Starting from the Kubo formula for conductance, we calculate the frequency-dependent response of a single-electron transistor (SET) driven by an ac signal. Treating tunneling processes within the lowest order approximation, valid for a wide range of
parameters, we discover a finite reactive part even under Coulomb blockade due to virtual processes. At low frequencies this can be described by an effective capacitance. This effect can be probed with microwave reflection measurements in radio-frequency (rf) SET provided that the capacitance of the surroundings does not completely mask that of the SET.
We consider coupled quantum two-state systems (qubits) exposed to a global relaxation process. The global relaxation refers to the assumption that qubits are coupled to the same quantum bath with approximately equal strengths, appropriate for long-wa
velength environmental fluctuations. We show that interactions do not spoil the picture of Dickes subradiant and superradiant states where quantum interference effects lead to striking deviations from the independent relaxation picture. Remarkably, the system possess a stable entangled state and a state decaying faster than single qubit excitations. We propose a scheme how these effects can be experimentally accessed in superconducting flux qubits and, possibly, used in constructing long-lived entangled states.
