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 (Cooper-pair box) and a larger superconductor (reservoir) connected with each other by a tunable Josephson junction. If such 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 Cooper-pair 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 reservoir to the box, ${\Gamma }_{in}^{-1}$, and quasiparticle relaxation time $\tau$. The former is determined by the dimensionless normal-state conductance $g_T$ of the Josephson junction and one-electron level spacing ${\delta }_r$ in the reservoir (${\Gamma }_{in}\sim g_T{\delta }_r$), and the latter is due to electron-phonon interaction. We find that phase coherence is damped on the time scale of ${\Gamma }_{in}^{-1}$. The qubit energy relaxation depends on the ratio of the two characteristic times, $\tau$ and ${\Gamma }_{in}^{-1}$, and also on the ratio of temperature $T$ to the Josephson energy $E_J$.

12 pages, 4 figures, final version as published in PRB, some changes, reference added

References in corpus (2)

• Quasiparticle decay rate of Josephson charge qubit oscillations
• Time-domain measurements of quasiparticle tunneling rates in a single-Cooper-pair transistor

Cited by in corpus (10)

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• Life after charge noise: recent results with transmon qubits
• Kinetics of non-equilibrium quasiparticle tunneling in superconducting charge qubits
• Microsecond resolution of quasiparticle tunneling in the single-Cooper-pair-transistor
• Kinetics of quasiparticle trapping in a Cooper-pair box
• Narrow band microwave radiation from a biased single-Cooper-pair transistor
• The parity effect in Josephson junction arrays
• Time-optimal performance of Josephson charge qubits: A process tomography approach
• Energy relaxation of superconducting charge qubit via Andreev processes