Demonstrating Strong Light–Matter Coupling of a Single Molecule in a Blue‑Detuned Plasmonic Nanohole Trap

Introduction

Optical dipole traps have become a cornerstone technology for manipulating atoms and molecules, enabling Bose‑Einstein condensation, precision tests of fundamental physics, and ultra‑accurate measurement of physical constants [1–3]. In red‑detuned traps, particles are drawn toward regions of maximal intensity, whereas blue‑detuned traps confine particles to the nodes of the optical field, reducing scattering‑induced heating and light‑shift perturbations [5–8]. However, creating stable blue‑detuned traps typically requires complex geometries [9,10]. Surface plasmon polaritons (SPPs) – hybrid modes of light and free‑electron oscillations at metal–dielectric interfaces – offer a compelling platform for integrating optical trapping with sub‑wavelength confinement, paving the way for compact, high‑field‑gradient traps [11–18]. Recent work has demonstrated atom trapping in plasmonic nanohole arrays [20] and highlighted the extraordinary optical transmission (EOT) phenomenon that enhances local fields [32–34]. Combining these advances, we explore the possibility of trapping a single molecule in a plasmonic nanohole array while simultaneously achieving strong light–matter coupling, a key ingredient for quantum information processing [21–23].

Achieving strong coupling with a single molecule remains a formidable challenge, largely because the interaction strength scales inversely with the mode volume and directly with the number of emitters. Plasmonic cavities can reduce mode volumes dramatically, enabling room‑temperature strong coupling with isolated emitters [24–26]. Here, we theoretically demonstrate that a quasi‑single molecule trapped in a blue‑detuned plasmonic nanohole array can reach the strong‑coupling regime, as evidenced by clear Rabi splitting in the transmission spectrum.

Methods

We designed a two‑dimensional gold nanohole array to generate a blue‑detuned trapping landscape. The array consists of circular holes with radius R = 250 nm arranged in a square lattice (period L = 1000 nm) within a 400‑nm‑thick Au film (Fig. 1). The dielectric constant of gold was taken from Johnson and Christy [27]. FDTD simulations were performed using the EAST software package, with a spatial grid of 5 nm and a perfectly matched layer (PML) of 32 cells along the z‑axis. Periodic boundary conditions were applied in the x and y directions. Circularly polarized light of wavelength λ = 696 nm was normally incident along +z, and the transmission was recorded 400 nm above the structure. The molecule was modeled as a two‑level system with resonant wavelength λₘ = 707 nm and decay rate γₘ = 1.1×10¹⁴ Hz, represented by a dipole source within the FDTD framework [28–30]. The transmission T was obtained by integrating the Poynting vector over the upper surface and normalizing to the incident field, following the convention T = I_T/(I_C+I_D) [31].

Results and Discussion

Trapping Structure

The periodic nanohole array exhibits extraordinary optical transmission (EOT), producing intense localized fields around each hole. When the plasmonic resonance is blue‑detuned relative to the molecular transition, a repulsive optical potential forms, creating a trapping minimum a few hundred nanometers above the surface. Figure 2 shows the transmission spectrum of the bare array, revealing a resonant peak at 707 nm (1.756 eV) that coincides with the (1,1) Wood anomaly [35]. The electromagnetic field distribution at resonance (Fig. 3a) displays three intensity minima (P, M, N) arising from the superposition of surface‑plasmon and near‑field scattering. The |E|² versus z plot (Fig. 3b) confirms a pronounced minimum at the trap location.

Using the relation U_opt = –0.25α|E|² with α = –7.87×10⁻³⁸ F·m² [20], we computed the optical potential along the line x=y=0 (Fig. 4). The deepest minimum lies at point P, located 675 nm above the surface. With an incident power of 120 mW, the trapping depth is 0.53 mK, comparable to the 2.02 mK depth reported for ⁸⁷Rb in a similar blue‑detuned trap [20]. This depth is sufficient to confine a rhodamine molecule (MW ≈ 400) at thermal equilibrium. Accordingly, we selected the trapping position (0,0,675 nm) for subsequent coupling simulations (Fig. 5).

Strong Coupling Between Structure and a Molecule

We placed a dipole at the trapping minimum (point P, 275 nm above the surface) and examined three dipole orientations (x, y, z). The transmission spectra (Fig. 6) show that only when the dipole is aligned along z does the spectrum exhibit a clear Rabi splitting, indicating strong coupling. The two split resonances correspond to the dressed states ω± = ω₀ – 0.25i(γ_c+γ_m) ± √[g²–0.25(γ_c–γ_m)²] (Eq. 2), where γ_c = 4.08×10¹³ Hz and g = 144 meV. The calculated Rabi splitting Ω = |ω₊–ω₋| ≈ 16 meV, matching experimental values reported for hybrid metal–molecule systems [39–42]. When the dipole is oriented along x or y, a strong collective interaction S_k dominates, suppressing the coupling and leaving only the Wood anomaly peak near 707 nm (Fig. 7). Thus, the strong‑coupling regime is achievable only for a z‑polarized molecule in this architecture.

Conclusion

We have theoretically demonstrated that a single molecule can be stably trapped in a blue‑detuned plasmonic nanohole array and that the trapped molecule exhibits strong coupling with the cavity, evidenced by Rabi splitting in the transmission spectrum. The approach relies on the extraordinary optical transmission of sub‑wavelength holes, the repulsive blue‑detuned optical potential, and precise alignment of the molecular dipole. This integrated trapping‑coupling platform holds promise for scalable quantum information devices and nanoscale light–matter interaction studies.