Photoelectron counting in quantum optics

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Quantum jump method, Monte-Carlo for master equationExample: spontaneous emission from TLS (rotating frame)˙ρ t = −β (σ + σ − ρ t + ρ t σ + σ − − 2σ − ρ t σ + )Monte-Carlo procedure. Fixed time step ∆t.Step 1: start with pure wave function |Ψ〉.Step 2: calculate collaps probability, P col = β∆t〈Ψ|σ + σ − |Ψ〉Step 3: compare P col with random number 0 ≤ r ≤ 1.◮ If P col > r, replace |Ψ〉 → σ − |Ψ〉/‖σ − |Ψ〉‖.◮ If Pcol ≤ r, no emission but time-evolution |Ψ〉 → (1 − i∆tH eff |Ψ〉/N ,where H eff ) = −iβσ + σ − .Go back to Step 2.Repeat procedure in order to obtain average.Widely used in quantum optics community.Note: splitting L = L 0 + J is not unique.Literature: Carmichael (book); Plenio,Knight (review).
SummaryMulti-mode quantum optics: field as ‘bath’.Correlation (coherence) functions.Resonance fluorescence: ‘counting at the source’, sub-Poissonian,anti-bunched.Multi-mode photo-detector theory.Quantum trajectories.
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Photoelectron counting in quantum o
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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
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‘Quantum Mandel formulas’Kelley
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Scully-Lamb photodetectorM. Scully,
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Master equationEffective density ma
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Scully-Lamb PhotodetectorDetector m
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Scully-Lamb PhotodetectorDetector m
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Scully-Lamb PhotodetectorState with
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Scully-Lamb PhotodetectorState with
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Summary: counting statistics in Scu
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Solve d dt Ĝ = −i[H F, Ĝ] −
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(a † aĜ + Ĝa † a − 2saĜa
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Solve ∂ ∂t P s = [ −yz∂ z
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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 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 92: SummaryMulti-mode quantum optics: f
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