## Abstract

We consider a quantum control problem involving a spin-1/2 particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the x-y plane, serves as a control parameter that can be varied to govern the evolution of the system. We analytically solve for the time dependence of the control parameter that will synthesize a given target SU(2) transformation in the least possible amount of time, and we show that the time-optimal solutions have a simple geometric interpretation in terms of the fiber bundle structure of SU(2). We also generalize our time-optimal solutions to a control problem that includes a constant bias field along the axis and to the case of inhomogeneous control, in which a single control parameter governs the evolution of an ensemble of spin-1/2 systems.

Original language | English (US) |
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Article number | 012317 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 85 |

Issue number | 1 |

DOIs | |

State | Published - Jan 19 2012 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics