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arXiv:1412.5051 · Physical Review Letters

Smooth Optimal Quantum Control for Robust Solid-State Spin Magnetometry

Tobias Nöbauer, Andreas Angerer, Björn Bartels, Michael Trupke, Stefan Rotter, Jörg Schmiedmayer, Florian Mintert, Johannes Majer

Published Nov 6, 2015• 86 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.115.190801

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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.
The sensitivity of a practical quantum magnetometer is challenged by both inhomogeneous coupling between sensors and environment and errors in quantum control. Based on the physical criteria of modern quantum sensing, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening of sensor and control errors via optimized modulation of control field. Such a technique is verified on nitrogen-vacancy (NV) center in diamond to keep almost perfect operation up to a detuning as larger as 110%110\%110%. The sensitivity of the magnetometer with NV center ensemble is experimentally improved by a factor of 444, comparing to dynamical decoupling with normal rectangular pulse. Our work marks an important step towards high trustworthy ultra-sensitive quantum sensing with imperfect quantum control in realistic systems. The used principle however, is universal and not restricted to NV center ensemble magnetometer.
Shallow nitrogen-vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization and readout process. In a second step, we optimize microwave pulses for pulsed optically detected magnetic resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{T}$ ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ for an 83% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100 nT ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ giving a twofold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.
Shallow Nitrogen-Vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization/readout process. In a second step, we optimize microwave pulses for pulsed Optically Detected Magnetic Resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below 1μμμT\,Hz−12^{-\frac{1}{2}}−21​ for an 83\% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100\,nT\,Hz−12^{-\frac{1}{2}}−21​ giving a two-fold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.
The sensitivity of practical solid quantum sensing can be boosted up by increasing the number of probes. However, the effects of spin dephasing caused by inhomogeneous broadening and imperfect quantum control can reduce the fidelity of quantum control and the sensitivity of quantum sensing with the dense ensemble of probes, such as nitrogen-vacancy (NV) centers in diamond. Here, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening and control errors via optimized modulation of the control field. Such a composite-pulse was verified on NV center to keep high fidelity quantum control up to a spectrum detuning as large as 110% of Rabi frequency. The sensitivity of the magnetometer with NV center ensemble was experimentally improved by a factor of 4, comparing to dynamical decoupling with a normal rectangular pulse. Our work marks an important step towards high trustworthy ultra-sensitive quantum sensing with imperfect quantum control in practical applications. The used principle is universal and not restricted to NV center ensemble magnetometer.
During the last ten years, basic quantum operations on a single electronic spins in the nitrogen-vacancy defect center in diamond have been a rich field of study. Quantum operations coherently manipulating the spin of the nitrogen-vacancy center have become promising candidates for easy to manipulate qubits. However in order to implement these qubits in quantum computers robust high-fidelity control is needed. Building on an existing confocal microscopy setup, pulsed and quadrature-amplitude modulated microwave signals were used to realize coherent spin manipulation measurements. Especially designed Smooth Optimal Control pulses (robust against detuning and different control amplitudes) were used to develop measurement schemes resulting in the aforementioned increase of fidelity. The first part of the thesis describes the implementation of these pulses into the existing experimental setup and the calibration work necessary prior to measurements, due to imperfections of devices in the microwave chain. The second part is dedicated to the analysis of the pulses applied to a single spin by comparing the experimental results to theoretical simulations. This was done not only for one resonant spin with accurate control amplitude, but also for a range of different detunings and amplitudes. A more thorough analysis of the pulses was then achieved by using state/process tomography, resulting in a complete description of the process induced by these optimized pulses. Finally, after verifying the effect of the pulses, measurement schemes for sensing alternating magnetic fields were implemented, resulting in measurements with improved sensitivity for magnetic fields.
Nitrogen-vacancy (NV) centers in diamond are a promising platform for ambient, high-spatial resolution magnetometry relevant to biological signals such as cardiac and muscle activity. One of the challenges is the development of pulse sequences tailored to biological signals in the near DC-range. The spatial environment of NV centers within the diamond lattice is highly complex, e.g. due to magnetic field inhomogeneities, limiting the sensors performance. To overcome these experimental constraints, quantum optimal control (QOC) aims at a precise manipulation of the systems dynamics via optimally shaped microwave pulses increasing the overall robustness of spin-based quantum sensors.