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 si, applying this method.