标题： 时间最优的自旋1/2旋转：应用于金刚石中的NV中心自旋 显示英文标题

标题： Time-optimal rotation of a spin 1/2: application to the NV center spin in diamond

摘要： 我们研究了为自旋-1/2设计的时间最优bang-bang控制的适用性 [U. Boscain和P. Mason, J. Math. Phys.{\bf 47}, 062101 (2006)]，该控制用于金刚石中氮空位(NV)中心的电子自旋旋转。NV中心的自旋是一个三能级系统，其中两个能级形成一个相关量子比特子空间，在该子空间中，随时间变化的磁控场执行旋转，第三个能级处于闲置状态。我们发现，与传统的正弦振荡驱动相比，bang-bang控制协议将旋转时间减少了20--25%。我们还发现，对于大多数偏置磁场值，泄漏到闲置能级的量非常小，因此NV中心是实验研究时间最优协议的合适平台。然而，对于某些特殊的偏置磁场值，不需要的泄漏显著增加。我们证明这是由bang-bang驱动场的高阶傅里叶谐波共振引起的。 显示英文摘要

摘要： We study the applicability of the time optimal bang-bang control designed for spin-1/2 [U. Boscain and P. Mason, J. Math. Phys. {\bf 47}, 062101 (2006)] to the rotation of the electron spin of a nitrogen-vacancy (NV) center in diamond. The spin of the NV center is a three-level system, with two levels forming a relevant qubit subspace where the time-varying magnetic control field performs rotation, and the third level being idle. We find that the bang-bang control protocol decreases the rotation time by 20--25% in comparison with the traditional oscillating sinusoidal driving. We also find that for most values of the bias field the leakage to the idle level is very small, so that the NV center is a suitable testbed for experimental study of the time-optimal protocols. For some special values of the bias field, however, the unwanted leakage is greatly increased. We demonstrate that this is caused by the resonance with higher-order Fourier harmonics of the bang-bang driving field.