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Theoretical and Mathematical Physics

Fresnel Tomography: A Novel Approach to Wave-Function Reconstruction Based on the Fresnel Representation of Tomograms

Sergio M. De Nicola, Renato Fedele, Margarita A. Man’ko, Vladimir I. Man’ko

Published Aug 1, 2005• 18 citations
Publisher
DOI
10.1007/s11232-005-0151-5

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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 F 2 † ρ F 2 , where F 2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.
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 coordinate—momentum 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 ρ is equal to the marginal integration of the classical Weyl correspondence function of F † ρ F , 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.