where ω c is the frequency of the mode in the cavity, â † and â are the photonic creation and annihilation operators, and qc = ℏ/2ω c (â † + â) and pc = i ℏω c /2(â † -â) are the photonic coordinate and momentum operators, respectively. Choosing the Coulomb gauge, ∇ • Â = 0, the vector potential becomes purely transverse Â = Â⊥ . Under the long-wavelength approximation,