The author examines the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency. Using the evolution operator method developed by Cheng and Fung, he investigates the evolution of a coherent state of a time-dependent harmonic oscillator as well as its squeezing and coherence property. Two specific models of frequency variation are explored; namely, one whose frequency is exponentially decreasing in time and the other with a periodic frequency. His analyses indicates that the wavefunction of the time-dependent oscillator starts as a coherent state at t=O and evolves as a squeezed state at a later time. It is also shown that squeezing cannot be generated by an adiabatic change of the oscillator frequency because the variances of q and p turn out to be adiabatic invariants, whereas a sudden change can produce squeezing.
The behaviour of an oscillator may be controlled by the frequency time-dependence. For example, one can kick the oscillator frequency by short pulses and this kicking produces an excitation of the parametric oscillator. The amplitude of the oscillator vibrations and its energy may increase due to the external influence expressed as the frequency time-dependence. Also the statistical properties of the oscillator state may be changed due to the action of external forces. The aim of the talk is to discuss the exact solution of the time-dependent Schrodinger equation for a damped quantum oscillator subject to a periodical frequency delta-kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola-Kanai model [1], [2].