The solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification and its application to the optimum realization of EPR paradox

In this paper, the solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein--Podolsky--Rosen (EPR) paradox. The analytics and numerical calculation show the influence of pump depletion on the error in the measurement of continuous variables. The optimum realization of EPR paradox can be achieved by adjusting the parameter of squeezing. This result is of practical importance when the realistic experimental conditions are taken into consideration.