Non-Abelian Geometric Dephasing

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.

5 pages, 2 figures; accompanying paper to arXiv:1904.11673

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• Weak-measurement-induced asymmetric dephasing: manifestation of intrinsic measurement chirality
• Non-Hermiticity stabilized Majorana zero modes in semiconductor-superconductor nanowires
• Weak-measurement-induced phases and dephasing: broken symmetry of the geometric phase
• Multi-particle interferometry in the time-energy domain with localized topological quasiparticles
• Thermal effects on a nonadiabatic spin-flip protocol of spin-orbit qubits
• Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field
• Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot
• How pure can we go with adiabatic state manipulation?