where σ † = |e⟩⟨g| and σ = |g⟩⟨e| are the creation and annihilation operators for the molecular excitation, respectively, and â † and â are raising and lowering operators of the cavity field, respectively, with the cavity frequency ω c . The term ℏω c (â † â + 1 2 ) describes the cavity field (under the single mode approximation); its eigenstate |n⟩ describes the number of photons inside the empty cavity (without the presence of the emitter), where n = ⟨n|â † â|n⟩. Lastly, g c is the coupling strength between the matter and the cavity field, which is often expressed as