Slowly Passing through Resonance Strongly Depends on Noise

The response of a periodically driven nonlinear oscillator slowly passing through resonance has long been suspected but never been shown to be dramatically affected by noise. The slow passage in the presence of noise is studied analytically and experimentally using a periodically modulated laser. Hysteresis in the magnitude of the oscillations of the laser output intensity is produced by sweeping back and forth the modulation frequency near resonance with the laser relaxation oscillations. The area of the hysteresis loop at first increases with the amplitude of the modulation but then exhibits a plateau determined by the noise level.