Effect of decoherence on resonant Cooper-pair tunneling in a voltage-biased single-Cooper-pair transistor

We analyze how decoherence appears in the I-V characteristics of a voltage-biased single-Cooper-pair transistor. Especially the effect on resonant single or several Cooper-pair tunneling is studied. We consider both a symmetric and an asymmetric transistor. As a decoherence source we use a small resistive impedance (Re[Z(w)]<<R_Q=h/4e^2) in series with the transistor, which provides both thermal and quantum fluctuations of the voltage. Additional decoherence sources are quasiparticle tunneling across the Josephson junctions and quantum f-noise caused by spurious charge fluctuators nearby the island. The analysis is based on a real-time diagrammatic technique which includes Zeno-like effects in the charge transport, where the tunneling is slowed down due to strong decoherence. As compared to the Pauli-master-equation treatment of the problem, the present results are more consistent with experiments where many of the predicted sharp resonant structures are missing or weakened due to decoherence.