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Communications in Theoretical Physics

A Compact Exponential Operator for Generating Rotating and Squeezing Transformations

Fan Hong‐Yi

Published Sep 1, 1990• 4 citations
Publisher

Abstract

We point out that the compact exponential operator (where are real; and are momentum and coordinate operators, respectively; the units of is taken, and are harmonic oscillator's mass and frequency, respectively) is a generalized single-mode squeeze operator which can generate mixed squeezing and rotating transformations. The decomposition of as a product of a squeeze operator and a rotating operator is derived through the technique of integration within an ordered product. The fluctuation in quadrature phases for the squeezed vacuum state generated by is analyzed.

DOI
10.1088/0253-6102/14/2/181

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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.
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