We experimentally demonstrate a simple yet versatile optimal quantum control technique that achieves tailored robustness against qubit inhomogeneities and control errors while requiring minimal bandwidth. We apply the technique to nitrogen-vacancy (NV) centers in diamond and verify its performance using quantum process tomography. In a wide-field NV center magnetometry scenario, we achieve a homogeneous sensitivity across a 33% drop in control amplitude, and we improve the sensitivity by up to 2 orders of magnitude for a normalized detuning as large as 40%, achieving a value of 20 nT Hz(-1/2) μm(3/2) in sensitivity times square root volume.
This paper describes an approach to construct temporally shaped control pulses that drive a quantum system towards desired properties. A parametrization in terms of periodic functions with pre-defined frequencies permits to realize a smooth, typically simple shape of the pulses; their optimization can be performed based on a variational analysis with Floquet theory. As we show with selected specific examples, this approach permits to control the dynamics of interacting spins, such that gate operations and entanglement dynamics can be implemented with very high accuracy.PACS numbers: 42.50. Dv, 03.65.Yz, 02.30.Yy Research on quantum mechanical systems is currently undergoing a process of substantial changes: whereas in the last decades the effort was mostly on the observation and description of quantum mechanical properties, currently the option to manipulate and control quantum systems is moving into focus. On the one hand, this is due to the technological advances that permit isolating quantum systems e.g. in ion traps [1,2] or optical lattices [3], manipulating them coherently and letting quantum systems of different kinds interact with each other [4,5]. On the other hand, there is the prospect to exploit intrinsically quantum mechanical properties to engineer devices with performance characteristics far beyond the classically achievable. Whereas secure communication [6] or teleportation [7] based on quantum protocols is well established by now and the possibility to simulate quantum mechanical many-body systems with quantum simulators [8, 9] is a growing field, new perspectives to exploit quantum mechanical coherence phenomena, for example in energy provision [10,11], are just emerging.Beyond the experimental capability to control quantum systems, any type of quantum engineering also needs appropriate theoretical tools that allow an experimentalist to extract optimal performance under given limitations of control, as typically imposed by power or frequency range of driving fields. Optimal control theory [12][13][14][15] provides elaborate and efficient schemes to identify e.g. shapes of laser or microwave pulses that drive a system towards desired properties. A particularly astonishing property of pulses designed by optimal control techniques is their robustness against experimental imperfections [16,17]; for example inhomogeneous broadening in ensembles of quantum systems can be compensated essentially completely through suitably designed control pulses [18][19][20].A disadvantage of these pulses is that they typically contain many frequency components; besides potential experimental challenges to generate such pulses, the complicated structure of these pulses renders it essentially impossible to understand why they result in their astonishing performance. In particular if we want to push the envelope to large many-body systems, the answer to the question of 'why' will become more and more important rather than the observation 'that' one can identify suitable pulses. The aim here is therefore to strive fo...
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