RF critical current of Josephson junction

The Josephson junction is the only radio-frequency electrical element which can be both non-dissipative and non-linear at low temperatures. While the stability of the junction dynamics in presence of a DC drive has been extensively studied, the microwave drive case is relatively poorly understood, at least experimentally. It is explored by driving an increasing AC current through a Josephson junction which is effectively biased by an AC voltage generator in series with a finite linear imbedding impedance $Z\left( \omega \right)$. For small signal amplitude, the junction behaves as a linear inductor. For higher signal amplitudes, we show that there exists a critical current $I_{c}^{RF}$ beyond which the dynamics of the junction changes qualitatively as a result of its non-linear characteristic. This AC critical current depends strongly on the biasing impedance. We provide a detailed stability diagram from experimental measurements and show that it obeys the simple theory of nonlinear resonance.