Dissipative and stochastic geometric phase of a qubit within a canonical Langevin framework

Abstract

Dissipative and stochastic effects in the geometric phase of a qubit are taken into account using a geometrical description of the corresponding open--system dynamics within a canonical Langevin framework based on a Caldeira--Leggett like Hamiltonian. By extending the Hopf fibration $S^3\to S^2$ to include such effects, the exact geometric phase for a dissipative qubit is obtained, whereas numerical calculations are used to include finite temperature effects on it.

arXiv comment5 pages, 2 figures

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• Dissipative evolution of a two-level system through a geometry-based classical mapping
• Quantum thermodynamics in chiral two--level systems. The quantum stochastic resonance