Fig. 1. Schematic illustration of energy level and spectra in emitter-field coupling system. (a) Upper panel, energy-level splitting in single atom interacting with optical field. Here ωa is the transition frequency of the atom and ωc is the resonance frequency of the field; ℏ is the reduced Planck constant; |e⟩ and |g⟩ mean the atom is in the excited state and ground state, respectively; |c⟩ means cavity resonance state. Lower panel, anticrossing for Rabi splitting. Δδ is the frequency detuning between atom and field. (b) Quantum Rabi splitting of single atom in photoluminescence spectra; (c) spectral splitting in the system, which consists of plasmon interacting with the J aggregate. ω0 is the transition frequency of the molecular emitter, and Δδ′ is the frequency detuning between the J aggregate and the field.

Fig. 2. Schematic illustration of methylene blue molecules embedded in the nanogap of an NPoM structure and their quantum and optical interaction with plasmons excited by incident light. (a) A single methylene blue molecule placed in the hot spot (with the maximum electric field enhancement) of the nanogap, as depicted by the red circle. The Rabi splitting due to plasmon–molecules strong coupling can be reflected by the scattering light and fluorescence, but the weak fluorescence will be absorbed by plasmonic structure and become hard to detect. (b) In multi-molecule level, the real Rabi splitting can only be reflected by fluorescence, while the scattering light involves not only the Rabi splitting but also complex optical interaction. (c) Chemical structure of methylene blue molecule.

Fig. 3. Engineering plasmonic resonance in an NPoM structure by changing the physical and geometric properties. (a) Schematic diagram of the NPoM structure; (b) electric field intensity distributions of NPoM in the vertical x-z plane (top) and horizontal x-y plane (bottom), respectively. The diameter of the hot spot is 6 nm as shown by the x-y plane field pattern. (c) Simulated scattering spectra when the plasmonic nanogaps are filled with pure dielectric films whose refractive index varies from 1.0 to 1.6. The plasmonic resonance peak redshifts from 610 to 684 nm (from 2.03 to 1.81 eV in energy). (d) Simulated scattering spectra with the thickness of pure dielectric film changing from 0.8 to 0.2 nm, showing plasmon resonance peak blueshifting from 643 to 614 nm (from 1.93 to 2.02 eV in energy).

Fig. 4. Vacuum Rabi splitting in a single molecule–plasmon system, when a methylene blue molecule is in resonance with plasmon (detuning δ=0). (a) Scattering spectrum of plasmon coupling to a single molecule with radius of 0.5 nm. The hybrid plasmon–exciton branches, ω+ and ω− are separated by 79.4 meV. (b) Scattering spectrum of plasmon coupling to a huge molecule with diameter of 6 nm. The interval of two peaks splitting is 395 meV.

Fig. 5. Scattering spectra of an optical interaction system that consists of multiple methylene blue molecules coupling to plasmon. (a) Two molecules, the interval of the splitting peaks Δ=120  meV (ω+=602.6  nm and ω−=640  nm); (b) five molecules, Δ=182  meV (ω+=597.6  nm and ω−=655  nm); (c) thirteen molecules, Δ=290  meV (ω+=591  nm and ω−=686  nm); (d)–(f) schematic diagram of placing two molecules, five molecules, and thirteen molecules into the NPoM, respectively; (g) calculated spectral splitting in dependence on the number of molecules (blue dots) as compared with the theoretical curve (black line) of optical interaction, which points to splitting with the number of molecules increasing Ωoptical=NΩR. Red horizontal line represents the real Rabi splitting when considering only the molecular fluorescence spectra.