QUTEMAGs experimental work was based on the development of high-sensitivity magnetometry setups, proven tools for quantum-enhancement of atomic instruments, and advanced signal-processing techniques for state estimation and control. First we developed a versatile experimental setup for QND measurements of atomic spins in alkali atoms in thermal equilibrium using both classical and quantum probing light. Using this setup we studied the fundamental limits of noise spectroscopy using estimation theory, Faraday rotation probing of the atomic spin system, and squeezed light. We developed spectral models for the sensor dynamics and studied how quantum statistical fluctuations, i.e. spin noise and shot noise in the read out, affect the precision of estimates of sensor’s parameters obtained through noise spectroscopy. For the particular case of optically detected spin ensembles we found that optical shot noise imposes “local” standard quantum limits for any given probe power and atom number, and also “global” standard quantum limits when probe power and atom number are taken as free parameters. By experimentally corroborating these theoretical findings we demonstrated a practical approach to analyze the statistical sensitivity of noise spectroscopy, which is required for the rigorous use of the technique in parameter identification.
In a follow up experiment we used the developed dynamical models to study causal waveform estimation (tracking) of time-varying signals coupled to atomic spins. We used Kalman filtering techniques, which optimally track known linear Gaussian stochastic processes, to estimate stochastic input signals that we generated by optical pumping. Comparing the known input to the estimates, we confirmed the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor’s intrinsic time resolution. With proper filter choice, we obtained similar benefits when tracking partially known and non-Gaussian signal processes, as are found in most practical sensing applications. This work not only demonstrated a technique to evade the trade-off between sensitivity and time resolution in coherent sensing but also how to track waveforms with dynamics unknown prior to the measurement. The results are of particular interest for employing Kalman filtering techniques in a wide range of atomic sensing applications.
Finally a unique and fascinating aspect of our work has been the analysis of QND measurements on atomic spins in the SERF regime using Kalman filtering techniques, a powerful Bayesian inference technique to perform optimal state estimation in real time. In our experiments the optimality of KF has been key in extracting all relevant information from QND measurements with minimum uncertainty, generating entanglement-type correlations among the probed spins. This particular work has shown that the unique properties of SERF-regime ensembles are extremely attractive for QND-based quantum technologies, with potential applications in quantum memories, quantum sensing, and quantum simulation.
