Reduction of quantum phase fluctuations implies antibunching of photon

A clear physical meaning of the Carruthers–Nieto symmetric quantum phase fluctuation parameter (U)(U) has been provided in Susskind–Glogower and Barnett–Pegg formalism of quantum phase and it is shown that the reduction of phase fluctuation parameter U with respect to its coherent state value corresponds to an antibunched state. Thus nonclassicality of a state may be manifested through the phase fluctuation parameters. As examples, quantum phase fluctuations in different optical processes, such as four wave mixing, six wave mixing and second harmonic generation have been studied by using Carruthers–Nieto quantum phase fluctuation parameters. The operators required for the calculation of quantum phase fluctuations are expressed in closed analytical forms (up to second order in coupling constant). It is also found that the reduction of phase fluctuations compared to their initial values are possible in all the three cases studied here. Thus nonclassical (antibunched) state exists in all these cases.