Higher-order resonant behavior in asymmetric nonlinear stochastic systems

We study periodically modulated bistable dynamic elements subject to Gaussian noise and a symmetry-breaking de signal. The skewing of the bistable potential function by the de signal leads to the appearance of even multiples of the drive frequency in the output power spectral density. The spectral amplitudes of ail the harmonics are found to exhibit maxima as functions of the noise statistics and the de signal; the maxima can be shown to depend on matchings of characteristic deterministic and stochastic time scales. A phenomenological description based on a generic bistable system is followed by actual perturbation calculations of the first two spectral amplitudes for a real system, a Josephson junction shorted by a superconducting loop (the mainstay of the rf superconducting quantum interference device). This behavior underlies a recently proposed ''frequency-shifting'' technique for circumventing detector noise limitations which would otherwise constrain the detection of very low-amplitude signals.