Further making a single cavity mode approximation (only keeping one k with k x = 0, where ê is along x), with frequency ω c ) and the long wavelength approximation, this Hamiltonian reduces to the Tavis-Cummings Hamiltonian discussed in Sec. 1.2. The benefit of having this generalized Tavis-Cummings model is that now it is easier to run simulations in the single excited subspace since different excitation levels are now decoupled from each other. This drastically reduces the computational cost of modeling large systems. In particular, since even in simulations N is typically fairly large, most numerical calculations using this model consider only the first excitation subspace. This drastically reduces the basis size from 2 N × N F for N F Fock states to (N + 1). Recently, studies involving this GTC Hamiltonian have been able to shine new light on the dispersion plots seen in experiments (see Fig. )).