s-Ordered Exponential of Quadratic Forms Gained via IWSOP Technique

Abstract

Using the generalized $\bar{s}$-ordered Wigner operator, in which $\bar{s}$ is a vector over the field of complex numbers, the technique of integration within an s-ordered product of operators (IWSOP) has been extended to multimode case. We derive the $\bar{s}$-ordered form of the widely applicable multimode exponential of quadratic form $\exp\{\sum_{i,j = 1}^{n} a_{i}^{\dag}\varLambda_{ij}{a_{j}}\}$, each mode being in some particular order s _i , applying this method.