Quantum Zeno Effect

Repeated measurement freezes quantum decay — survival probability vs measurement frequency
P_surv(t) = [cos²(Ω·τ/2)]^{t/τ} → e^{−Γt} for τ→∞
Zeno regime: τ≪1/Ω → P≈[1−(Ωτ)²/4]^{t/τ} → e^{−Ω²t·τ/4}
No measurement (free decay)
τ = 0.5 (frequent)
τ = 1.0
τ = 2.0 (infrequent)
Custom τ
Rabi Ω: 2.0
Custom τ: 0.3
Total time T: 8
The quantum Zeno effect (Misra & Sudarshan 1977): a two-level system oscillating at Rabi frequency Ω, measured every τ, has survival probability P = cos²(Ωτ/2) per measurement. With n=t/τ measurements: P(t) = cos²ⁿ(Ωτ/2). For τ→0, P→1 (Zeno freezing). For τ→∞, unitary evolution. There's also an anti-Zeno effect: at intermediate τ matching the bath spectral density, measurements can accelerate decay (Facchi et al 2000).