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See detailTime-optimal control of a 3-level quantum system and its generalization
Chang, Dong Eui; Sepulchre, Rodolphe ULg

in Dynamics of Continuous, Discrete and Impulsive Systems Series (2007), 14

We solve the problem of steering a three-level quantum system from one eigen- state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level ... [more ▼]

We solve the problem of steering a three-level quantum system from one eigen- state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: Z2 ×S3 discrete sym- metry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. [less ▲]

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