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Communications in Theoretical Physics

Normalized Excited Squeezed Vacuum State and Its Applications

Meng Xiang-Guo, Ji‐Suo Wang, Liang Bao-Long

Published May 1, 2007• 0 citations
Publisher

Abstract

By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state (ESVS), the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 (1992) 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.

DOI
10.1088/0253-6102/47/5/033

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By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state (ESVS), the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 (1992) 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.
In this paper, the two-mode excited squeezed vacuum state (TESVS) is studied by using the statistical method. By calculating the normalization of the TESVS, a new form of Jacobi polynomials and some new identities are obtained. The photon number distribution of the TESVS is given and it is a simple form of Jacobi polynomials. Using the entangled state representation of Wigner operator, the Wigner function of the TESVS is obtainded and the variations of the Wigner function with the parameters m, n, and r are discussed. Here from the phase space point of view the TESVS can be well interpreted and described.
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.
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.