Photoelectron counting in quantum optics

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.