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--Planckequation of non-degenerate optical parametric amplification isused to deduce the condition demonstrating theEinstein--Podolsky--Rosen (EPR) paradox. The analytics andnumerical calculation show the influence of pump depletion onthe error in the measurement of continuous variables. Theoptimum realization of EPR paradox can be achieved by adjustingthe parameter of squeezing. This result is of practicalimportance when the realistic experimental conditions are takeninto consideration.