Non-Abelian Berry phase for open quantum systems: Topological protection versus geometric dephasing

2019/04/30 by Kyrylo Snizhko, Reinhold Egger, Yuval Gefen · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Abelian group #Adiabatic process #Coupling (piping) #Dephasing #Dissipative system #Engineering #Geometric phase #Mathematics #Mechanical and Optical Resonators #Phase (matter) #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevb.100.085303

published as Phys. Rev. B 100, 085303 (2019) · 26 pages, 5 figures; accompanying paper to arXiv:1904.11262

openalex created_date 2019/05/03 · openalex publication_date 2019/08/09 · arxiv created 2020/07/28 · arxiv updated 2020/07/29 · openalex updated_date 2026/08/05

Abstract

To what extent can coupling to a dissipative environment hinder the emergence of a geometric phase? And does dissipation undermine its possibly non-Abelian nature? Here, the authors show that non-Abelian geometric phase survives the presence of an environment, albeit modified. The dissipative coupling is manifest in the non-Abelian dynamics. Moreover, it gives rise to non-Abelian geometric dephasing, which may suppress or enhance coherent contributions, depending on the order of adiabatic operations.

Citations

• Non-Abelian Geometric Dephasing
• Geometric quantum computation using nuclear magnetic resonance
• Appearance of Gauge Structure in Simple Dynamical Systems
• Geometric Nature of the Environment-Induced Berry Phase and Geometric Dephasing
• Observation of Berry's Phase in a Solid-State Qubit
• Dissipationless Quantum Spin Current at Room Temperature
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Quantal phase factors accompanying adiabatic changes
• Topological Insulators
• Berry Phase Effects on Electronic Properties
• Non-Abelian Anyons and Topological Quantum Computation
• Optimal diabatic dynamics of Majorana-based quantum gates

Cited by

• Non-Abelian Geometric Dephasing