Stochastic resonance of vortices in a washboard pinning potential

Abstract

In a bistable potential at low temperatures, stochastic resonance can be characterized as a synchronization effect of the hopping mechanism induced by an external periodic stimulus, where synchronization attains a maximum by fine-tuning the forcing frequency close to the relevant switching rate. In this work, we theoretically investigate the nonlinear single-vortex dynamics in a tilted cosine (multistable) washboard pinning potential at nonzero temperature in the presence of dc and ac currents of arbitrary amplitudes and frequency. The conditions for stochastic resonance to appear are derived on the basis of the exact solution of the corresponding Langevin equation for non-interacting vortices in terms of a matrix continued fraction. The nonlinear ac voltage response is analyzed as a function of temperature, dc bias, ac amplitude and frequency, with particular focus on the amplification of the external harmonic signal and its conversion to the third harmonics of the input frequency.