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Modern Physics Letters B

Squeezing Transformation for Dynamics of An Electron in Uniform Magnetic Field and a Harmonic Potential

Hong-Yi Fan, Yan Zhang

Published Mar 10, 1997• 17 citations
Publisher

Abstract

By virtue of the <λ| representation (Hong-yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996)), which is useful for studying quantum Hall effect, we reveal that a squeezing mechanism directly corresponding to the variation of electron's cyclotron frequency is involved in the dynamics of an electron in a uniform magnetic field and a harmonic potential. Electron's wave functions are also derived by the squeezing transformation in the <λ| representation.

DOI
10.1142/s021798499700030x

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By virtue of the <λ| representation (Hong-yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996)), which is useful for studying quantum Hall effect, we reveal that a squeezing mechanism directly corresponding to the variation of electron's cyclotron frequency is involved in the dynamics of an electron in a uniform magnetic field and a harmonic potential. Electron's wave functions are also derived by the squeezing transformation in the <λ| representation.
By using the technique of integration within an ordered product (IWOP) of operators, we derive the normal-product form of the gauge-invariant Wigner operator of an electron in a uniform magnetic field and its expression in the newly constructed |λ> representation. The virtue of working in the |λ> representation lies in the fact that it is expressed in terms of the ladder operators Π±, K±(see Eq. (10)), thus the magnetic vector potential can naturally be included. On these bases we can easily obtain Wigner functions of some important electron states.
Recent papers [A. Bechler, Phys. Lett. A 130, 481 (1988); M. S. Abdalla, Phys. Rev. A 44, 2040 (1991)] investigate the generation of squeezing for a charged oscillator in a constant and uniform magnetic field. Here we pursue further this line by investigating the extended system of a charged particle oscillating in a uniform and arbitrary time-dependent magnetic field. Since we do not particularize the functional time dependence, our expressions for the variances of quadratures are quite general, so the possible occurrence and amount of squeezing will depend on that specification. The corresponding results mentioned above become a particularization of ours.