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.

5 pages, 2 figures

References in corpus (5)

• Observation of Berry's Phase in a Solid State Qubit
• Geometric nature of the environment-induced Berry phase and geometric dephasing
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Geometric phase distributions for open quantum systems
• Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems

Cited by in corpus (3)

• Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• Dissipative evolution of a two-level system through a geometry-based classical mapping