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arXiv:0710.1942 · Journal of Physics A Mathematical and Theoretical

Spatial confinement effects on a quantum harmonic oscillator: nonlinear coherent state approach

M Bagheri Harouni, R Roknizadeh, M. H. Naderi

Published Dec 17, 2008• 17 citations
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Abstract

In this paper we study some basic quantum confinement effects through investigation of a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the framework of nonlinear coherent states theory. We construct the coherent states associated with the spatially confined quantum harmonic oscillator in a one-dimensional infinite well and examine some of their quantum statistical properties, including sub-Poissonian statistics and quadrature squeezing.

DOI
10.1088/1751-8113/42/4/045403

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In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using non-linear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs modell. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface is appeared as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
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