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

TL;DR

This paper investigates the application of time-optimal bang-bang control protocols, originally designed for spin-1/2 systems, to the electron spin of NV centers in diamond, showing significant speed improvements and analyzing leakage effects.

Contribution

It extends time-optimal control methods to NV center spins, demonstrating reduced rotation times and analyzing leakage phenomena due to harmonic resonances.

Findings

Bang-bang control reduces rotation time by 20-25%.

Leakage to idle level is minimal for most bias fields.

Resonance with higher harmonics causes increased leakage at certain bias fields.

Abstract

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.