Calculating the quantum characteristic function and the photon-number generating function in quantum optics
Rockower, Edward B.
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A new operator derivation of the relation giving the photon-number generating function, G (y), in terms of the quantum characteristic function, C(s,5*), is presented. The inverse problem is then solved, calculating C( s.s*) directly from G ( y). Because G ( y) contains less phase information than C(s,s*), we can either assume that the field has a completely random phase (e.g., a stationary field) or be content with calculating the phase average of C(s,s*). We then derive an expression giving G ( r> for the superposition of two arbitrary, independent fields in terms of the individual G (y)'s for each (stationary) field. A number of examples illustrate the methods, including a determination of the quantum characteristic function for a field with K-distributed amplitude fluctuations.
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