Figure 5. Energy splitting and bending behaviors for the coupled plasmon-QEs system with dissipation.

(a) Schematic representation of the QED system comprising of a two-level atomic system representing QEs with a transition frequency ω₀ and decay rate γ₀ coherently interacting with a single mode of the oscillating bosonic field in a plasmonic cavity with a resonant frequency ω_b and dissipation rate γ_b. The effective coupling strength is λ. (b) Energy diagram of the system featuring two plexcitonic states (UP and LP) with the energy eigenvalues of $E_{\pm }^C$. (c) Energy levels of the system as a function of the energy detuning Δ = ω₀ − ω_b for different coupling strengths as marked. The two thin black lines are the bare atomic and plasmonic states. (d) Energy levels of the system as a function of the energy dissipation γ₋ for different energy detuning. At zero detuning Δ = 0, the threshold for Rabi splitting occurs at γ₋/(2λ)=1. In (c) and (d), the dash-dot lines represent upper plexcitonic states while the solid represent lower plexcitonic states. Yellow-shaded area: an energy-bending region where no energy splitting is allowed; instead, the energy level of QEs undergoes an energy shift of ΔE^C owing to the perturbation of the plasmonic field. Light blue-shaded area: an energy-splitting region where distinct anti-crossing plexcitonic states are γ₋ is defined as γ₋ = |γ₀ − γ_b|/4.