Operators＇ s-parameterized ordering and its classical correspondence in quantum optics theory

Fan Hong-Yi, Yuan Hong-Chun, Liyun Hu

In reference to the Weyl ordering , where X and P are coordinate and momentum operator, respectively, this paper examines operators' s -parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence and its complementary relation where H m,n is the two-variable Hermite polynomial, a , a † are bosonic annihilation and creation operators respectively, s ′ is a complex parameter. The s -ordered operator power-series expansion of s -ordered operator in terms of the two-variable Hermite polynomial is also derived. Application of operators' s -ordering formula in studying displaced-squeezed chaotic field is discussed.

Heng-Mei Li, Hong‐Chun Yuan

Fan Hong‐Yi, Liyun Hu, Yuan Hong-Chun

Based on the theory of integration within s -ordering of operators and the bipartite entangled state representation we introduce s -parameterized Weyl–Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.

A. Lukš, Vlasta Peřinová

Xiang‐Guo Meng, Ji‐Suo Wang, Xiaoyan Zhang +1 more

By virtue of the technique of integral within an ordered product of operators, we construct a new parameterized entangled state |τs, r and prove the set of |τs, r making up a new complete and orthogonal representation. As applications, we use the state |τs, r representation to derive a two-mode entangled Fresnel operator, to formulate quantum correspondence theory of the classical circular harmonic correlator, and to develop quantum tomography of entangled systems.

G. Dattoli, Juan Carlos Gallardo, A. Torre