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Physical Review A

Generation of squeezing for a charged oscillator and for a charged particle in a time-dependent electromagnetic field

B. Baseia, Salomon Sylvain Mizrahi, M. H. Y. Moussa

Published Nov 1, 1992• 50 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.46.5885

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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 consider the most general Time-Dependent (TD) quadratic Hamiltonian written in terms of the bosonic operators a and a + , which may represent either a charged particle subjected to a harmonic motion, immersed in a TD uniform magnetic field, or a single mode photon field going through a squeezing medium. We solve the TD Schrödinger equation by a method that uses, sequentially, a TD unitary transformation and the diagonalization of a TD invariant, and we verify that the exact solution is a complete set of TD states. We also obtain the evolution operator which is essential to express operators in the Heisenberg picture. The variances of the quadratures are calculated and a phase space of parameters introduced, in which we identify squeezing regions. The results for some special cases are presented and as an illustrative example the parametric oscillator is revisited and the trajectories in phase space drawn.
By successive applications of time-dependent rotation, translation and dilatation, it is shown that a charged time-dependent harmonic oscillator in a uniform time-dependent electromagnetic field is equivalent to a free particle. This equivalence is employed to present a simple derivation of the Feynman kernel as well as to obtain a concrete picture of the time evolution of a generic wave packet. A compact formula for an evolving anisotropic Gaussian packet is also derived. A special case of this formula gives a squeezed coherent state for a harmonic oscillator whose frequency is an arbitrary function of time. Finally we discuss an Aharonov-Bohm-Berry-like phase associated with a wave packet whose center traces a closed circuit.