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

Understand

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space.

• For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths.
• We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator.
• This operator plays a key role in all experimental protocols proposed in this work for the detection of NAGD.