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We present experimental current-voltage (I-V) measurements on an Al-Al₂O₃-Al single-electron tunneling transistor in the superconducting state. We observe a variety of features which result from Cooper-pair tunneling processes. At low bias voltages and low temperatures we find that the I-V curve is 2e periodic with respect to the gate-induced charge. Remarkably, this periodicity persists up to 300 mK, a behavior which we interpret as strong evidence of an incremental free energy which depends on whether the number of electrons on the superconducting island is even or odd.
Tuominen et al. (Mon,) studied this question.