Charge and current fluctuations in a superconducting single electron transistor near a Cooper pair resonance

We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even--odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasi-particle tunneling rates are comparable to the coherent Cooper-pair oscillation frequency. Furthermore the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.