Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems

Area of Science:

• Topological physics
• Quantum mechanics
• Condensed matter physics

Background:

• Non-Abelian gauge fields are crucial for topological phenomena but typically studied in Hermitian systems.
• Gauge flux definition requires closed loops in Hermitian systems, limiting broader applications.
• Exploring non-Hermitian systems offers new avenues for gauge field phenomena.

Purpose of the Study:

• To investigate the relaxed conditions for non-Abelian gauge fields in non-Hermitian systems.
• To explore the topological consequences of non-Abelian gauge fields in a generalized Hatano-Nelson model.
• To propose an experimental realization of non-Abelian gauge fields in non-Hermitian systems.

Main Methods:

• Generalized Hatano-Nelson model with imbalanced non-Abelian hopping.
• Analysis of SU(2) gauge fields and their effect on braiding degrees.
• Investigation of non-Hermitian skin modes at open chain ends.
• Extension to two-dimensional non-Hermitian lattices and Wilson loops.
• Proposal utilizing the synthetic frequency dimension in fiber ring resonators.

Main Results:

• Non-Abelian gauge fields induce topological phenomena in non-Hermitian systems even without traditional gauge flux.
• SU(2) gauge fields enable braiding degrees twice the highest hopping order, leveraging spinful freedom.
• Simultaneous non-Hermitian skin modes appear at chain ends, tunable near exceptional points.
• Gauge invariance of Wilson loops breaks down in 2D non-Hermitian lattices.
• A concrete experimental proposal using fiber ring resonators is presented.

Conclusions:

• Non-Hermitian systems provide a fertile ground for novel non-Abelian gauge field phenomena.
• The study demonstrates the potential for high-order braiding and tunable topological states.
• The proposed experimental platform offers a pathway for realizing these non-Hermitian topological effects.