Charge Oscillations in Superconducting Nanodevices Coupled to External Environments

Charge oscillations in certain nanodevices, more specifically the so-called Superconducting Cooper Pair Boxes (SCB), are usually interpreted as an effect of macroscopic quantum coherence; an alternative explanation is however possible in terms of the Gross-Pitaewski equation for the classical order parameter. These two explanations are based on different quantum states assigned to the SCB, occupation number states in the first case, coherent-like states in the second one. We show that, when the SCB is weakly coupled to an external source of noise and dissipation, occupation number states are much more unstable than coherent ones. 1. Among the various experimental implementations of qubits, the ones based on superconducting devices have recently attracted much interest. In particular, in a series of measures [1, 2] it has been shown that the so-called Superconducting Cooper Pair Boxes (SCB) [see section 2 below for a detailed definition] allow external control of charge oscillations. Because of the large number of Cooper pairs involved, these oscillations have been interpreted as a manifestation of macroscopic quantum coherence as theoretically explained by the so-called quantum phase model [3, 4] which essentially describes a quantized non-linear oscillator. A different explanation of the experimental results is however possible in terms of the solution of a classical Gross-Pitaewski equation [5]. In this approach, the charge oscillations naturally emerge from the time-behaviour of the SCB order parameter on the basis of a mean-field treatment. While the quantum phase model describes the system in terms of occupation number states, the ones appearing in the mean-field formulation are close to coherent states.