We calculate the full frequency spectral density of voltage fluctuations in a Single Electron Transistor (SET), used as an electrometer biased above the Coulomb threshold so that the current through the SET is carried by sequential tunnel events. We consider both a normal state SET and a superconducting SET. The whole spectrum from low frequency telegraph noise to quantum noise at frequencies comparable to the SET charging energy (EC/ℏ), and high frequency Nyquist noise is described. We take the energy exchange between the SET and the measured system into account using a real-time diagrammatic Keldysh technique. The voltage fluctuations determine the back-action of the SET onto the measured system and we specifically discuss the case of superconducting charge qubit read-out and measuring the so-called Coulomb staircase of a single Cooper pair box.
@article{arxiv.cond-mat/0211055,
title = {Full frequency voltage noise spectral density of a single electron transistor},
author = {Andreas Kack and Goran Johansson and Goran Wendin},
journal= {arXiv preprint arXiv:cond-mat/0211055},
year = {2015}
}