm{ex}}\end{array}\right]-i\left[\begin{array}{cc}0& {\gamma }_{xp}\\ {\gamma }_{xp}& 0\end{array}\right]){\left[\begin{array}{c}\alpha \\ \beta \end{array}\right]}_{\pm }=E_{\pm }{\left[\begin{array}{c}\alpha \\ \beta \end{array}\right]}_{\pm },$$(2)where ${\overline{\omega }}_{\text{pl}}={\omega }_{\text{pl}}-i{\gamma }_{\text{pl}}$ and ${\overline{\omega }}_{\mathrm{ex}}={\omega }_{\mathrm{ex}}-i{\gamma }_{\mathrm{ex}}$ are the complex resonance frequencies of the plasmon mode and exciton, respectively. ${\mathrm{\Omega }}_R$ represents the coupling strength, ${\gamma }_{xp}$ denotes the incoherent coupling strength, and $\alpha$ and $\beta$ are elements of the eigenvector (Hopfield coefficients) and satisfy ${|\alpha |}^2+{|\beta |}^2=1$. The diagonalization of this Hamiltonian results in the emergence of two polaritonic eigenvalues^[23]: $$E_{\pm }=\left(\frac{{\overline{\omega }}_{\text{pl}}+{\overline{\omega }}_{\mathrm{ex}}}{2}\right)\pm \sqrt{{\left(\frac{{\overline{\omega }}_{\text{pl}}-{\overline{\omega }}_{\mathrm{ex}}}{2}\right)}^2+({|{\mathrm{\Omega }}_R|}^2-{\gamma }_{xp}^2)-2i{\gamma }_{xp}\mathrm{Re}({\mathrm{\Omega }}_R)}.$$(3)

Figures 5(a) and 5(b) show the fitting results to the peak energies of the upper polariton branch (UPB) and lower polariton branch (LPB) using Eq. (3). The Rabi splitting energy of the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC coupled system can be obtained as 120 meV at zero detuning $\delta =|{\omega }_{\text{pl}}-{\omega }_{\text{ex}}|=0$, satisfying the criterion for strong coupling $2{\mathrm{\Omega }}_R>({\mathrm{\Gamma }}_{\text{pl}}+{\mathrm{\Gamma }}_{\text{ex}})/2$. In Fig. 5(b), we display the anticrossing behavior of the ${\mathrm{WS}}_2\text{-}\mathrm{Au}$ NC coupled system, where the Rabi splitting was found to be 140 meV, indicating that the system also falls into the strong coupling regime. The Hopfield coefficients of the UPB and LPB versus the detuning $\delta$ are shown in Figs. 5(c) and 5(d) for two coupled systems. At zero detuning, both polaritons equally incorporate contributions from the plasmon and the exciton. In a system with $\delta >0$, the UPB primarily exhibits plasmon-like characteristics, while the LPB predominantly manifests excitonic attributes. Conversely, in a system with $\delta <0$, there is a reversal in the composition of polaritons. The fit to the spectral width of the UPB and LPB using Eq. (3) is shown in Figs. 5(e) and 5(f). It is worth noting that the spectral widths of the UPB in the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NCs and ${\mathrm{WS}}_2\text{-}\mathrm{Au}$ NCs exceed that of LPB by 2 and 10 meV at zero detuning, respectively. In particular, the incoherent coupling strengths (${\gamma }_{xp}=1\mathrm{meV}$) of ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs are found to be three times lower than the previously reported optimal results in plasmon–exciton hybrid systems^[3,22–24]. Therefore, the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NCs coupled system significantly reduces incoherent coupling strength while preserving coherent energy exchange in strong coupling for two reasons: (i) the narrower exciton linewidth and (ii) the modest coupling strength between the tilted electric dipole and the in-plane exciton.

To evaluate the exciton number evolved in the strong coupling, the coupling strength can be expressed as $${\mathrm{\Omega }}_R={\mu }_0\sqrt{\frac{4\pi \hslash Nc}{\lambda \epsilon {\epsilon }_{0}V}},$$(4)where $N$, $V$, $\lambda$, and $\epsilon$ are the effective exciton numbers participating in the coupling, mode volume, exciton wavelength, and relative dielectric function, respectively. The transition dipole moment value of monolayer ${\mathrm{WS}}_2$ was taken from Ref. [21], i.e., ${\mu }_0=7.53\mathrm{D}$. The coupling strength of ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC is determined to be 60 meV when it undergoes strong coupling. Considering the effective mode volume of $7.04\times {10}^3{\mathrm{nm}}^3$, the exciton number is estimated to be $N\approx 114$ at resonance, which is much smaller than that in monolayer ${\mathrm{WS}}_2\text{-}\mathrm{Au}$ NC ($N\approx 1036$). As a result, the ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs-Au NC coupled system facilitates coherent coupling between a reduced number of excitons and a plasmonic dipole mode, achieved by effectively suppressing the incoherent coupling strengths. The reduction in the exciton number can enhance the response speed of optical modulation and improve the fidelity and coherence time of quantum gates, making it highly favorable for quantum computing and communication technologies^[46,47].

In conclusion, we have proposed a coherent plasmon–exciton coupling system consisting of the monolayer ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs and the Au NCs. The defect-free lattices and smooth surface of Gr effectively suppress the nonradiative pathways of neutral excitons in ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs, resulting in a narrower PL linewidth of 20 meV compared with monolayer ${\mathrm{WS}}_2$ (64 meV). By integrating the Au NC with the monolayer ${\mathrm{WS}}_2/\mathrm{Gr}$ vdWhs, we have demonstrated strong coupling between the in-plane neutral exciton and a tilted plasmonic dipole. Simultaneously, coherence is preserved by suppressing the photon exchange between the two subsystems through the continuum reservoir. The coupled system has not only achieved a large Rabi splitting energy of 120 meV but also ensured an exceptionally low incoherent coupling strength of 1 meV. Our results open up an avenue to maintain high coherence in coupled systems and hold promise for enhancing the performance of novel quantum nanophotonic devices.