Photoelectron counting in quantum optics

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Single-mode counting formula: discussion ofp m (t) = Trρ(0) : ( a † aη t) mm!e −a† aη t:, η t ≡ 1 − e −γtCoherent state ρ(0) = |z 0 〉〈z 0 | p m (t) = (〈n〉η t) me −〈n〉ηt .m!◮ Poisson-distribution.◮ Average 〈n〉 ≡ 〈a † a〉 = |z 0 | 2 .◮ Coincides with semiclassical Mandel formula for γt ≪ 1.Fock-state ρ(0) = |n〉〈n| ( np m (t) =m)η m t (1 − η t ) n−m , n ≥ m.◮◮Bernoulli-distribution.m successful events (counts), n − m failures (no counts) regardless oforder.
Summary part 1Done so farPhoton counting: photo-electron counting.Semiclassical Mandel formula.Photo-detector theory: Scully/Lamb.Some techniques: quantum master equations, P−representation,counting variables and generating functions/operators.
Page 1 and 2: Photoelectron counting in quantum o
Page 3 and 4: Overview: photons, photon-counting,
Page 5 and 6: Overview: photons, photon-counting,
Page 7: Overview: photons, photon-counting,
Page 11: Semiclassical theory for p n (t, t
Page 14 and 15: 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 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 66 and 67: Resonance fluorescence: sub-Poisson
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 88 and 89:
Quantum jump method, Monte-Carlo fo
Page 90 and 91:
Quantum jump method, Monte-Carlo fo
Page 92:
SummaryMulti-mode quantum optics: f
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Photoelectron counting in quantum optics

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