Models of Environment and $T_1$ Relaxation in Josephson Charge Qubits

A theoretical interpretation of the recent experiments of Astafiev et al. on the $T_1$-relaxation rate in Josephson charge qubits is proposed. The experimentally observed reproducible nonmonotonic dependence of $T_1$ on the splitting $E_J$ of the qubit levels suggests further specification of the previously proposed models of the background charge noise. From our point of view the most promising is the “Andreev fluctuator” model of the noise. In this model the fluctuator is a Cooper pair that tunnels from a superconductor and occupies a pair of localized electronic states. Within this model one can naturally explain both the average linear $T_1(E_J)$ dependence and the irregular fluctuations.

Figure 1

The three models.

Figure 2

The relaxation rate as a function of frequency for Model III. The curve shows one typical realization of the disorder while the solid line is the average over realizations. The dashed line shows $⟨{\Gamma }_1(\omega {)}^2⟩$.

Figure 3

The relaxation rate as a function of frequency for Model I. The curve shows one typical realization of the disorder while the solid line is the average over realizations. The dashed line shows $⟨{\Gamma }_1(\omega {)}^2⟩$.