Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

• Geometric phase under noise phase laser.
• Dynamics of the geometric phase under non-Markovian dynamics in the presence of classical noise.
• Solution of master equation of the system in terms atomic inversion.
• Nonlocal correlation between the system and its environment under non-Markovianity.

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.