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

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