From a quite general form of the Lindblad-like master equation of open two-level systems(qubits), we study the effect of Lamb shift on the non-Markovian dynamics. We find that the Lamb shift can induce a non-uniform rotation of the Bloch sphere, but that it does not affect the non-Markovianity of the open system dynamics. We determine the optimal initial-state pairs that maximize the backflow of information for the considered master equation and find an interesting phenomenon–the sudden change of the non-Markovianity. We relate the dynamics to the evolution of the Bloch sphere to help us comprehend the obtained results.
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