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

Abstract

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. In particular, we formulate interference measurements providing full access to NAGD. Apart from a factor due to the dynamic phase and its fluctuations, the averaged evolution operator contains the averaged Berry matrix. A polar decomposition of this non-unitary matrix into the product of a unitary, $V$, and a positive semi-definite Hermitian matrix, $R$, reveals the physics of the NAGD contributions. Unlike the conventional dynamic dephasing rate, the NAGD eigenrates encoded by $R$ depend on the loop orientation sense and, in particular, change sign under a reversal of the direction. A negative rate then implies amplification of coherences as compared to the ones when only dynamic dephasing is present. The non-Abelian character of geometric dephasing is rooted in the non-commutativity of $V$ and $R$ and causes smoking-gun signatures in interference experiments. We also clarify why systems subject to topological protection do not show geometric dephasing. Without full protection, however, geometric dephasing can arise and has to be taken into account. As concrete application, we propose spin-echo NAGD detection protocols for modified Majorana braiding setups.

26 pages, 5 figures; accompanying paper to arXiv:1904.11262

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• Non-Abelian Anyons and Topological Quantum Computation
• Dissipationless Quantum Spin Current at Room Temperature
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• Majorana box qubits
• Roadmap to Majorana surface codes
• Geometric nature of the environment-induced Berry phase and geometric dephasing
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators
• Non-Abelian Geometric Dephasing
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Cited by in corpus (11)

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• Thermal effects on a nonadiabatic spin-flip protocol of spin-orbit qubits
• Multi-particle interferometry in the time-energy domain with localized topological quasiparticles
• Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field
• Longitudinal coupling between electrically driven spin-qubits and a resonator
• Berry-phase induced entanglement of hole-spin qubits in a microwave cavity
• Exceptionally deficient topological square-root insulators
• How pure can we go with adiabatic state manipulation?
• Distinct Berry Phases in a Single Triangular Möbius Microwave Resonator