Microwave Photon Interaction with Superconducting Tunneling Currents

Abstract

The photon-assisted tunneling, originally observed by Dayem and Martin, has been remeasured for Al-In junctions and extended to Sn-Pb junctions. Particular attention has been devoted to obtaining detailed quantitative measurements of the current $I$ and the conductance $\frac{\mathrm{dI}}{\mathrm{dV}}$ versus voltage and for various microwave power levels. In addition to the steps in the tunneling current at $e{V}_{0}={\ensuremath{\Delta}}_{1}+{\ensuremath{\Delta}}_{2}\ifmmode\pm\else\textpm\fi{}n\ensuremath{\hbar}\ensuremath{\omega}$ observed by Dayem and Martin, we have observed an additional set at $e{V}_{0}={\ensuremath{\Delta}}_{2}\ensuremath{-}{\ensuremath{\Delta}}_{1}\ifmmode\pm\else\textpm\fi{}n\ensuremath{\hbar}\ensuremath{\omega}$. We can conclude that the phase shift in peak position above the tunneling edge is from an almost exact superposition of these two sets of peaks, a consequence of the near coincidence of the microwave photon energy and one-half the energy gap of indium. A detailed comparison of our results with the theory of Tien and Gordon gives good agreement as to peak positions and shapes while the dependence of peak amplitude on microwave power level is poor, particularly at higher power levels. We have extended the Tien and Gordon theory to provide for a modulation of the density of states in both superconductors and have recalculated the tunneling current. The agreement with experiment is good, in particular, the nonvanishing of the conductance for any value of the microwave power is accounted for.