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Modern Physics Letters B

WAVE FUNCTION OF THE PARTICLE TRAPPED BY OSCILLATING FIELDS

CELIA M. A. DANTAS, Vanderlei Salvador Bagnato, B. Baseia

Published Oct 30, 1994• 0 citations
Publisher

Abstract

In a previous paper [Quantum Opt.5, 155 (1993)] we have employed a recent model by Glauber for particle trapping by oscillating fields to investigate the occurrence of the squeezing effect for this system. Here we construct a linear time-dependent invariant which allows us to obtain the wave function of the system. The treatment is general for a class of time-dependent Hamiltonian, the application to our previous work being a particularization of the present procedure.

DOI
10.1142/s0217984994001503

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In a previous paper [Quantum Opt.5, 155 (1993)] we have employed a recent model by Glauber for particle trapping by oscillating fields to investigate the occurrence of the squeezing effect for this system. Here we construct a linear time-dependent invariant which allows us to obtain the wave function of the system. The treatment is general for a class of time-dependent Hamiltonian, the application to our previous work being a particularization of the present procedure.
The first observation of the squeezing effect outside the optical domain was reported very recently for trapped atoms [D. M. Meekhof et al., Phys. Rev. Lett.76, 1796 (1996)]. Pursuing this line and a sequel of previous works of ours we employ a model by Glauber and a method of invariants by Lewis and Riesenfeld to establish a connection between the squeezing and the cooling effects in the system. From this connection the occurrence of squeezing could be detected through the measurement of the dispersion in the variable [Formula: see text] and of the temperature.
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.