In reality, optical cavities are composed of many photonic modes/wavevectors (i.e., cavity dispersion relations) whose form depends on the type of cavity. For example, in typical Fabry-Perot (parallel mirror cavities, Fig. ), the dispersion relation can be written as E ph (θ) = ħ nc c k 2 z + k 2 x = ħ nc ck z 1 + tan 2 θ, which depends on the angle of the external probe, θ = tan -1 (k x /k z ). Here c is the speed of light in vacuum, n c is the refractive index inside the cavity, and ħk is the momentum of the photon. It should be noted that there are many other cavity designs, most notably the plasmonic cavity which contain many varied geometrical arrangements of nanoparticles-on-metal-surfaces which lead to a wide variety of cavity dispersion relations. As shown in Fig. , the total wavevector k = ⟨k x , k z ⟩ is related to the quasicontinuous parallel k x and strictly quantized perpendicular k z modes. Additionally, there may be many molecules N mol collectively coupled to these cavity modes N mode , The scaling of such a Hilbert space (given by the Hamiltonian in Eq. 17) can be written as dim