A parametric oscillator for classroom demonstration or student laboratory

We describe a simple and intuitive parametric oscillator apparatus which is suitable for a classroom demonstration or an upper-division laboratory. In order to facilitate the incorporation of this apparatus into the physics curriculum, we provide the learning objectives for an upper-division physics laboratory experiment. We present typical experimental data illustrating the main features of parametric oscillators including oscillation threshold, frequency shifting at large amplitude and bistability. Our experiments and theory emphasize identifying the lowest-order threshold for oscillation in terms of the modulation depth and quality factor. This experiment provides a foundation for understanding current research such as that in quantum opto-mechanics and nonlinear dynamics.