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 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 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 the reservoir to the box ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and quasiparticle relaxation time $\ensuremath{\tau}$. The former is determined by the dimensionless normal-state conductance
gT of the Josephson junction and one-electron level spacing ${\ensuremath{\delta}}_{r}$ in the reservoir $({\ensuremath{\Gamma}}_{\text{in}}\ensuremath{\sim}{g}_{T}{\ensuremath{\delta}}_{r})$, and the latter is due to the electron-phonon interaction. We find that phase coherence is damped on the time scale of ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$. The qubit energy relaxation depends on the ratio of the two characteristic times $\ensuremath{\tau}$ and ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and also on the ratio of temperature
T to the Josephson energy
EJ.
We demonstrate superconducting qubits using epitaxially grown Josephson junctions. A fully epitaxial NbN/AlN/NbN trilayer on MgO (100) substrate is processed by photolithography and dry-etching into transmon qubits with a large Josephson energy. The tunnel barrier made of cubic-phase AlN, rather than the ordinary hexagonal phase, is the key to avoid piezoelectric coupling to the phonon bath. The energy-relaxation time and the spin-echo decay time of ∼500 ns are observed in the qubits that are coupled to a monolithically made coplanar waveguide resonator.
We demonstrate superconducting qubits using epitaxially grown Josephson junctions. A fully epitaxial NbN/AlN/NbN trilayer on MgO (100) substrate is processed by photolithography and dry-etching into transmon qubits with a large Josephson energy. The tunnel barrier made of cubic-phase AlN, rather than the ordinary hexagonal phase, is the key to avoid piezoelectric coupling to the phonon bath. The energy-relaxation time and the spin-echo decay time of ∼500 ns are observed in the qubits that are coupled to a monolithically made coplanar waveguide resonator.