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Modern Physics Letters A

ENTANGLED STATE REPRESENTATION, NEW TWO-VARIABLE HERMITE-POLYNOMIAL-OPERATOR IDENTITIES FOR TWO-MODE QUADRATURE'S PHYSICAL QUANTITY CALCULATION

Hong-Yi Fan, Jieyu Jiang

Published Dec 2, 2011• 3 citations
Publisher

Abstract

By virtue of the entangled state representation and the technique of integration within an ordered product (IWOP) of operators we derive some new two-variable Hermite-polynomial-operator identities, their application for calculating moment and cumulant for two-mode quadratures in quantum field theory are presented. The new operator identities make all calculations neat and concise.

DOI
10.1142/s0217732311037170

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By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
We study the optical field's quadrature excitation state X m |0〉, where X = ( a + a † )/√2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.