Atomic Control Boosts Magnetometry Precision with Quantum Learning

Researchers at the College of Physics, led by CC. Z. Cao and collaborators at Nanjing University of Aeronautics and Astronautics have demonstrated a new approach to controlling internal spin squeezing in atomic qudits for magnetometry. The method effectively addresses a known limitation by transforming the nonlinear Zeeman (NLZ) effect into a sustained resource. Physics-informed reinforcement learning rapidly generates strong squeezed states within a single atom of dysprosium, achieving over 4 dB of fixed-axis spin squeezing despite ongoing nonlinear evolution. This learned control protocol improves single-atom magnetic sensitivity to 13.9 pT/√Hz, a 3 dB enhancement beyond the standard quantum limit, and establishes learning-based control as a viable method for optimising multilevel quantum sensors.

Nonlinear Zeeman effect exploited to enhance atomic spin squeezing and magnetic sensing

Magnetic sensitivity now reaches 13.9 pT/√Hz, a substantial improvement of approximately 3 dB over the standard quantum limit. This represents a significant advance in the field of atomic magnetometry, where achieving sensitivity beyond the standard quantum limit is a key objective. Previously, the nonlinear Zeeman effect, a distortion of atomic energy levels arising from strong magnetic field interactions with the atom’s internal structure, hindered precision measurements. The NLZ effect causes a nonlinear redistribution of internal spin fluctuations, complicating the creation and maintenance of spin-squeezed states. However, researchers have successfully used this effect as a sustained resource for generating and preserving spin-squeezed states within a single atom of dysprosium. Physics-informed reinforcement learning proved key, enabling a control policy that rapidly prepares strongly squeezed states and stabilises them despite ongoing nonlinear evolution, establishing a viable method for optimising multilevel quantum sensors. Spin squeezing reduces the uncertainty in one component of the atomic spin, at the expense of increased uncertainty in another, thereby enhancing the precision of measurements along the squeezed axis.

The protocol stabilised more than 4 decibels of fixed-axis spin squeezing, exceeding levels achievable without active control. Achieving 4 dB of squeezing requires careful manipulation of the atomic state to reduce quantum noise below the standard quantum limit, which is fundamentally limited by Heisenberg’s uncertainty principle. Dysprosium-161, a specific atomic isotope chosen for its suitability in precision sensing applications due to its large magnetic moment and relatively long coherence times, hosted this successful implementation within the $f=21/$2 manifold, highlighting the adaptability of the technique to different atomic systems. The $f=21/$2 manifold refers to a specific energy level within the dysprosium atom, characterised by a total angular momentum of 21/2. This manifold provides a rich set of quantum states suitable for encoding and manipulating information. Analysis of the learned control sequences revealed a surprisingly simple pulse structure, suggesting the agent discovered an efficient method for suppressing unwanted distortions of the spin state while maintaining squeezing, indicating the potential for practical implementation and optimisation. The reinforcement learning agent was ‘physics-informed’ meaning it was initially guided by established principles of atomic physics, accelerating the learning process and improving the robustness of the control policy.

Although the 13.9 pT/√Hz sensitivity represents a step forward, further work is needed to address the complexities of building a full-scale sensor array, alongside challenges related to long-term durability and shielding from external noise sources. Scaling up to an array of atoms introduces interatomic interactions that can decohere the spin-squeezed state and reduce the overall sensitivity. Maintaining coherence, the preservation of quantum information, is crucial for achieving high-precision measurements. Effective shielding from environmental noise, such as vibrations and electromagnetic interference, is also essential for stable operation. A pathway to more precise atomic magnetometry is now available, important for applications ranging from medical imaging, where highly sensitive magnetic field detection can improve the resolution of techniques like magnetoencephalography, to fundamental physics research, such as the search for dark matter and tests of fundamental symmetries. Controlling a single atom of dysprosium was demonstrated, prompting investigation into scalability to larger atomic ensembles where interatomic interactions could introduce unforeseen complexities and diminish the observed gains. Understanding and mitigating these interactions will be critical for realising the full potential of this technology.

Atomic magnetometry, which measures magnetic fields with extreme precision, underpins diverse technologies including brain imaging and navigation systems, and this advancement promises to improve those technologies. The principle behind atomic magnetometry relies on the sensitivity of atomic energy levels to external magnetic fields. By precisely measuring the shift in these energy levels, one can infer the strength and direction of the magnetic field. Physics-informed reinforcement learning offers a new model for optimising multilevel quantum sensors, moving beyond simply preparing quantum states to actively managing inherent atomic behaviours. Traditional approaches to quantum sensing often focus on static preparation of quantum states, whereas this method dynamically adjusts the control parameters to compensate for the NLZ effect and maintain squeezing. By transforming the nonlinear Zeeman effect from a limitation into a sustained resource, magnetic sensitivity in a single dysprosium atom was enhanced. The resulting control policy, learned through readily measurable properties, stabilises spin-squeezed states despite ongoing nonlinear evolution, representing a major advance in quantum metrology. The ability to learn optimal control policies directly from experimental data, without requiring detailed knowledge of the underlying physics, is a significant advantage of this approach.

The research demonstrated that physics-informed reinforcement learning successfully converted unavoidable nonlinear dynamics into a sustained metrological resource within a single dysprosium atom. This is important because it improves the sensitivity of atomic magnetometry, a technique used in applications such as brain imaging and navigation. By actively managing the nonlinear Zeeman effect, researchers achieved a magnetic sensitivity of 13.9 pT/√Hz, representing a 3 dB improvement beyond the standard quantum limit. The authors suggest future work will focus on understanding and mitigating interatomic interactions when scaling this technology to larger ensembles.