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

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dc.creatorSarandy, M. S.
dc.creatorLidar, D. A.
dc.date2005-07-01
dc.date2006-04-28
dc.date.accessioned2026-07-07T06:43:35Z
dc.date.available2026-07-07T06:43:35Z
dc.descriptionWe 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.
dc.descriptionv3: 10 pages, 2 figures. Substantially expanded version. Includes a proof of gauge invariance of the non-Abelian geometric phase, and an appendix on the left and right eigenvectors of the superoperator in the Jordan form
dc.identifierhttps://arxiv.org/abs/quant-ph/0507012
dc.identifierhttp://arxiv.org/abs/quant-ph/0507012
dc.identifierPhys. Rev. A 73, 062101 (2006)
dc.identifierdoi:10.1103/PhysRevA.73.062101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102467
dc.subjectQuantum Physics
dc.subjectMesoscale and Nanoscale Physics
dc.titleAbelian and non-Abelian geometric phases in adiabatic open quantum systems
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