Measurements of quantum noise in resistively shunted Josephson junctions

Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\nu }_J$) to the measurement frequency ($\ll {\nu }_J$) is in the regime $h{\nu }_J>k_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\nu$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $\left(\frac{2h\nu }{R}\right)coth\left(\frac{h\nu }{2k_{B}T}\right)$. The presence of the zero-point term, $\frac{2h\nu }{R}$, at frequencies $h\nu >k_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\beta }_L\equiv \frac{2\pi L_s{I}_0}{{\Phi }_0}\sim 1$ and ${\beta }_C\equiv \frac{2\pi I_0{R}^{2}C}{{\Phi }_0}\ll 1$, where $I_0$ is the critical current, $C$ is the junction capacitance, and $L_s$ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the $L_{s}C$ resonant frequency. The additional nonlinearity of the $I-V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.