Double stochastic resonance over an asymmetric barrier

In a recent experiment [Müller et al., Phys. Rev. A 79, 031804(R) (2009)] reported a splitting of the stochastic resonance peak, which they attributed to the asymmetry of an effective double-well restoring potential in their optomechanical read-out device. We show here that such an effect, though smaller than reported, is indeed consistent with a characterization of stochastic resonance as a synchronization phenomenon, while it proves elusive in terms of spectral quantifiers.

Figure 1

(Color online) Our model ADW potential Eq. (1) for $b_{+}=0.5$, $b_{-}=5$ and $V_0=1$. The barrier turns out to be centered at $x_0\simeq 0.5$ and $\Delta V=1$ high. The curvatures of the potential at $x=\pm 1$ and $x_0$ are, respectively, ${\omega }_{-}^2=2.1$, ${\omega }_{+}^2=85.2$, and ${\omega }_0^2=5.7$.

Figure 2

(Color online) Residence time distributions $N_{\pm }\left(T\right)$ in the ADW potential Eq. (1) for different values of $D$ (in the legends). The subscripts $\pm$ denote the transitions, respectively, right-to-left and left-to-right (see text). Other simulation parameters: $A=0.2$, $\Omega =0.2$ and the ADW parameters as in Fig. 1.

Figure 3

(Color online) Degree of coherence in the ADW potential (1): $C_{+}$ (squares), $C_{-}$ (triangles), and $\overline{C}$ (circles) vs $D$ for different $A$ (in the legend). Vertical arrows locate the peaks, $D_{\pm }$ of $C_{\pm }$. Other simulation parameters: $ϵ\equiv \Delta t/T_{\Omega }=0.1$. $\Omega =0.2$ and the ADW parameters as in Fig. 1 Inset: dependence of the curves $\overline{C}\left(D\right)$ on $ϵ$ and $A$.

Figure 4

(Color online) Subtracted strength $\Delta S_1$ of the first spectral peak at $\omega =\Omega$ versus $D$ for different $A$. Other simulation parameters: $\Omega =0.2$ and the ADW parameters as in Fig. 1