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Acta Optica Sinica

Generation of squeezed state and quantum scaling evolution

Heng Fan

Published Jan 1, 1986• 0 citations
OpenAlex

Abstract

By means of integral techniques within normal product we have studied the dynamic mechanism of the generation of squeezed state and its intrinsic relationship with the quantum scaling evolution.

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In this paper, we consider quantum multidimensional problems solvable by using the second quantization method. A multidimensional generalization of the Bogolyubov factorization formula, which is an important particular case of the Campbell-Baker-Hausdorff formula, is established. The inner product of multidimensional squeezed states is calculated explicitly; this relationship justifies a general construction of orthonormal systems generated by linear combinations of squeezed states. A correctly defined path integral representation is derived for solutions of the Cauchy problem for the Schrödinger equation describing the dynamics of a charged particle in the superposition of orthogonal constant ( E,H )-fields and a periodic electric field. We show that the evolution of squeezed states runs over compact one-dimensional matrix-valued orbits of squeezed components of the solution, and the evolution of coherent shifts is a random Markov jump process which depends on the periodic component of the potential.