Superconducting microwave cavities and Josephson junctions

The possibility of using very‐high‐Q superconducting microwave cavities to obtain a strong coupling between the electromagnetic field and a Josephson junction has prompted a study of such systems. Expressions have been obtained describing the dc I‐V characteristic of a junction biased so that the Josephson radiation frequency is near a resonance of the cavity in which it is located. The rf power coupled into an X‐band (10 GHz) TE₀₁₁ mode cavity from a weakly coupled junction is approximately ${\text{3×10}}^{\text{−13}}{\mathrm{\hspace{0.17em}I}}_0^2\mathrm{\hspace{0.17em}Q\hspace{0.17em}}\mathrm{W}$ , where I₀ is the critical current of the junction and Q is the cavity Q. When the coupling between the junction and cavity is large enough, the I‐V characteristic becomes multiple valued and the power coupled to the cavity depends on the state of the system. The maximum power which can be coupled to the cavity is approximately 0.58I₀V_dc, where V_dc is the voltage required to bias the junction to the resonant frequency of the cavity.