By using the noise correlation functions of Eq. (15), we compute the RI-1 coefficients Eq. (6) of the master equation and solve it numerically to obtain the qubit dynamics. We shall study the absolute value of the Bloch vector and the decay of off-diagonal terms to study the decoherence process suffered by the qubit, as we have done for the ohmic environment.
In Fig. 6 we present the temporal evolution of the absolute value of Bloch vector R while the qubit is evolving under the presence of 1/f1/f noise. We consider σa=0.1Δσa=0.1Δ (ζa=0.2Δζa=0.2Δ) for the black solid line and σa=0.5Δσa=0.5Δ (ζa=0.75Δζa=0.75Δ) for the red dashed curve (a=0,1a=0,1). We can see Monera as the value of σaσa becomes bigger, the sooner purity is lost. This is so because σaσa represents the coupling with the system (a=0a=0 in the longitudinal coupling, and a=1a=1 in the transverse case). Similar to the case of an ohmic environment at high-T , the 1/f1/f noise is very efficient in inducing decoherence on the system. The choice of parameters has been done to assure that there are no memory effects in the evolution, namely ζ>σζ>σ in our weak coupled model. In both cases, we see that purity is a monotonic decaying function.