Dissipation in Josephson tunneling junctions at low temperatures

TL;DR

This paper investigates the mechanisms of energy dissipation and decoherence in Josephson junction-based qubits at low temperatures, focusing on energy transfer to two-level systems and deriving equations to predict qubit behavior.

Contribution

It introduces a general equation of motion for the phase difference in Josephson junctions, accounting for electromagnetic and electron tunneling dissipation mechanisms, and applies it to qubit decoherence analysis.

Findings

Decay of Rabi oscillations due to two-level systems

Frequency shift in qubits caused by dissipation mechanisms

Results align with previous Fermi's Golden rule calculations

Abstract

It is important to know the decoherence mechanism of a qubit based on Josephson junctions. At low temperatures, as quasiparticle concentration becomes exponentially small, one needs to consider energy transfer from tunneling electrons to other degrees of freedom to find dissipation in Josephson junctions and decoherence in qubits. Here we discuss the energy transfer to two-level systems, i.e. the transitions between two different configurations of ions inside insulating layer separated by a potential barrier. We derive a general equation of motion for the phase difference between two superconducting electrodes and we find a retarded dissipation term due to electromagnetic mechanism and also contribution due to electron tunneling mechanism. Using the equation of motion we calculate the decay of Rabi oscillations and frequency shift in qubits due to the presence of the two-level systems. In the long time limit our results coincide with those obtained by Martinis et al. [J. M. Martinis et al.. Phys. Rev. Lett. 95, 210503 (2005)] within the Fermi's Golden rule approach up to a numerical factor.