Uniform microwave field formation for control of ensembles of negatively charged nitrogen vacancy in diamond

Abstract: 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.

• The paper demonstrates that optimized barrel-shaped coils achieve an order-of-magnitude improvement over planar and Helmholtz designs for uniform MW field control in NV ensembles.
• The methodology employs COMSOL simulations to benchmark several MW field-forming geometries, highlighting the superior performance of parallel-connected multi-turn coil designs.
• Experimental validation shows sustained Rabi oscillations with a uniformity parameter (Δζ < 0.1) over key regions, ensuring scalable integration for quantum sensing devices.

Uniform Microwave Field Formation for NV Ensemble Control in Diamond

Context and Motivation

Negatively charged nitrogen-vacancy (NV) centers in diamond function as versatile quantum sensors, providing high sensitivity for magnetic, electric, and thermal measurements. The fidelity and homogeneity of the microwave (MW) magnetic field controlling NV spin ensembles is critical in applications such as quantum magnetometry, where the volume of active NV centers must be maximized while maintaining pulse uniformity. Existing field-forming technologies—planar antennas, strip lines, dielectric resonators, and coil-based geometries—are either limited in spatial uniformity or constrained by integration, cost, or compatibility with multifrequency applications. This study addresses a systematic comparison and optimization of MW field-forming systems, identifying geometric parameters and engineering strategies that achieve superior MW uniformity in volumetric NV ensembles.

Comparative Simulation of MW Field-Forming Systems

A comprehensive COMSOL simulation framework was developed to analyze five MW field-forming geometries:

• Planar antenna (A)
• Dielectric resonator (B)
• Cylindrical inductor (C)
• Helmholtz coils (D)
• Barrel-shaped coil (E)
• Nested barrel-shaped coil (F, advanced version of E)

All systems were benchmarked with identical excitation power and impedance, focusing on magnetic field homogeneity ($\text{Opp}$, defined as $$(B_\text{max} - B_\text{min})/(B_\text{max} + B_\text{min})$$) in the inner cylindrical domain matching the typical NV ensemble geometry.

Simulations reveal that traditional planar approaches provide adequate uniformity only in a limited spatial region (planar: $|z|<0.075$ mm, $\text{Opp}<0.5\%$). Dielectric resonators extend this region ($|z|<0.35$ mm), but their high Q-factor and size challenge integration and multifrequency operation. Coil-based approaches, particularly the barrel-shaped geometry, achieve notable improvements. The six-turn barrel-shaped coil (geometry E) yielded $\text{Opp}<0.1\%$ in $|z|<0.25$ mm, outperforming Helmholtz coils (geometry D) and standard cylindrical inductors, while maintaining practical bandwidth and integration compatibility.

The nested barrel-shaped coil (geometry F) further increases field uniformity, though the operational homogeneity plateaued due to increased inductance and practical circuit limitations.

Optimization and Physical Realization

A practical manufacturing workflow for the barrel-shaped coil was developed, employing parallel-connected multi-turn conical windings assembled with polyimide tape and copper wires. The parallel configuration mitigates excessive inductance and optimizes current density distribution within the field-forming region, resulting in lower resistance and improved MW field uniformity.

Experimental impedance matching was achieved using circuit synthesis and vector network analyzer calibration. The fabricated system demonstrated robust compatibility with PCB technologies, facilitating integration into compact devices and sensors.

Experimental Validation with NV Ensemble

Rabi oscillation measurements on NV ensembles (with spatially resolved positioning) quantified the MW field inhomogeneity. The barrel-shaped coil exhibited slower decay rates and sustained oscillations compared to planar antenna configurations. Decay modeling (integrated Lorentzian-distributed cosine functions) and extracted width parameters demonstrated that inhomogeneity with the barrel-shaped coil is consistently lower over extended measurement regions.

Specifically, the width parameter ($\Delta\zeta$) for the barrel geometry remained below $0.1$ across key spatial positions, while the planar system was characterized by rapid attenuation, especially at offsets from the MW source. Helmholtz coil data from prior literature were referenced; the attenuation degree of Rabi oscillations in the barrel-shaped configuration was approximately 20% lower compared to Helmholtz designs, substantiating the superior homogeneity claim.

Practical and Theoretical Implications

This work provides a validated path to scalable, uniform MW field generation for large-volume NV center ensembles. The barrel-shaped coil configuration achieves field uniformity at least twice as large as Helmholtz designs and an order-of-magnitude improvement over planar systems. Given its compatibility with PCB and flexible circuit integration, the approach supports miniaturized, multi-frequency, and portable quantum sensors.

Reduced MW source power requirements, increased uniformity, and optimization of current density advance both sensitivity and practicality of diamond-based quantum magnetometers and related devices. The findings have broader implications for the engineering of quantum device control fields, especially where ensemble coherence and spatial uniformity are paramount.

Future research directions include systematic exploration of matching networks for further integration, optimization for multi-frequency or vector magnetometry, and adaptation of flexible circuit technologies to scale sensor array architectures.

Conclusion

Modeling and experimental validation confirm that barrel-shaped multi-turn coils, specifically with parallel-connected windings, provide markedly improved MW field uniformity in NV diamond ensembles. This geometry outperforms planar antennas and Helmholtz coil designs, enables scalable integration, and meets the requirements for sensitive quantum devices where spatial homogeneity of the control field is critical. The methods outlined set the stage for enhanced performance in quantum sensing, scalable device fabrication, and new protocols in synchronous spin manipulation (2605.13267).