Critical Phenomenon of a Consistent q-Deformed Squeezed State

Details Critical Phenomenon of a Consistent q-Deformed Squeezed State Critical Phenomenon of a Consistent q-Deformed Squeezed State

2000-10-20

arxiv.org/abs/hep-th/0010176v1

Annals Phys. 290 (2001) 45-52

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX, including 2 figures

Scientific paper

10.1006/aphy.2001.6138

Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special q-deformed squeezed states are constructed. Besides the similar local maximum squeezing as the one in the undeformed case, new strong squeezing appears when the amplitude of the related coherent state increases to large values. A critical phenomenon appears at a large value of the amplitude: the variance of one component of the quadrature of the light field approaches zero, but the variance of the corresponding conjugate quantity remains finite, which is a surprising deviation from Heisenberg's uncertainty relation. The qualitative character exposed by this q-squeezed state may provide some evidence about q-deformed effects in current experiments.

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