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Physical Review A

Statistical properties of a charged oscillator in the presence of a constant magnetic field

M. Sebawe Abdalla

Published Aug 1, 1991• 20 citations
Publisher

Abstract

From the quantum-optics point of view the problem of a charged particle in the presence of a constant magnetic field is presented. The photon numbers as well as bunching and antibunching are considered. Statistical investigations are carried out for the quasiprobability distribution function (Wigner function). The phenomenon of squeezing is also discussed.

DOI
10.1103/physreva.44.2040

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From the quantum-optics point of view the problem of a charged particle in the presence of a constant magnetic field is presented. The photon numbers as well as bunching and antibunching are considered. Statistical investigations are carried out for the quasiprobability distribution function (Wigner function). The phenomenon of squeezing is also discussed.
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.
We investigate a free monochromatic electromagnetic field which is in the even or odd coherent state with thermal noise. The main tool in our analysis is the characteristic function. We establish an alystic formula for an arbitrary correlation function. We point out the non-classical oscillations of the photon-number distribution and find its generating function as well as the degree of purity of the field. We also examine the squeezing properties and antibunching feature. Besides, the usual quasiprobability densities are derived.
The statistical properties of the time evolution operator for the Hamiltonian describing the simultaneous non-degenerate parametric amplifier, and mixing of two modes in the rotator frame is considered. Here we study the effects of this operator on the photon number sum and difference. The Glauber second-order correlation function is calculated, and the squeezing related to the frequency converter and the parametric amplifier has been discussed. The statistical investigations for the quasiprobability distribution functions are carried out.