Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters

Abstract

Two-mode squeezed coherent states with complex squeeze and displacement parameters are studied, taking advantage of the SU(2) dynamical symmetry underlying two-mode systems. Expressions for the photon distributions in such states are derived using an SU(2) identity and the fact that the two-mode squeeze operator can be viewed as a rotated version of the product of reciprocal single-mode squeeze operators. An important U(1)×U(1) invariance of this photon distribution is established. As a consequence, the three phases of the complex squeeze and displacement parameters enter the photon distribution through just one U(1)×U(1) invariant combination. An associated Gouy effect is noted. Numerical examples of two-mode photon distributions are shown, and interesting new features demonstrated. Second-order coherence properties and their nonclassical nature are briefly studied.