which is the usual quadratic dispersion relation observed in the experiments. On the other hand, the matter energy is considered to be invariant in the typical range of the angles θ measured in the experiments, and thus E M = ℏω eg + E g = E e , where ω ge = (E e -E g )/ℏ. If one considers θ as a parameter (under the continuous limit of k x ), and the Tavis-Cummings model to describe light-matter interactions (see Sec. 1.2), one can then write down the following two-by-two matrix for polari-ton Hamiltonian in the {|G, 1⟩, |B, 0⟩} subspace 121