Quasiparticle decay rate of Josephson charge qubit oscillations

TL;DR

This paper investigates how quasiparticles in superconductors cause decay in Josephson charge qubit oscillations, revealing temperature-dependent behaviors and differences based on system isolation and electron parity.

Contribution

It provides a detailed analysis of quasiparticle-induced decay rates in charge qubits, including temperature dependence and effects of system isolation and electron parity.

Findings

Decay rate has an activation energy of Δ in open systems.

In isolated systems, activation energy is 2Δ for even electrons.

Decay rate remains finite at zero temperature for odd-electron systems.

Abstract

We analyze the decay of Rabi oscillations in a charge qubit consisting of a Cooper pair box connected to a finite-size superconductor by a Josephson junction. We concentrate on the contribution of quasiparticles in the superconductors to the decay rate. Passing of a quasiparticle through the Josephson junction tunes the qubit away from the charge degeneracy, thus spoiling the Rabi oscillations. We find the temperature dependence of the quasiparticle contribution to the decay rate for open and isolated systems. The former case is realized if a normal-state trap is included in the circuit, or if just one vortex resides in the qubit; the decay rate has an activational temperature dependence with the activation energy equal to the superconducting gap $\Delta$. In a superconducting qubit isolated from the environment, the activation energy equals $2\Delta$ if the number of electrons is even, while for an odd number of electrons the decay rate of an excited qubit state remains finite in the limit of zero temperature. We estimate the decay rate for realistic parameters of a qubit.