in many text books of quantum optics, the second order correlation function g(2)(r,t0) interpreted as a probability of finding of one photon in position 'r' at the time 't' and finding the second photon in that position at time t+t0.
but we know that g(2)(r,t0) can be greater or equal than 1 (for example for thermal state of light); my question is that is it right to interpret a function of amounts greater than one as a probability function?
Probability is not the same thing as probability distribution function, a non-negative function whose integral over the range of the relevant (stochastic) variable is equal to 1. A probability distribution function can perfectly be greater than 1.
Dear Behnam Farid ,
Thank you for your answer.
But I see in many text books that for example, g2(0) is interpreted as a 'probability' of detection of two photons at the same time. and when we calculate g(2)(0) for some states (states of supper-poissonian distribution), we find that g(2)(0) is greater than 1. you mean an interpretation of g(2)(0) as a probability is not right? and we have to say g(2)(t) is a probability distribution and can get amounts greater than 1?
can you refer me to some references to read more about this?
Thank You
Hossein
Hossein Allahverdi : For a probability distribution function f(x) concerning the stochastic variable x and for dx → 0, the probability that x is inside the interval [x,x+dx] is equal to f(x) dx. For a finite Δx, the probability that x is inside [x,x+Δx] is equal to ∫xx+Δx dx' f(x') ≤ 1. Since experimental probes have finite resolutions (in time, in frequency, etc.), what one measures is never a distribution function itself, but an integral of this distribution function over the resolution window, which is a probability. In any case, these concepts are clearly defined, so that there is no reason to be confused by inaccurate choice of wards (often jargons) in some publications.
Behnam Farid
Thank you very much for your hint. I understand it now. I was confused when I read inaccurate interpretations in some articles but it's become clear for me now.
Thank You
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