where µ eg is the transition dipole vector between the |g⟩ and |e⟩ states, ê is the cavity field polarization direction (with the hat indicating its status as a unit vector), ϵ is the permittivity inside the cavity (for vacuum, ϵ = ϵ 0 ), and V is the effective cavity quantization volume. A rigorous derivation of the JC model Hamiltonian from the minimal coupling Hamiltonian (Eqn. 35) can be found in Sec. 2.5. Experimentally, such single emitter-cavity strongly coupled systems can be realized in plasmonic cavity setups as shown schemati-cally in Fig. . This Jaynes-Cummings Hamiltonian is used ubiquitously across the field of quantum optics, from quantum computing applications to fundamental physics experiments. The eigenstates of the JC Hamiltonian can be obtained analytically, using a convenient basis of matter and photon states, |g⟩⊗|n⟩ ≡ |g, n⟩ and |e⟩⊗|n⟩ ≡ |e, n⟩ for n = 0, 1, .... The polariton ground state of the hybrid system is |g, 0⟩, and the n th excited upper polariton state (|+, n⟩) and the n th excited lower polariton state (|-, n⟩) are