Tunable non-Markovian and quantum coherence in the single-qubit dephasing noise channel

In this paper, we construct a single-qubit dephasing noise channel based on the nuclear magnetic resonance（NMR） system by employing the bath-engineering technology, and achieve the construction of the tunable non-Markovian environment in the dephasing noise channel. Our findings indicate that for the single-qubit system, the transition of system dynamics from Markovian to non-Markovian can be achieved by adjusting the base frequency of the noise power spectrum. However, the base frequency corresponding to this phase transition point is not fixed, and there is a certain relationship between it and the total evolution time of the single-qubit system. Through our research, we discovered a fundamental relationship: if the single-qubit system dynamics undergoe a transition from Markovian to non-Markovian at ω0 within 0-2t ms, shortening the evolution time to 0-t ms results in an increase of the phase transition point to 2ω0. This insight offers crucial guidance for artificially crafting non-Markovian environments across arbitrary time scales in single-qubit systems, and it is not limited by the type of noise. Apart from system dynamics, quantum coherence is also a focal point of our research. We find that when the system dynamics exhibit non-Markovian behavior, the quantum coherence of the single-qubit system experiences revivals. Notably, the timing of these coherence revivals aligns with the instants of the non-Markovianity enhancement. Therefore, our research also serves as a pivotal foundation for the artificial manipulation and realization of quantum coherence revivals within diverse single-qubit systems.