Cyclic quantum evolution and Aharonov-Anandan geometric phases in SU(2) spin-coherent states

Journal Article · Mon Jan 01 00:00:00 EST 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.42· OSTI ID:7165056

Layton, E; Huang, Y; Chu, S ^[1]

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1. Department of Chemistry, University of Kansas, Lawrence, Kansas 66045 (US)

We show that cyclic quantum evolution can be realized and the Aharonov-Anandan (AA) geometric phase can be determined for any spin-{ital j} system driven by periodic fields. Two methods are extended for the study of this problem: the generalized spin-coherent-state technique and the Floquet quasienergy approach. Using the former approach, we have developed a {ital generalized} Bloch-sphere model and presented a SU(2) Lie-group formulation of the AA geometric phase in the spin-coherent state. We show that the AA phase is equal to {ital j} times the solid angle enclosed by the trajectory traced out by the tip of a generalized Bloch vector. General analytic formulas are obtained for the Bloch vector trajectory and the AA geometric phase in terms of external physical parameters. In addition to these findings, we have also approached the same problem from an alternative but complementary point of view without recourse to the concept of coherent-state terminology. Here we first determine the Floquet quasienergy eigenvalues and eigenvectors for the spin-{ital j} system driven by periodic fields. This in turn allows the construction of the time-evolution propagator, the total wave function, and the AA geometric phase in a more general fashion.

• OSTI ID: 7165056
• Journal Information: Physical Review, A (General Physics); (USA), Vol. 41:1; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM MECHANICS
PHASE STUDIES
EIGENVALUES
GEOMETRY
LIE GROUPS
MAGNETIC FIELDS
SPIN
SU-2 GROUPS
ANGULAR MOMENTUM
MATHEMATICS
MECHANICS
PARTICLE PROPERTIES
SU GROUPS
SYMMETRY GROUPS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics