Abelian and non-Abelian geometric phases in adiabatic open quantum systems
- Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Sao Carlos, SP, 13560-970 (Brazil)
- Departments of Chemistry, Electrical Engineering-Systems, and Physics, University of Southern California, Los Angeles, California 90089 (United States)
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.
- OSTI ID:
- 20787429
- Journal Information:
- Physical Review. A, Vol. 73, Issue 6; Other Information: DOI: 10.1103/PhysRevA.73.062101; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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