Detecting Charge Noise with a Josephson Junction: A Problem of Thermal Escape in Presence of Non-Gaussian Fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.

Figure 1

Rate asymmetry $R_{\Gamma }$ according to (13) for ${\omega }_0\hslash \beta =0.5$, $\beta E_J=200$, $Q=2.5$, and various $s_m$ vs the bias current $s_b$: $s_m=3$ (solid), $s_m=2.3$ (long-dashed), $s_m=1.7$ (short-dashed), $s_m=1.1$ (dotted). The inset shows $R_{\Gamma }$ for the same parameters and $s_b=0.75$, $s_m=1.1$ as a function of $Q$.