where λ = λ • characterizes the photon-matter coupling strength, is the direction of the field polarization. The coupling strength is determined by the volume of the cavity as λ = 1/ 0 V . Another way to define the lightmatter coupling strength is using g c = ω c /2λ. Note that the g c used in this work differs from the common notation used in the literature, which often include the magnitude of the dipole inside g c . Further, the total dipole operator of both electrons and nuclei is defined as