Speaker
Description
Bogolyubov quasiparticles represent an important sources of errors in superconducting
qubits. Unlike the quasiparticle contribution to $1/T_1$ qubit relaxation rate, the pure dephasing rate $1/T_\phi$ can not be obtained by the perturbative golden rule calculation due to
the logarithmic divergence of the quasiparticle noise correlator at low frequency (1). For
such noises with a divergent correlator, non-perturbative calculations usually reveal a non-
exponential decay of the qubit coherence. Particularly, for the quasiparticles in the work (2)
the dephasing function of the form $F(t) = \exp[-t \log(t T)]$ was found for qubits based on
Josephson junctions with a large number of transmission channels $N$ at temperature $T$. We
treat this problem for a finite number of channels and find that the exponential form of the
decay is restored at large times. Instead of expanding in the coupling strength or inverse number of channels $1/N$ we take advantage of the low quasiparticle concentration $x_{qp} \ll 1$ and use it a small parameter. In this case the fermionic nature of the quasiparticle
bath becomes important; it can be handled using Levitov formula (3), which allows to rewrite the dephasing function $F(t)$ as a determinant of single-particle operators. We find that the non-exponential decay of the dephasing function $F(t)$ described in (2) is followed by the longest-time exponential regime. It is governed by the energy scale of the depth of the Andreev bound states $\epsilon_A$ in the Josephson junction, namely $F(t) = \exp[-t \log(T/\epsilon_A )]$ for $t \gg 1/\epsilon_A$. Our results are especially relevant for qubits built on medium- or small-area junctions for which the time scale $1/\epsilon_A$ is comparable to the qubit lifetimes.
(1) G. Catelani et al., Phys. Rev. B 84, 064517 (2011).
(2) S. Zanker and M. Marthaler, Phys. Rev. B 91, 174504 (2015).
(3) I. Klich ,arXiv:cond-mat/0209642 (cond-mat.mes-hall) (2002).