Tunneling rates of electron pumping in the R-SINIS transistor

We consider the influence of the electromagnetic fluctuations on the transport properties of a hybrid single electron transistor, consisting of superconducting electrodes and a normal-metal island, when operated as a turnstile. We derive the analytic expressions for the rates near the thresholds of single electron tunneling, Andreev reflection, and Cooper-pair--electron cotunneling processes. These results show that the dissipative on-chip impedance suppresses the rates of the undesirable higher-order tunneling processes much stronger than the single electron tunneling which can therefore be utilized to increase the accuracy of such a device in quantum metrological applications. \\[4pt] [1] J.P. Pekola, J.J. Vartiainen, M. M\"{o}tt\"{o}nen, O.-P. Saira, M. Meschke, D.V. Averin, Nat. Phys. 4, 120 (2008).\\[0pt] [2] D.V. Averin, J.P. Pekola, Phys. Rev. Lett. 101, 066801 (2008).\\[0pt] [3] V. Bubanja, Phys. Rev. B 83, 195312 (2011).\\[0pt] [4] V. Bubanja, submitted.