Harmonic entanglement in a degenerate parametric down-conversion

A detailed study of the harmonic entanglement and two-mode squeezing of radiation generated in a degenerate parametric down-conversion process when the cavity is coupled to a two-mode vacuum reservoir is presented. It is found that there is a quadrature entanglement between the harmonically related fundamental and residual pump modes where the superimposed radiation exhibits a higher degree of two-mode squeezing. It turns out that the two-mode squeezing can exist when there is no entanglement, since the correlations leading to these phenomena are essentially different. It is also shown that the more the external pumping radiation is down-converted by the nonlinear crystal, the stronger the entanglement and intensity of the two-mode radiation would be; this condition is not generally true for squeezing.