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Time-optimal Control of independent Spin-1/2 Systems under Simultaneous Control
1, 2 , 1, 2 , 1, 2 , * 3 , * 1, 2, 4
1  CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of china, Hefei, Anhui 230026, China
2  Synergetic Innovation Center of Quantum Information and Quantum Physics, University o Science and Technology of China, Hefei, Anhui 230026, China
3  Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
4  Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China


We derive the explicit solution of the problem of time-optimal control (TOC) by a common magnetic fields for two independent spin-1/2 particles. Our approach is based on the Pontryagin Maximum Princple (PMP) and a novel symmetry reduction technique. We experimentally implement the optimal control via a home-built zero and ultralow filed NMR spectrometer. This is the first analytical solution and experimental demonstration of time-optimal control in such a system and it provides a route to achieve time optimal control in more general quantum systems.

Keywords: quantum control; magnetic resonance; optimal control; magnetometer