The Tavis-Cummings Hamiltonian in general can be used with various matter Hamiltonians. One specific model that is commonly used is the Holstein-Tavis-Cummings (HTC) model. In this model, the matter Hamiltonian consists of an array of two-level systems with phenomenological phonon modes added to the system. This HTC Hamiltonian can then be extended from Eq. 12 as,