Squeezing and broadening effects in mechanical oscillators

The general theory of harmonic oscillators with time-dependent frequency and 'effective mass' is related in the present work to the use of the adiabatic approximation. A slow 'pumping' of energy into the mechanical oscillator leads to a slow increase of the amplitude and frequency with squeezing effects by which the noise in one quadrature is increasing and in the other quadrature is decreasing. An order of magnitude for the squeezing effect is calculated. It is suggested to use this theory for mechanical oscillators in traps and for resonant detectors. The other extreme case of 'impulse' interaction in which the time of interaction is very small relative to the time period of the harmonic oscillator is analyzed. In the 'impact' approximation the time development is without any squeezing, but broadening effects might be important under special conditions. The 'impact' approximation might be related to the detection of gravitational waves by Michelson interferometers.