Photoelectron counting in quantum optics

Master equation for TLS-‘source’ density operator ρ t˙ρ t = i Ω 2 [σ + + σ − , ρ t ] − β (σ + σ − ρ t + ρ t σ + σ − − 2σ − ρ t σ + )Spontaneous emission rate β = π ∑ Q γ2 Q δ(ω L − ω Q ), effect of drivingin β neglected (↔ ‘intra-collisional field effect).Compare with our previous ( detector equation,)˙ρ (m)t = −i[H F , ρ (m)t ] − γ 2a † aρ (m)t + ρ (m)t a † a − 2aρ (m−1)t a † .Remember spontaneous emission: field at the detector in terms ofatom dipole operator,E (+)s (r, t) ≈ E(ˆr)σ − (t − r/c).Thus a ∼ E (+)s ∼ σ − . detector photon absorption ∼ electron jumps from up to down, σ − .