where ω c is the cavity frequency and â † ( â) is creation (annihilation) ladder operator for the photon field. The Hamiltonian can be factored into the form of a shifted harmonic oscillator via the definition of the canonical coordinates (i.e. the operators of positions and momentum) of the quantum harmonic oscillator: qc = ħ 2ωc ( â † + â ) and pc = ħωc 2 ( â † -â ). Here λ is the light-matter coupling strength commonly used in the literature. Another common choice is the transverse vector potential of the photonic field A 0 , related to λ as