Kinetics of the superconducting charge qubit in the presence of a quasiparticle
Abstract
We investigate the energy and phase relaxation of a superconducting qubit caused by a single quasiparticle. In our model, the qubit is an isolated system consisting of a small island (Cooperpair box) and a larger superconductor (reservoir) connected with each other by a tunable Josephson junction. If such a system contains an odd number of electrons, then even at lowest temperatures a single quasiparticle is present in the qubit. Tunneling of a quasiparticle between the reservoir and the Cooperpair box results in the relaxation of the qubit. We derive master equations governing the evolution of the qubit coherences and populations. We find that the kinetics of the qubit can be characterized by two time scales—quasiparticle escape time from the reservoir to the box Γ_{in}^{1} and quasiparticle relaxation time τ . The former is determined by the dimensionless normalstate conductance g_{T} of the Josephson junction and oneelectron level spacing δ_{r} in the reservoir (Γ_{in}∼g_{T}δ_{r}) , and the latter is due to the electronphonon interaction. We find that phase coherence is damped on the time scale of Γ_{in}^{1} . The qubit energy relaxation depends on the ratio of the two characteristic times τ and Γ_{in}^{1} and also on the ratio of temperature T to the Josephson energy E_{J} .
 Publication:

Physical Review B
 Pub Date:
 August 2006
 DOI:
 10.1103/PhysRevB.74.064515
 arXiv:
 arXiv:condmat/0603640
 Bibcode:
 2006PhRvB..74f4515L
 Keywords:

 74.50.+r;
 03.67.Lx;
 03.65.Yz;
 85.25.Cp;
 Tunneling phenomena;
 point contacts weak links Josephson effects;
 Quantum computation;
 Decoherence;
 open systems;
 quantum statistical methods;
 Josephson devices;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Superconductivity
 EPrint:
 12 pages, 4 figures, final version as published in PRB, some changes, reference added