Low-temperature decoherence of qubit coupled to background charges

We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures $T$ the decoherence rate $\Gamma$ is linear in $T$ while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high $T$. In contrast to the classical picture, impurity states spread in a wide interval of energies $(⪢T)$ may essentially contribute to $\Gamma$.

Figure 1

Dependence of the decoherence rate on a temperature, Eq. (12), for strong and weak coupling. The main picture shows a fluctuator with ${\nu }_{\epsilon }\left(\omega \right)$ centered at $\tilde{\epsilon }=3$, the insert shows $\tilde{\epsilon }=0$. $\tilde{T},\tilde{\Gamma },\tilde{\epsilon }$ are measured in units of $\gamma ∕2$.

Figure 2

Nonmonotonic dependence of the decoherence rate on the coupling strength at different temperatures for $\tilde{\epsilon }=3$.