Control Protocol Unlocks Precise Magnetic Field Sensing

Scientists are tackling the fundamental challenge of simultaneously determining multiple parameters with maximum precision, a pursuit often limited by incompatibilities in estimation techniques. Takuya Isogawa, Ayumi Kanamoto, and Nutdech Phadetsuwannukun from the Research Laboratory of Electronics at Massachusetts Institute of Technology, working with colleagues from the Department of Mechanical and Automation Engineering at The Chinese University of Hong Kong, the Pritzker School of Molecular Engineering at The University of Chicago, Mathematics and Computer Science Division at Argonne National Laboratory, and Guoqing Wang also of the Massachusetts Institute of Technology, have demonstrated a novel control protocol to overcome a key limitation in AC magnetometry. Their research resolves the singularity that arises when estimating the amplitude and frequency of alternating magnetic fields, previously preventing optimal joint estimation. By strategically manipulating the sensor’s evolution, the team restored optimal precision scaling for both parameters, validating the protocol experimentally using a nitrogen-vacancy centre in diamond at room temperature, and representing a significant advance towards the limits of multiparameter sensing. For decades, accurately measuring multiple properties at once has been limited by fundamental physical constraints. Now, a clever technique overcomes these limitations, allowing for precise simultaneous measurement of previously incompatible parameters. This advance promises improvements in sensing and precision measurement across diverse applications. Scientists are continually refining the precision of quantum sensors, devices that exploit quantum mechanics to measure physical quantities with exceptional sensitivity. A major challenge in this field lies in simultaneously estimating multiple parameters at their fundamental quantum limits, a task often hampered by incompatibilities between optimal estimation strategies. At its most extreme, this incompatibility manifests as a fundamental impossibility when the quantum Fisher information matrix (QFIM) becomes singular, preventing joint estimation altogether. This occurs when determining both the amplitude and frequency of an alternating current (AC) magnetic field with aligned field generators.

Scientists have devised a control protocol that addresses this singularity, reshaping how information about these parameters is encoded within the quantum sensor. Strategic engineering of the sensor’s time evolution renders the generators, mathematical representations of the sensor’s response, orthogonal. Here, this step eliminates the singularity in the QFIM and restores the expected scaling of precision with measurement time for both parameters. The protocol tested a nitrogen-vacancy (NV) centre in diamond, a promising platform for quantum sensing, at room temperature. Demonstrating the concurrent achievement of optimal scaling for both amplitude and frequency estimation. By carefully manipulating the sensor’s evolution, they overcame a limitation inherent in traditional AC magnetometry, where information about amplitude and frequency is intrinsically linked. The new approach allows for independent and precise measurement of both quantities, with implications for biomedical imaging, materials science, and navigation. Unlike previous quantum control schemes focused on maximising precision for each parameter individually, this protocol specifically targets the resolution of the QFIM singularity. By altering the directions of the generators’ time evolution while preserving optimal scaling. Researchers have opened a new avenue for tackling multiparameter estimation problems. Currently, the demonstrated control strategy achieves sensitivities for simultaneous estimation of the amplitude and frequency of an AC field in the long-time, high-frequency regime. Further refinement could unlock even greater precision and expand the capabilities of quantum sensors. Nitrogen-vacancy centre qubit preparation and alternating current magnetic field sensing Although this effort utilizes a nitrogen-vacancy (NV) centre in diamond as the sensing platform, it builds upon a 72-qubit superconducting processor. Meanwhile, scientists defined sensor and ancilla qubits within a four-level subspace using the electronic and nuclear spin system of the NV centre, represented by the states |mS, mI⟩, where mS and mI represent the spin quantum numbers. It was initially prepared in the optically polarized state |0, +1⟩, followed by a radio-frequency π/2 pulse on the nuclear spin and a selective microwave π pulse on the electronic spin to create the Bell state |Φ+⟩, equal to 1/√2(|0, 0⟩ + |−1, +1⟩). Here, the sensing stage then commenced, where the target alternating current (AC) magnetic field interacted with the sensor qubit. To address the singularity arising when simultaneously estimating the amplitude and frequency of the AC magnetic field, a control protocol implemented a strategic reshaping of the geometric relationship between the generators of the parameters, enabling simultaneous information extraction. In turn, the control Hamiltonian, defined as Hc = −H(Bc, ωc) + ωc 2 σz, designed to counteract the estimated Hamiltonian based on prior data, utilising estimates Bc = B and ωc = ω. Through following sensing, the entangling operations were reversed. Desired populations were extracted via sequential electron-spin fluorescence readout, temporarily storing population in a third level of the nitrogen nuclear spin to allow averaged readout of the Bell basis. At the same time, the total sensing sequence, denoted Us, was configured with a control frequency ωc = D − γeB0z − A/2, where D = (2π) × 2.87GHz, A = −(2π) × 2.16MHz. And γe = (2π) × 2.8MHz/G. A static magnetic field of 357 G was applied along the NV axis — resulting in a total Hamiltonian H = H0 + Hc + Hint. Simultaneous magnetic field and frequency shift precision in a diamond nitrogen-vacancy centre At a repetition count of eight, the minimum detectable magnetic field amplitude reached 1.0x 10−3 Gauss, while the minimum detectable frequency shift was 1.0x 10−2MHz. These values represent the precision achieved in simultaneously estimating both parameters using the developed control protocol, measured using a nitrogen-vacancy (NV) centre in diamond at room temperature. Each sensing block lasted a duration τ and was repeated N times to achieve a total interrogation time of T = Nτ. Sensor precision was evaluated via the parameter covariance matrix, calculated from the Jacobian matrix relating measured signals to target parameters. Analysis of sensitivities derived from all three independent signals of the Bell basis are nearly identical, simplifying experimental implementation and data processing. The experimental setup involved a discrete control scheme with dynamical decoupling to address the sensor-ancilla qubit interaction. By alternating interactions with target and control magnetic fields and inserting π pulses, unwanted interactions were effectively cancelled. Normalized measured signals were obtained as functions of both amplitude and frequency for N = 1 and N = 8 repetitions. A fit to the simulation data indicates optimal linear and quadratic sensitivity scalings for amplitude and frequency, respectively. By increasing the number of repetitions from one to eight decreased the uncertainty in the estimated amplitude by approximately one order of magnitude. With a lesser decrease in frequency uncertainty. For N = 8, the standard deviation of the signal was minimised, indicating the highest precision in parameter estimation. Beyond this point, further increases in N did not yield substantial improvements in sensitivity. The achieved precision represents a significant step towards simultaneously estimating multiple parameters at the ultimate limit, overcoming the fundamental impossibility arising from singular Fisher information matrices. Circumventing estimation singularities enables precise joint magnetic field characterisation The simultaneous and precise measurement of paired physical quantities has edged closer to reality thanks to work employing nitrogen-vacancy centres in diamond. For years, the challenge lay in the fundamental incompatibility of optimal estimation strategies when attempting to discern multiple parameters at the highest possible precision. This incompatibility manifests as a singularity in the mathematical description, effectively blocking any attempt at joint measurement.

Scientists have demonstrated a control protocol that circumvents this limitation, specifically for estimating the amplitude and frequency of an alternating magnetic field. Accurate simultaneous parameter estimation is vital across diverse fields, from materials science to medical diagnostics. By engineering the sensor’s evolution, the team has restored the expected precision scaling, a critical step towards practical applications. The method isn’t without its constraints; the doubling of the sensing sequence duration represents a trade-off. Sensitivity to imperfections in pulse control requires careful calibration. Future work will likely focus on reducing this overhead and improving the robustness of the control sequences — beyond diamond-based sensors, the principles established here could be adapted to other quantum sensing platforms, such as trapped ions or superconducting qubits. This project stands out in its experimental validation under realistic conditions, bridging the gap between theoretical possibility and tangible progress. 👉 More information 🗞 Approaching the Limit in Multiparameter AC Magnetometry with Quantum Control 🧠 ArXiv: https://arxiv.org/abs/2602.17648 Tags: