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Chinese Physics Letters

New ⟨ q , n || Representation for Studing Two-Mode Nonlinear Phase Operator

Hong-Yi Fan, Hui Zou

Published Aug 1, 1999• 0 citations
Publisher

Abstract

A new complete and orthonormal ⟨ q, n || representation is constructed in which Hradil's two-mode phase operator exhibits its phase behavior manifestly and can be put into = ∑ q=∞ ∞ ∑ n=0 ∞ || q -1, n ⟩ ⟨ q , n ||, which resembles S-G phase operator ( + 1) -1/2 â = ∑ n=1 ∞ | n - 1⟩ ⟨ n |. The corresponding phase state is also obtained, which is qualified to make up a phase representation.

DOI
10.1088/0256-307x/16/8/001

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A new complete and orthonormal ⟨ q, n || representation is constructed in which Hradil's two-mode phase operator exhibits its phase behavior manifestly and can be put into = ∑ q=∞ ∞ ∑ n=0 ∞ || q -1, n ⟩ ⟨ q , n ||, which resembles S-G phase operator ( + 1) -1/2 â = ∑ n=1 ∞ | n - 1⟩ ⟨ n |. The corresponding phase state is also obtained, which is qualified to make up a phase representation.
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.
The coherent-intermediate-entangled state |α, x ⟩ λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α, x ⟩ λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α, x ⟩ λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α, x ⟩ λ,ν and the Schmidt decomposition of |α, x ⟩ λ,ν is investigated.