Unconditional full vector magnetometry using spin selectivity in Nitrogen Vacancy centers in diamond

The gist: This work introduces an unconditional vector-field estimation protocol for nitrogen vacancy (NV) centers in diamond by exploiting spin selectivity using elliptically polarized microwave fields, thereby removing the need for external magnetic field knowledge or bias fields.

Quantum Sensors and Magnetic Field Detection

NV centers in diamond are prominent quantum platforms for developing commercial quantum sensors due to their extraordinary room-temperature spin system properties (Page 2). The electronic spin in NV centers is extremely sensitive, making diamond-based magnetic sensors of special interest for applications in medical, industrial, or navigation solutions (Page 2). The magnetic field dependent energy level structure of the ground state, dominated by Zeeman-splitting, makes NV centers one of the most sensitive sensors for magnetic fields at room temperature (Page 2). NV magnetometry relies on Electron Spin Resonance measurements (ESR) of the ground-state Zeeman splitting (Page 3).

Limitations of Previous Vector Magnetometry Methods

Previous NV-based vector magnetometry methods require partial knowledge of the magnetic field, such as a calibrated bias field, to fully exploit their benefits (Page 1). Existing vector-magnetometry methods solve this problem by requiring additional sensors or a bias field to limit measurements to one of the colored zones in Fig. (1 c), which imposes constraints on hardware and limits the dynamic range (Page 3). This constraint hinders measurements in samples experiencing magnetic forces or responding to a different range of their magnetic hysteresis (Page 5).

Spin Selectivity via Microwave Fields

The proposed method exploits the possibilities of selecting particular directions of the spins in the diamond with elliptically polarized microwave fields (Page 2). The protocol uses MW fields with controlled elliptical polarization to selectively address NV spin states, enabling unconditional vector-field estimation without a bias field or prior knowledge (Page 3). This approach allows for the use of the full dynamic range of NV sensors and makes them competitive magnetometers (Page 6). Spin selectivity using microwave polarization and orientation has been previously proposed, as well as using a single-axis configuration to demonstrate axis selectivity (Page 6).

Protocol for Vector Magnetometry

The protocol involves several steps:

1. A preliminary system calibration step is performed to account for the real response of the instrument, compensating for quadrature phase and amplitude imbalances and diamond tilts among others (Page 11). This calibration aims to find the relative MW amplitude and phase conditions that optimize spin selectivity achieving the highest attenuation of NV peaks (Page 11).

2. The measurements can be optimized by choosing four of the configurations with their respective handedness, which provides a sufficient measurement basis (Page 13). The four configurations that obtain the highest peak attenuation can be used to resolve all field projections (Page 13).

3. For any ESR spectrum, the peak attenuated with each MW configuration corresponds to the axis linked to the configuration during calibration process (Page 13).

4. Knowing the axis orientations with respect to the antenna, a vector magnetic field in the laboratory-frame can be calculated using techniques such as Moore-Penrose pseudo-inverse or best linear unbiased estimator (BLUE) of the A matrix (Page 13).

Experimental Verification and Results

The experimental proof of concept shows that each row in Fig. (2) represents the optimizations of MW fields to target individual NV directions (Page 8). The results confirm the possibility of deterministically using MW field configurations to label transition lines using the proposed method (Page 8). Theoretical calculations predict optimal IQ phase differences for NV1(+), NV2(-), NV3(-), and NV4(+) respectively, which is in close agreement with the values reported in Fig. (2 b) (Supplementary Text) (Page 9). The results are consistent with an independent field measurement and confirm the possibility of labeling NV axes with their corresponding transition peaks and extracting the sign of the projection of the field over them (Page 9). The protocol is shown to resolve magnetic fields generating arbitrary peak orientations with similar ESR signatures, lifting the degeneracy of 48 fields producing the same spectra (Page 12).

Conclusion and Future Directions

The proposed method can resolve, without constraint, the direction of the magnetic field, which is a crucial advantage over prevailing approaches (Page 13). This method does not need a bias field to determine the magnetic field, removing errors introduced with hardware precision limitations of the bias and enabling measurement in their natural state (Page 13). A limitation is that most antennas are linearly polarized, but tailored designs may be needed for elliptical polarization (Page 14). The protocol requires four different ESR spectra with different MW field configurations to resolve the vector magnetic field (Page 14). The method shows that the directional resolution of the vector external magnetic field is possible using only MW fields in the X-Y plane (Page 17).

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J. F. Barry, et al.

1. textbfProcessing of Unconstrained Magnetic Field Vectors in Quantum Sensors: Vector Magnetometry without Bias Field Constraints (B-F): The improved system can perform unconditional vector magnetometry without a bias field or prior knowledge by using MW fields with controlled elliptical polarization to selectively address NV spin states.

2. The improved AI system can achieve this by implementing the proposed protocol where the control of elliptically polarized MW fields with planar resonant antennas in diamond is an effective method to achieve spin selectivity and determine vector magnetic fields. This removes the dynamic-range limitations imposed by the need to maintain well-separated ESR peaks, significantly extending the usable field range.

3. The system can be enhanced to utilize geometric characterization for speed, as suggested by the text: this shows the deterministic nature of the protocol where geometric characterization of the setup is sufficient to perform full vector magnetometry. This allows for calibration and measurement without wide phase and gain ratio sweeps in future measurements.

4. The system can incorporate a calibration step to handle experimental imperfections, as described: a preliminary system calibration step to account for the real response of the instrument, which compensates quadrature phase and amplitude imbalances and diamond tilts among others. This ensures that the resulting vector field is determined by the geometry of the system rather than being constrained by hardware precision limitations.

5. The improved AI can resolve ambiguities in degeneracy: When all axis transition lines and signs have been identified (step two in Fig. 3) the field projection vector can be constructed. This enables the discrimination of fields that would otherwise be indistinguishable in typical NV-based magnetometry or would be mutually inaccessible due to the limitations imposed by an external bias magnetic field.

6. The system can handle complex environmental factors through adaptive modeling: The method allows for resolving fields even when the system under measurement or its environment does not have a linear response to magnetic fields, and it can compensate for small tilts on the crystal directions and antenna imperfections with prior characterization.

Quantum sensors based on nitrogen vacancy (NV) centers in diamond have been a central topic in the sensing community for more than a decade. The extraordinary properties at room temperature of the spin system in diamond have made it one of the most prominent quantum platforms for the development of commercial quantum sensors. In particular, the sensitivity of the electronic spin in NV centers has made diamond-based magnetic sensors of special interest for their potential application in medical, industrial or navigation solutions. However, the use of these sensors for universal vector magnetometry was constrained by the need for previous knowledge on the field being measured to fully exploit their benefits. In this work, we show a method to perform unconditional vector magnetometry without the need of external information on the magnetic field, based only on the spatial arrangement of the diamond and the microwave antenna combination. While previous NV-based vector magnetometry methods require partial knowledge of the magnetic field (e.g. a calibrated bias field), we exploit the possibilities of selecting particular directions of the spins in the diamond with elliptically polarized microwave fields. We prove that our method allows to estimate both magnitude and direction of external magnetic fields without further assumptions or constraints.