Phonon-induced decoherence of Andreev level qubit

We use the kinetic equation for the density matrix to investigate the decoherence of the Andreev level qubit [1] due to coupling to soft acoustic modes in the quantum point contact (QPC) electrodes [2], in the light of recent results concering intrinsic sources of decoherence of superconducting qubits caused by microscopic modes and losses within the Josephson Phonon-induced decoherence of Andreev level qubit junctions [3]. We find a result different from the conventional Bloch-Redfield equation describing decoherence of macroscopic superconducting qubits. Suppression of the interlevel transitions by the many body effects results non-exponential decay, and in dramatic reduction of the qubit decoherence rate at low temperature due to strong reduction of the relevant phonon phase space. Furthermore, the rate of phonon-induced transitions between the Andreev levels is found to be significantly smaller than the bulk transition rate. $\backslash \vert $1] A. Zazunov, et al., Phys. Rev. Lett. 90, 087003 (2003).2] A. Zazunov, et al., cond-mat/0404656.3] R. W. Simmonds, et al., Phys. Rev. Lett. 93, 077003 (2004); L. B. Ioffe, et al., Phys. Rev. Lett. 93, 057001 (2004)