General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

摘要

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061;quant-ph/9605032], the one dimensional squeezed and harmonic oscillatortime-displacement operators were reordered in coordinate-momentum space. Inthis paper, we give a general approach for reordering multi-dimensionalexponential quadratic operator(EQO) in coordinate-momentum space. An explicitcomputational formula is provided and applied to the single mode anddouble-mode EQO through the squeezed operator and the time displacementoperator of the harmonic oscillator.