Non-Abelian Geometric Dephasing

2019/04/30 by Kyrylo Snizhko, Reinhold Egger, Yuval Gefen · 2 citations
Mathematics · Physics and Astronomy · #Adiabatic process #Atomic and Subatomic Physics Research #Classical mechanics #Degenerate energy levels #Dephasing #Fermion #Geometry #MAJORANA #Mathematics #Parameter space #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevlett.123.060405

published as Phys. Rev. Lett. 123, 060405 (2019) · 5 pages, 2 figures; accompanying paper to arXiv:1904.11673

openalex publication_date 2019/08/09 · arxiv created 2020/07/28 · arxiv updated 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the adiabatic dynamics of degenerate quantum states induced by loop paths in a control parameter space. The latter correspond to noisy trajectories if the system is weakly coupled to environmental modes. On top of conventional dynamic dephasing, we find a universal non-Abelian geometric dephasing (NAGD) contribution and express it in terms of the non-Abelian Berry connection and curvature. We show that NAGD implies either decay or amplification of coherences as compared to the coherences when only dynamic dephasing is present. The full NAGD matrix structure can be probed through interference experiments. We outline such a detection scheme for modified Majorana braiding setups.

Citations

• Non-Abelian Berry phase for open quantum systems: Topological protection versus geometric dephasing
• Geometric quantum computation using nuclear magnetic resonance
• Adiabatic theorem without a gap condition: Two-level system coupled to quantized radiation field
• 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
• 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 Berry phase for open quantum systems: Topological protection versus geometric dephasing
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits