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Photoelectron counting in quantum optics

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Coherence functionsExample for bunch<strong>in</strong>g: cavity mode a † <strong>in</strong> thermal bath (temperature β −1 )Mode angular frequency ω, damp<strong>in</strong>g κ.Master equation.Use <strong>quantum</strong> regression theorem.Long-time limit, t → ∞, n B = [e βω − 1] −1limt→∞ 〈a† (t)a(t + τ)〉 = n B e −(κ+iω)τ (12)limt→∞ 〈a† (t)a † (t + τ)a(t + τ)a(t)〉 = nB2 (1 + e−2κτ ) . (13)Thus, g (2) (τ) = 1 + e −2κτ and g (2) (τ) < g (2) (0): photon bunch<strong>in</strong>g.(cf. Carmichael book etc.)

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