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Abelian and non-Abelian geometric phases in adiabatic open quantum systems

M. S. Sarandy·D. A. Lidar
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Abstract

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one for closed quantum systems, and we prove that it satisfies all the properties one might expect of a good definition of a geometric phase, including gauge invariance. A striking consequence is the emergence of a finite time interval for the observation of geometric phases. The formalism is illustrated via the canonical example of a spin-1/2 particle in a time-dependent magnetic field. Remarkably, the geometric phase in this case is immune to dephasing and spontaneous emission in the renormalized Hamiltonian eigenstate basis. This result positively impacts holonomic quantum computing.

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M. S. Sarandy, D. A. Lidar. 2006-04-28. Abelian and non-Abelian geometric phases in adiabatic open quantum systems. https://doi.org/10.1103/physreva.73.062101

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