We consider the energetics of a superconducting double dot, comprising two superconducting islands coupled in series via a Josephson junction. The periodicity of the stability diagram is governed by the competition between the charging energy and the
superconducting gap, and the stability of each charge state depends upon its parity. We also find that, at finite temperatures, thermodynamic considerations have a significant effect on the stability diagram.
We measure an aluminum superconducting double quantum dot and find that its electrical impedance, specifically its quantum capacitance, depends on whether or not it contains a single broken Cooper pair. In this way we are able to observe, in real tim
e, the thermally activated breaking and recombination of Cooper pairs. Furthermore, we apply external microwave light and break single Cooper pairs by the absorption of single microwave photons.
