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International Journal of Theoretical Physics

The Wigner Function and the Husimi Function of the One- and Two-Mode Combination Squeezed State

Qin Guo

Published Jun 5, 2007• 5 citations
Publisher
DOI
10.1007/s10773-007-9428-9

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Based on the two-mode squeezing operator which is the quantum version of the symplectic transformation, we find that the corresponding squeezed two-mode number state is just a two-variable Hermite polynomial excited state, which possesses well-behaved features, e.g. its Wigner function is a direct product of two Laguerre polynomials; its Husimi function, a Gaussian broaden version of the Wigner function, is related to two-variable Hermite polynomials. Moreover, its quantum statistical features, such as squeezing properties and the inter-mode photon bunching, are discussed.
We find that a kind of atomic coherent state, formed as exp[ξJ + – ξ*J − ] |00〉, when the SU(2) generators J± are taken as Fan's form, J + = (1/2)(a 1 – a 2 † )(a 1 † – a 2 ), J − = (1/2)(a † 1 + a 2 ) (a 1 + a 2 † ), and J 0 = (1/2)(a 1 † a 2 † – a 1 a 2 ), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.