Optical wavelet-fractional squeezing combinatorial transform

Abstract

By virtue of the method of integration within ordered product (IWOP) of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform (WFrST) operator. The way we successfully combine them to realize the integration transform kernel of WFrST is making full use of the completeness relation of Diracʼs ket–bra representation. The WFrST can play role in analyzing and recognizing quantum states, for instance, we apply this new transform to identify the vacuum state, the single-particle state, and their superposition state.

Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

“…where the symbol : : denotes normal ordering, [21][22][23][24] Q = (a + a † )/ √ 2 is the coordinate operator, and P = (a − a † )/( √ 2i) is the momentum operator. Thus, we can directly obtain…”