Weyl Ordering Symbol Method for Studying Wigner Function of the Damping Field

The symbolic method (including normal ordering. antinormal ordering and Weyl ordering symbol) is usually utilized to tackle miscellaneous operators which have different commutative relations. Considering the Weyl ordering symbol’s remarkable properties, we have efficiently and conveniently derived the Wigner distribution function for field damping in a squeezed bath and a vacuum bath respectively, and then examined the decoherence processes from the plots of Wigner function and its contour in quantum phase space. Alternatively, we can employ a general Wigner operator under phase space transform to calculate distribution function and discuss the damping process.