Non-Abelian Berry phase in a quantum mechanical environment

Jan Segert

Frank Gaitan

Kyrylo Snizhko, Reinhold Egger, Yuval Gefen

To what extent can coupling to a dissipative environment hinder the emergence of a geometric phase? And does dissipation undermine its possibly non-Abelian nature? Here, the authors show that non-Abelian geometric phase survives the presence of an environment, albeit modified. The dissipative coupling is manifest in the non-Abelian dynamics. Moreover, it gives rise to non-Abelian geometric dephasing, which may suppress or enhance coherent contributions, depending on the order of adiabatic operations.

Pratul Bandyopadhyay

Chang-Pu Sun

A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.