Time minimal trajectories for a spin 1∕2 particle in a magnetic field

By Ugo V. Boscain, Paolo Mason. 2005

174 citations recorded by the source corpus.

In this paper we consider the minimum time population transfer problem for the z component of the spin of a (spin 1/2) particle, driven by a magnetic field, that is constant along the z axis and controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e., after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on two-dimensional (2-D) manifolds. Let (−E,E) be the two energy levels, and ∣Ω(t)∣≤M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level −E, and we provide the explicit expression of the time optimal trajectories, steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M∕E≪1, every time optimal trajectory is bang-bang and, in particular, the corresponding control is periodic with frequency of the order of the resonance frequency ωR=2E. On the other side, for M∕E>1, the time optimal ...

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d647281c1c7e5f41bcb6258b41d05a5b48c16139

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Mario Sigalotti
2. Thomas Chambrion
3. Ugo V. Boscain
4. Paolo Mason
5. Ian R. Petersen
6. Daoyi Dong
7. Jerzy Klamka

In Computer Networks and Communications

1. Mario Sigalotti
2. Thomas Chambrion
3. Ugo V. Boscain
4. Paolo Mason
5. Daoyi Dong
6. Dominique Sugny
7. Christiane P. Koch

In Statistical and Nonlinear Physics

1. Mario Sigalotti
2. Thomas Chambrion
3. Ugo V. Boscain
4. Paolo Mason
5. Dominique Sugny
6. Christiane P. Koch

Citations in the corpus

• Quantum control theory and applications: A survey (2009, background): “Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], [36], [37].”
• Training Schrödinger’s cat: quantum optimal control (2015, unknown): “closed [124, 123, 26, 58, 57, 25, 87] and open quantum systems [24, 140].”
• Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, methodology): “Schr¨odinger equation by means of optimal control techniques (see for instance [15, 16, 17 , 24] for the finite-dimensional case and [11, 14, 23] for the infinite-dimensional one).”