Photoelectron counting in quantum optics

Mandel formula: many countsHow to obtain probability of n transitions p n (t, t + T )Short-time probability p 1 (t, t + ∆t) = ηI (r)∆t for single electrontransition (ηI (r) transition rate).Long-time probability of n transitions p n (t, t + T ) ↔ n electrons.Individual transitions are statistically independent... Poisson distribution.Characterized by average ¯n only p n (t, t + T ) = ¯nnn! e−¯n , ¯n = ηI (r)T . (2)