Advances in Quantum Magnetometry Enable Heisenberg Scaling Via Measurement-Induced Correlation

High-precision magnetic field measurements rely on optical magnetometers, devices which detect the rotation of polarised light caused by the Faraday effect. Georg Engelhardt, from the Shenzhen International Quantum Academy, alongside Ming Li and Xingchang Wang of the Southern University of Science and Technology, alongside JunYan Luo and J.F. Chen, have undertaken a detailed information analysis of these systems. Their research reveals that a commonly used semiclassical model can be significantly inaccurate, even violating fundamental limits on measurement precision for certain conditions. This finding is important because it demonstrates that the behaviour of these magnetometers is more complex than previously understood, and the team’s collective model predicts a Heisenberg scaling of Fisher information, suggesting measurement-induced correlations are key to achieving enhanced sensitivity. Ultimately, this work offers a new perspective on macroscopic quantum phenomena and provides a potential test for the foundations of mechanics when applied to large ensembles of atoms.

Chen, have undertaken a detailed quantum information analysis of these systems. Their research reveals that a commonly used semiclassical model can be significantly inaccurate, even violating fundamental limits on measurement precision for certain conditions. This finding is important because it demonstrates that the behaviour of these magnetometers is more complex than previously understood, and the team’s collective model predicts a Heisenberg scaling of Fisher information, suggesting measurement-induced correlations are key to achieving enhanced sensitivity.

Atomic Magnetometry via Quantum Trajectory Analysis

Optical magnetometers, renowned for high-precision magnetic field measurements, were the focus of a detailed quantum information analysis. Researchers engineered an experimental setup employing linearly polarized laser light directed through an atomic vapor, where the rotation of polarization reveals information about the magnetic field strength. The atomic level structure was carefully configured as a four-level system. To rigorously analyse the system, the team developed two distinct theoretical models: a semiclassical approach and one describing the atoms as a collective spin system.

Results demonstrate that the semiclassical model can violate the quantum Cramer-Rao bound under conditions of weak dissipation and large atom numbers, thus invalidating its use in such regimes. The collective model consistently respects the Cramer-Rao bound across all parameter values, offering a more robust theoretical framework. A key innovation was the implementation of full-counting statistics, amending the quantum trajectories to allow for ensemble-level description of the system, moving beyond simulating individual stochastic trajectories to characterise the macroscopic behaviour of the atomic ensemble.

Calculations revealed that the collective model predicts Heisenberg scaling for the Fisher information, indicating a correlation induced by the measurement process within the non-interacting system. The comparison of the two models, validated against experimental data, offers a novel test for the foundations of mechanics within a macroscopic atomic ensemble. Furthermore, the study pioneers a new paradigm in quantum sensing by demonstrating that Heisenberg scaling can emerge in a stationary state of a macroscopic quantum system, enabling a thorough quantum information analysis of established optical magnetometry protocols and opening avenues for probing fundamental quantum properties of light-matter interaction.

The system delivers the potential to improve technologies like dark matter searches and gravitational wave detectors, while simultaneously providing a platform for testing the limits of quantum mechanics itself.

Cramer-Rao Bound Violated in Optical Magnetometry

Scientists achieved a breakthrough in understanding the limits of precision in optical magnetometry, revealing a violation of the classical Cramer-Rao bound under specific conditions. The research team investigated two distinct models to describe the behaviour of atoms within the magnetometer, employing a semiclassical approach and a collective spin model. Experiments revealed that the semiclassical model falters when dealing with weak dissipation and large atom numbers, demonstrably violating the Cramer-Rao bound by several orders of magnitude, highlighting the need for a more accurate description.

The team measured the expectation value of polarization rotation, finding it adhered to the established dispersion relation linking refractive index and the Faraday effect. Detailed analysis of the variance of polarization rotation showed a flat minimum near zero magnetic field, dictated by photon-shot noise, but a dramatic increase at larger fields, scaling inversely with the pump power in the weak pumping regime. Crucially, the quantum Fisher information exceeded the signal-to-noise ratio for most magnetic field strengths, except near zero, where the Cramer-Rao bound was demonstrably violated.

Data shows that the quantum Fisher information increases linearly with the number of atoms, as predicted by analytical calculations, while the signal-to-noise ratio initially increases quadratically. However, above an atom number of 8x 10 10 , the research demonstrates a clear violation of the Cramer-Rao inequality, exceeding two orders of magnitude. Further investigation revealed that the ratio of signal-to-noise ratio to quantum Fisher information becomes dependent on the magnetic field strength and pump power, suggesting the possibility of a bound violation when the magnetic field exceeds the pump power.

The study confirms this violation in the weak pumping regime, demonstrating that the semiclassical approach fails to capture emergent collective quantum effects present in the atomic ensemble. The collective model, treating the atoms as a single spin, consistently respects the Cramer-Rao bound across all parameters and predicts Heisenberg scaling for the Fisher information.

Atomic Correlations Explain Heisenberg Scaling in Magnetometry

This research presents a detailed investigation into the operation of optical magnetometers, employing both semiclassical and collective models to describe the underlying physics. The authors demonstrate that the semiclassical model can overestimate precision and violate fundamental limits known as the Cramer-Rao bound under specific conditions , namely, weak dissipation and large atom numbers. Conversely, the collective model, which accounts for atomic correlations, adheres to this bound across all parameters and predicts a Heisenberg scaling of the Fisher information.

A key contribution of this work is the identification of measurement-induced correlations as the origin of this Heisenberg scaling, a phenomenon observed in a stationary state without requiring inherent interactions between the atoms. This finding offers a novel perspective on achieving enhanced precision in sensing applications. The authors acknowledge that their collective model simplifies the system by assuming all atoms occupy the same position, but emphasize the fundamental driver of correlation is the indistinguishability of atoms during light-matter interaction, meaning correlations can still arise even with spatial separation.

Importantly, the study proposes a means of experimentally distinguishing between the predictions of the two models through analysis of the time-integrated intensity and associated noise, predicting a vanishing polarization rotation at high magnetic fields for the semiclassical model, while the collective model predicts a plateau. Future research could focus on verifying these predictions through targeted experiments, potentially offering a test of foundational principles in macroscopic quantum systems and providing insights into the limits of classical descriptions of atomic ensembles.