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理论物理通讯：英文版

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials

FANHong-Yi, Hong-Yi, Yue Yue

Published Jan 1, 2002• 0 citations
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Abstract

Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators' ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa+man =:Hm,n(a+,a):, ana+m = (-i)m+n:Hm,n(ia+,ia): are obtained.

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Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators' ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa+man =:Hm,n(a+,a):, ana+m = (-i)m+n:Hm,n(ia+,ia): are obtained.
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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.
For directly normalizing the photon non-Gaussian states (e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product (IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.