Two-mode Coherent And Squeezed Vacuum States

Using the antinormally-ordered characteristic function, we have determined the Q functionrnfor a two-mode coherent state as well as a two-mode squeezed vacuum state. Using thernpertinent Q function, we have calculated the quadrature variance, the mean and thernnormally-ordered variance of the photon number sum and di erence. Furthermore, wernhave obtained the Q function for the superposition of two-mode coherent and squeezedrnvacuum states. Employing the resulting Q function, we have calculated the quadraturernvariance, the mean and the normally-ordered variance of the photon number sum andrndi erence.rnWe have found that the mean of the photon number sum for the superposition of two-rnmode coherent and squeezed vacuum states is the sum of the mean of the photon numberrnsums for the individual states. And the mean of the photon number di erence for thernsuperposition of two-mode coherent and squeezed vacuum states is the same as that ofrnthe two-mode coherent state. The quadrature variance for the superposition of two-moderncoherent and squeezed vacuum states is the same as that of a two-mode squeezed vacuumrnstate

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