Wigner-Weisskopf Spontaneous Emission

A two-level atom coupled to the electromagnetic vacuum spontaneously emits a photon. The Wigner-Weisskopf theory gives exponential decay of the excited state amplitude c_e(t) = e^{-(Γ/2 + iΔ)t}, with Lorentzian emission spectrum.

0.8
0.0
0.8
c_e(t) = exp[-(Γ/2 + iΔ)t]
S(ω) = Γ / [(ω-ω₀-Δ)² + (Γ/2)²] (Lorentzian)
Purcell effect: Γ_cavity = Γ_free × (3Q λ³)/(4π²V)