Geometric Phase for Adiabatic Evolutions of General Quantum States

Journal Article · Sat Jan 01 00:00:00 EST 2005 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.94.140402· OSTI ID:1003061

Wu, Biao ^[1]; Liu, Jie ^[2]; Niu, Qian ^[3]; Singh, David J ^[4]

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1. Institute of Physics, China and Oak Ridge National Laboratory (ORNL)
2. Institute of Applied Physics and Computational Mathematics, Beijing
3. University of Texas, Austin
4. ORNL

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1003061
• Journal Information: Physical Review Letters, Vol. 94, Issue 14; ISSN 0031--9007
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ADIABATIC PROCESSES
EIGENSTATES
NONLINEAR PROBLEMS
QUANTUM MECHANICS