We present a new theoretical framework, polarized Fock states (PFS), to describe the coupled molecule-cavity hybrid system in quantum electrodynamics. Through the quantum light-matter interactions under the dipole Gauge, the molecular permanent dipoles polarize the photon field by displacing the photonic coordinate. Hence, it is convenient to use these shifted Fock states (referred to as the PFS) to describe light-matter interactions under the strong coupling regimes. These PFS are non-orthogonal to each other and are light-matter entangled states. They allow an intuitive understanding of several phenomena that go beyond the prediction of the quantum Rabi model, while also offering numerical convenience to converge the results with much fewer states. With this powerful new theoretical framework, we explain how molecular permanent dipoles lead to the generation of multiple photons from a single electronic excitation (downconversion), effectively achieving the dynamical Casimir effect through the nuclear vibration instead of the cavity mirror oscillations.