where c is the speed of light in vacuum, n c is the refractive index inside the cavity, c/n c is the speed of the light inside the cavity, and θ is the incident angle, which is the angle of the photonic mode wavevector k relative to the norm direction of the mirrors. For simplicity, we drop n c throughout this paper . The expression of the manymode Hamiltonian is provided in Supplementary Note 9, Sec. A. When k ∥ = 0 (or θ = 0), the photon frequency is