Asymmetric Noise Probed with a Josephson Junction

Fluctuations of the current through a tunnel junction are measured using a Josephson junction. The current noise adds to the bias current of the Josephson junction and affects its switching out of the supercurrent branch. The experiment is carried out in a regime where switching is determined by thermal activation. The variance of the noise results in an elevated effective temperature, whereas the third cumulant, related to its asymmetric character, leads to a difference in the switching rates observed for opposite signs of the current through the tunnel junction. Measurements are compared quantitatively with recent theoretical predictions.

Figure 1

Top: Experimental setup. Noise from a tunnel junction (green double box) biased at dc with a current $I_N$ couples through capacitors $C_1=230\mathrm{pF}$ and $C_2=345\mathrm{pF}$ to a Josephson junction (JJ) detector (orange crossed box), which is current-biased on its supercurrent branch. The voltage $V_J$ across the junction monitors the switching to the dissipative state. Capacitor $C_J=12.5\mathrm{pF}$ lowers the JJ plasma frequency to ${\omega }_{p0}/2\pi \simeq 1.5\mathrm{GHz}$. Capacitors $C_N=190\mathrm{pF}$ and $C_g=140\mathrm{pF}$ shunt the external impedance at ${\omega }_{p0}$, so that the impedance across the JJ is determined only by on-chip elements. Resistors $R_1=R_3=215\Omega$ and $R_2=515\Omega$ were fabricated with thin Cr films. Bottom left: $IV$ characteristic of the tunnel junction, linear at this scale, with inverse slope $R_N=22.9\mathrm{k}\Omega$. Bottom right: $IV$ characteristic of the JJ detector, with critical current $I_0=437\mathrm{nA}$. We attribute a resonance near $V_J\sim 120\mu \mathrm{V}$ to a mode of the electromagnetic environment of the junction.

Figure 2

(a) Dependence of $B^{2/3}=\mathbf{(}-\log (\Gamma /A){\mathbf{)}}^{2/3}$ on the current $I_J$ through the JJ detector, for data taken at $T=20\mathrm{mK}$ and currents through the tunnel junction $I_N=0.02$ to $2.11\mu \mathrm{A}$, by steps of $0.42\mu \mathrm{A}$. Linear dependence is a signature of the thermal activation regime. (b) Effective temperature extracted from the slope of data sets as in (a), as a function $I_N$, for various temperatures $T$. Arrows indicate the data points corresponding to the plots in (a). Solid lines are linear interpolations. Dashed line are the predictions from full theory, taking into account the frequency dependence of the admittance $Y(\omega )$ across the JJ and of the transfer function $\alpha (\omega )$ from noise source to JJ detector.

Figure 3

(a) Rate asymmetry $R_{\Gamma }-1$ as a function of current in noise source $I_N$ for various temperatures $T$. Filled (open) symbols correspond to measurements with positive (negative) current through the JJ detector. Solid lines are theoretical predictions scaled by a factor 1.5. (b) Dependence of $R_{\Gamma }-1$ on $s=I_J/I_0$, at $I_N=0.334\mu \mathrm{A}$, obtained with measurement pulses of various lengths. Solid line is theoretical prediction scaled by 1.5.