Low temperature decoherence and relaxation in charge Josephson-junction qubits

TL;DR

This paper analyzes how charge Josephson-junction qubits lose coherence and relax at low temperatures, focusing on environmental noise effects, especially from fluctuating background charges, and provides exact and perturbative solutions.

Contribution

It offers an exact solution for pure decoherence models and a perturbative analysis of relaxation, clarifying temperature and coupling effects on qubit decoherence.

Findings

Decoherence rate saturates at high temperatures

Decoherence becomes linear in temperature at low temperatures

Spectral density of noise explains relaxation behavior

Abstract

In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoherence rate saturates at `high' temperatures while becoming linear in T at low temperatures and showing in all regimes a non-monotonic behaviour as a function of the coupling of the qubit to the fluctuating background charges. We have also considered, albeit only perturbatively, the qubit relaxation by the background charges and demonstrated that a quasi-linear behaviour of the spectral density of noise deduced from the measurements of the relaxation rate can be qualitatively explained.