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arXiv:1511.04833

Physical interpretation of generalized two-mode squeezing operator revealed by virtue of the transformation of entangled state representation

Fuping Gao, Y.X. Wang, Heng Fan, Xiaomeng Tang

Published Nov 16, 2015• 1 citation
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Abstract

By virtue of the integration method within P-ordered product of operators and the property of entangled state representation, we reveal new physical interpretation of the generalized two-mode squeezing operator (GTSO), and find it be decomposed as the product of free-space propagation operator, single-mode and two-mode squeezing operators, as well as thin lens transformation operator. This docomposition is useful to design of opticl devices for generating various squeezed states of light. Transformation of entangled state representation induced by GTSO is emphasized.

DOI
10.48550/arxiv.1511.04833

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By virtue of the integration method within P-ordered product of operators and the property of entangled state representation, we reveal new physical interpretation of the generalized two-mode squeezing operator (GTSO), and find it be decomposed as the product of free-space propagation operator, single-mode and two-mode squeezing operators, as well as thin lens transformation operator. This docomposition is useful to design of opticl devices for generating various squeezed states of light. Transformation of entangled state representation induced by GTSO is emphasized.
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In a previous paper Zhan et al. (2022) proposed the coherent state representation for linear operator, which shows a beautiful theoretical value. Inspired by the work, we further extend it to the nonlinear case, including single- and two-mode squeezing process. Based on squeezing operators’ transformation relation, we introduce their coherent state representations and derive their normal ordering forms by using the technique of integration within product of operator. As applications, we examine some operators’s normal ordering forms and show the entanglement property of prepared quantum states via the Schmidt decomposition. In particular, we further consider two cascaded two-mode squeezing operators, in which a generalized SU(1,1) interferometer is involved. In addition, the application of two-mode squeezing operator followed by photon-subtraction to generate non-Gaussian entangled states in quantum teleportation is discussed. Our results will be useful in preparation of quantum states and quantum metrology.
Using the technique of integration within an ordered product of operators we construct a generalized two-mode entangled state, which can be generated by an asymmetrical beam splitter (BS). Some important properties of this state, such as orthogonality and Schmidt decomposition, are also discussed by deriving the expression of BS operator in coordinate representation. As its applications, to conjugate state, obtain operator identities, generate new squeezing operators (squeezed state) are also presented. It is shown that the fidelity of quantum teleportation can be enhanced under certain case by using the asymmetrical new squeezed state as entangled resource.
By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operator, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotating coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.