Non-Markovian effect on the geometric phase of a dissipative qubit

Abstract

We study the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit the lowest-order correction to the geometric phase is derived analytically and the general case is calculated numerically. It is found that the correction to the geometric phase is significantly large if the spectral width is small and in this case the non-Markovian dynamics has a significant impact to the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.

6 pages, 3 figures

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• Information Flow, Non-Markovianity and Geometric Phases
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• Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits
• Preservation of quantum Fisher information and geometric phase of a single qubit system in a dissipative reservoir through the addition of qubits
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• Boundary-induced effect encoded in the corrections to the geometric phase acquired by a bipartite two-level system
• Decoherence of quantum gates based on Aharonov-Anandan phases in a multistep scheme
• Effect of decoherence on the Berry phase of a spin-half in a rotating magnetic field
• Entanglement dynamics via Geometric phases in Trapped-ions
• Geometric signature of non-Markovian dynamics