In quantum optics, coupling strengths can be classified as weak, strong, ultrastrong, and deep strong. The classification between weak and strong is governed by the relationship between the coupling strength, g c √ N , and the loss rate (whether cavity or molecule energy loss), γ. The coupling is considered weak for g c √ N /γ < 1 and strong for g c √ N /γ > 1. The classification between ultrastrong and deep strong, however, depends on the ratio g c /ω c , with the ultrastrong regime being 0.1 < g c √ N /ω c < 1, and the deep strong regime being g c √ N /ω c > 1. While the Jaynes-Cummings and Tavis-Cummings models provide valuable, intuitive insights into how light couples with matter inside optical cavities, these models are subject to many approximations: the rotating wave approximation, the dipole approximation, the twolevel approximation, and also the absence of permanent dipole and dipole self-energy. As coupling strengths increase, these approximations begin to break down, and more rigorous Hamiltonians should be used (such as those discussed in Sec. 2). In the ultrastrong and deep coupling regimes, the JC and TC models fail to accurately capture the results of more rigorous methods.