Josephson Junction as a Detector of Poissonian Charge Injection

We propose a scheme of measuring the non-Gaussian character of noise by a hysteretic Josephson junction in the macroscopic quantum tunneling regime. We model the detector as an (under)damped $LC$ resonator. It transforms Poissonian charge injection into current through the detector, which samples the injection statistics over a floating time window of length $\sim Q/{\omega }_{\mathrm{J}}$, where $Q$ is the quality factor of the resonator and ${\omega }_{\mathrm{J}}$ its resonance frequency. This scheme ought to reveal the Poisson character of charge injection in a detector with realistic parameters.

Figure 1

The scheme of the threshold measurement and the model. The current through the Josephson junction (or a dc-SQUID) is determined by those through the scatterer ($I_1$) and the ideal bias line ($I_2$), respectively. Switching to the normal state of the Josephson junction is signaled by a nonzero voltage $V$ at the output of the amplifier. The resonator model and the charge injection are discussed in the text.

Figure 2

Simulated $I(t)$ (thin solid lines) with the following parameters: $\overline{I}=100$ and $p=0.01$, and, with two values of quality factor, $Q=1$ and $Q=10$, respectively. Thick solid lines are expectations of $⟨I(t)⟩$ according to Eq. (4).

Figure 3

Simulated current distribution at ${\omega }_{\mathrm{J}}t=40$, $Q=2$, and $\overline{I}=10e^{*}{\omega }_{\mathrm{J}}$. The main frame shows the number of counts (out of 300 000) in solid dots, and the solid line is the best Gaussian fit to it. The inset shows the same results but as the true distribution, $=\mathrm{\text{counts}}/300000$, and on linear scale.

Figure 4

Escape probability $P$ of a Josephson junction as a function of the average current $\overline{I}$ through the detector under different noise conditions. The shift between the solid and the dashed lines arises from Poisson statistics of charge injection. The dash-dotted line is the escape probability with the corresponding Gaussian noise (same $⟨\delta I^2⟩$). Escape in the ideal case of noiseless current is shown by the dotted line.