Photoelectron counting in quantum optics

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Resonance fluorescence: sub-Poissonian counting statisticsInformation contained inTrĜ(s, z) =f (z)zf (z) + βΩ 2 (1 − s) , f (z) ≡ (z + β)(z + 2β) + Ω2 .Need to transform back into time-domain.p n (0, t) = ∂n∂s n TrG(s, t)| s=0 . (19)〈n〉 t = ∂ ∂s TrG(s, t)| s=11st moment. (20)〈n(n − 1) t 〉 = ∂2∂s 2 TrG(s, t)| s=12nd factorial moment.(21)
Resonance fluorescence: sub-Poissonian counting statisticsInformation contained inTrĜ(s, z) =f (z)zf (z) + βΩ 2 (1 − s) , f (z) ≡ (z + β)(z + 2β) + Ω2 .Large t: pole z 0 closest to z = 0.Expand z 0 = ∑ ∞m=1 c m(s − 1) mβΩ 2 〈n〉 t→∞ =2β 2 + Ω 2 t (19)[ σt 2 ≡ 〈∆n 2 〉 t→∞ = 〈n〉 t→∞ 1 − 6β2 Ω 2 ](2β 2 + Ω 2 ) 2 .Negative Mandel Q-parameter Q ≡ F − 1, Fano factorF ≡ 〈∆n 2 〉/〈n〉 < 1.
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Photoelectron counting in quantum o
Page 3 and 4:
Overview: photons, photon-counting,
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Semiclassical theory for p n (t, t
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Mandel formula: many countsHow to o
Page 16 and 17: ‘Quantum Mandel formulas’Kelley
Page 18 and 19: Scully-Lamb photodetectorM. Scully,
Page 20 and 21: Master equationEffective density ma
Page 22 and 23: Scully-Lamb PhotodetectorDetector m
Page 24 and 25: Scully-Lamb PhotodetectorDetector m
Page 26 and 27: Scully-Lamb PhotodetectorState with
Page 28 and 29: Scully-Lamb PhotodetectorState with
Page 30 and 31: Summary: counting statistics in Scu
Page 32 and 33: Solve d dt Ĝ = −i[H F, Ĝ] −
Page 34 and 35: (a † aĜ + Ĝa † a − 2saĜa
Page 36 and 37: Solve ∂ ∂t P s = [ −yz∂ z
Page 38 and 39: Single-mode counting formula: discu
Page 40 and 41: Summary part 1Done so farPhoton cou
Page 42 and 43: 5 Correlation functions6 Source-fie
Page 44 and 45: Coherence functionsDefinitionsNotat
Page 46 and 47: Coherence functionsExample for bunc
Page 48 and 49: Quantization of Maxwell’s equatio
Page 50 and 51: Spontaneous emission from a two-lev
Page 56 and 57: Resonance fluorescence: analogy to
Page 58 and 59: Master equation for TLS-‘source
Page 60 and 61: Cook’s ‘counting at the source
Page 68 and 69: Resonance fluorescence: sub-Poisson
Page 70 and 71: Counting in quantum optics: towards
Page 72 and 73: Ueda’s photodetector theoryM. Ued
Page 74 and 75: Multi-mode photodetectorH = H 0 + H
Page 76 and 77: Formal solutionGenerating operator
Page 78 and 79: Formal solutionGenerating operator
Page 80 and 81: Relation with Kelley-Kleiner formul
Page 82 and 83: Relation with Kelley-Kleiner formul
Page 84 and 85: Multi-mode form×p m (0, t) ≡ Tr
Page 86 and 87: Quantum jump method, Monte-Carlo fo
Page 92: SummaryMulti-mode quantum optics: f
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