Photoelectron counting in quantum optics

Spontaneous emission from a two-level atomTwo-level atom with states |1〉, |0〉H = ω 02 σ z + ∑ Qγ Q(σ + a Q + σ − a † Q)+ ∑ Qω Q a † Q a Q. (14)Pauli matrices, photon creation operators a † Q .Electric field E (+) (r, t) = E (+)f(r, t) + E (+)s (r, t), source field in termsof source operatorsHeisenberg EOM ȧ Q (t) = −iω Q a Q (t) − iγ k σ − (t) ∫ ta Q (t) = a Q e −iωQt − iγ Q dt ′ σ − (t ′ )e −iω Q(t−t ′) . (15)0