Abstract Negatively charged nitrogen-vacancy (NV) centers in diamonds are commonly used in quantum magnetometry. However, the potential of this approach is often limited by the inhomogeneity of the driving field. In this study, we explore the potential of closed-loop quantum optimal control to improve DC Ramsey magnetometry with NV-ensembles suffering from inhomogeneous microwave (MW) fields and MW power limitations. We demonstrate an improvement of the optically detected Ramsey contrast up to a factor of 3.13. This enables noticeable power savings for miniaturized devices without loss in magnetometry performance. Additionally, we show a recovery of 86.3% of the Ramsey contrast in presence of a five times less homogeneous MW field compared to the homogeneous field of a MW Helmholtz coil pair.
Abstract Negatively charged nitrogen-vacancy (NV) centers in diamonds are commonly used in quantum magnetometry. However, the potential of this approach is often limited by the inhomogeneity of the driving field. In this study, we explore the potential of closed-loop quantum optimal control to improve DC Ramsey magnetometry with NV-ensembles suffering from inhomogeneous microwave (MW) fields and MW power limitations. We demonstrate an improvement of the optically detected Ramsey contrast up to a factor of 3.13. This enables noticeable power savings for miniaturized devices without loss in magnetometry performance. Additionally, we show a recovery of 86.3% of the Ramsey contrast in presence of a five times less homogeneous MW field compared to the homogeneous field of a MW Helmholtz coil pair.
Ensembles of nitrogen-vacancy (NV) centers in diamond are a well-established platform for quantum magnetometry under ambient conditions. One challenge arises from the hyperfine structure of the NV, which, for the common 14N isotope, results in a threefold reduction of contrast and thus sensitivity. By addressing each of the NV hyperfine transitions individually, triple-tone microwave (MW) control can mitigate this sensitivity loss. Here, we experimentally and theoretically investigate the regimes in which triple-tone excitation offers an advantage over standard single-tone MW control for two DC magnetometry protocols: pulsed optically detected magnetic resonance (ODMR) and Ramsey interferometry. We validate a master equation model of the NV dynamics against ensemble NV measurements, and use the model to explore triple-tone vs single-tone sensitivity for different MW powers and NV dephasing rates. For pulsed ODMR, triple-tone driving improves sensitivity by up to a factor of three in the low-dephasing regime, with diminishing gains when dephasing rates approach the hyperfine splitting. In contrast, for Ramsey interferometry, triple-tone excitation only improves sensitivity if MW power is limited. Our results delineate the operating regimes where triple-tone control provides a practical strategy for enhancing NV ensemble magnetometry in portable and power-limited sensors.
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.
The homogeneity of the microwave magnetic field is essential in controlling a large volume of ensemble spins, for example, in the case of sensitive magnetometry with nitrogen-vacancy (NV) centers in diamond. This is particularly important for pulsed measurement, where the fidelity of control pulses plays a crucial role in its sensitivity. So far, several magnetic field-forming systems have been proposed, but no detailed comparison has been made. Here, we numerically study the homogeneity of five different systems, including a planar antenna, a dielectric resonator, a cylindrical inductor, a barrel-shaped coil, and a nested barrel-shaped coil. The results of the simulation allowed us to optimize the design parameters of the barrel-shaped field-forming system, which led to significantly improved magnetic field uniformity. To measure this effect, we experimentally compared the homogeneity of a field-forming system having a barrel shape with that of a planar field-forming system by measuring Rabi oscillations of an ensemble of NV centers with them. Significant improvements in inhomogeneity were confirmed in the barrel-shaped coil.
Quantum sensing with solid-state spins has attracted considerable attention following the development of single quantum systems. In particular, sub-picotesla level magnetometry has been demonstrated using negatively-charged nitrogen-vacancy (NV) centers in diamond by increasing the number of spins simultaneously employed for sensing. However, scaling up the number of spins inevitably introduces inhomogeneities in detuning and control field amplitudes across the ensemble system, which degrades the achievable sensitivity. Although several techniques, including pulsed dynamical decoupling and shaped pulses, have been studied to overcome such noises, they are not generally compatible with GHz-range AC magnetometry based on Rabi oscillations. This dissertation presents the development of an experimental platform and the demonstration of robust GHz-range AC magnetometry using a large ensemble of NV centers under inhomogeneous fields. Particular emphasis is placed on the effects of control-field amplitude inhomogeneity. To improve the homogeneity of the control field, barrel-shaped microwave forming systems are experimentally characterized, and their performance is compared with that of planar systems. Then, to mitigate detuning noise as well as control-field amplitude noise, concatenated continuous dynamical decoupling (CCDD) is applied to the inhomogeneous ensemble system, and the resulting dynamics are investigated with several initial states prepared with composite pulses. Finally, the CCDD sequence is applied for GHz-range AC magnetometry and compared with the conventional direct Rabi method. The results demonstrate that the robust dressed states generated by CCDD extend the lower bound of measurable amplitudes in GHz-range AC magnetometry.
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.
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 1μT\,Hz−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−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.