Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a ...Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.展开更多
According to Fan Hu＇s formalism （Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734） that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coord...According to Fan Hu＇s formalism （Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734） that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinatemomentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator p is equal to the marginal integration of the classical Weyl correspondence function of F1pF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.展开更多
Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of...Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of Fl2pF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.展开更多
Based on the technique of integration within an ordered product of operators,the Weyl ordering operatorformula is derived and the Fresnel operators' Weyl ordering is also obtained,which together with the Weyl tran...Based on the technique of integration within an ordered product of operators,the Weyl ordering operatorformula is derived and the Fresnel operators' Weyl ordering is also obtained,which together with the Weyl transformationcan immediately lead to Fresnel transformation kernel in classical optics.展开更多
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China (Grant No. 33190059)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113401120004)the Open Funds from National Laboratory for Infrared Physics,Chinese Academy of Sciences (Grant No. 201117)
文摘Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059)the National Natural Science Foundation of China (Grant No. 10874174)
文摘According to Fan Hu＇s formalism （Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734） that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinatemomentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator p is equal to the marginal integration of the classical Weyl correspondence function of F1pF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China(Grant No.33190059)the National Natural Science Foundation of China(Grant No.10874174)the President Foundation of Chinese Academy of Sciences
文摘Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of Fl2pF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.
基金Supported by the National Natural Science Foundation of China under Grant No.10475056the Research Foundation of the Education Department of Jiangxi Province
文摘Based on the technique of integration within an ordered product of operators,the Weyl ordering operatorformula is derived and the Fresnel operators' Weyl ordering is also obtained,which together with the Weyl transformationcan immediately lead to Fresnel transformation kernel in classical optics.
