Full frequency voltage noise spectral density of a single electron transistor

TL;DR

This paper calculates the complete frequency spectrum of voltage noise in single electron transistors, covering from low-frequency telegraph noise to high-frequency quantum noise, and discusses implications for quantum measurement back-action.

Contribution

It provides a comprehensive analysis of voltage noise spectral density in SETs, including both normal and superconducting states, using a real-time diagrammatic Keldysh technique.

Findings

Spectrum covers low to high frequencies, including quantum noise.

Voltage fluctuations impact qubit read-out and Coulomb staircase measurement.

Analysis applies to both normal and superconducting SETs.

Abstract

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 $(E_{C}/\hbar)$, 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.