Photoelectron counting in quantum optics

Revision: towards a counting formula in quantum opticsMandel (Poissonian)p n (t, t + T ) = ¯nnn! e−¯n , ¯n = ηI (r)T .◮ Classical field with intensity I (r). Golden rule (photo-electric effect).Mollow, Scully-Lamb single mode1( ) np n (0, t) = Trρ(0) : a † aη t exp(−a † aη t ) :, η t ≡ 1 − e −γt .n!◮ Correctly describes detector backaction. ‘Closed system’. Free cavityfields only, no sources.‘Quantum Mandel’, Kelley-Kleiner◮◮p n (t, t + T ) = 〈: ˆΩ nn! e−ˆΩ :〉.∫ t+THeisenberg operators, Ω ≡ ξ dt ′ Ê − (t ′ )Ê + (t ′ ).tNot correct for long times. ‘Open system’. Various generalisations onthe market.