Quantum Noise, Effective Temperature, and Damping in a Superconducting Single-Electron Transistor

We have directly measured the quantum noise of a superconducting single-electron transistor (S-SET) embedded in a microwave resonator consisting of a superconducting LC tank circuit. Using an effective bath description, we find that the S-SET provides damping of the resonator modes proportional to its differential conductance and has an effective temperature that depends strongly on the S-SET bias conditions. In the vicinity of a double Cooper pair resonance, when both resonances are red detuned the S-SET effective temperature can be well below both the ambient temperature and the energy scale of the bias voltage. When blue detuned, the S-SET shows negative differential conductivity,