Photoelectron counting in quantum optics

Spontaneous emission from a two-level atomTwo-level atom with states |1〉, |0〉H = ω 02 σ z + ∑ Qγ Q(σ + a Q + σ − a † Q)+ ∑ Qω Q a † Q a Q. (14)Pauli matrices, photon creation operators a † Q .Algebra of Pauli matrices( 0 1σ x ≡1 0( 0 0σ − ≡1 0) ( 0 −i, σ y ≡i 0), σ + ≡( 0 10 0) ( 1 0, σ z ≡0 −1))σ ± = 1 2 (σ x ± iσ y ), σ x = σ + + σ − , σ y = −i(σ + − σ − )[σ + , σ − ] = σ z , [σ z , σ ± ] = ±2σ ± . (15)