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淮南师范学院学报

A simple method of the introduction of single-mode squeezing operator

YU Hai-ju

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In this paper,the Fock representation of the coordinate eigenstate is gived.The normal ordering form of the vacuum projection operator is derived.The single-mode squeezing operator is derived using IWOP technique,and the compression properties are analysed.

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The state |x〉λ,v was derived by using the technique of integration within an ordered product of operators(IWOP)that was the eigenstate of two rotational quadrature components λQ^+vP of light field.The basic vector |x〉λ,v becomes a new quantum mechanics representation which is between coordinate representation and momentum representation.With the help of the new representation,we obtain the normal product of the operators exp[-f(λQ +vP )2] and(λQ+vP)n.Furthermore,we construct a new quantum unitary operator which is used on vacuum state can obtain a new quantum optics squeezing state.
It is known that exp [iλ ( Q 1 P 1 – i/2)] is a unitary single-mode squeezing operator, where Q 1 , P 1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator , is an n -mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S n 's normally ordered expansion and obtain new n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
We find that the exponential operator V ≡exp[ i λ( Q 1 P 2 + Q 2 P 3 +⋅⋅⋅+ Q n −1 P n + Q n P 1 )], Q i , P i are, respectively, the coordinate and momentum operators, is an n -mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V 's normally ordered expansion and obtain the n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.