Squeezing an harmonic oscillator with a sawtooth pulse

In recent years there has been a marked increase in quantum-system states called squeezed and correlated. The aim of this article is an examination of the case of a sawtooth time dependence of an oscillator frequency so as to obtain an exact solution. A sawtooth pulse simulates an experimental situation of interest and makes it possible to consider, in limiting cases, both a delta-function excitation and a slow variation of the frequency. The next section (Section 2) describes the approach based on the method of time-dependent integrals of motion. The classical equations of motion for a parametric oscillator with a sawtooth time dependence of the frequency are solved in Section 3, in a form convenient for finding the transition amplitudes of a quantum oscillator. In Section 4 the explicit forms of the transition amplitudes in the case of a sawtooth pulse are found. Section 5 investigates the excitation of an oscillator from an initial thermal-equilibrium state. The analysis of the results is presented in Section 6. 29 refs., 5 figs