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Quantum-Enhanced Optical Magnetometers

Periodic Reporting for period 1 - QUTEMAG (Quantum-Enhanced Optical Magnetometers)

Reporting period: 2016-04-01 to 2018-03-31

Optical magnetometers, implemented by optical interrogation of alkali atoms contained in a vapour cell, are among the most sensitive detectors of magnetic fields. By operating at large atomic densities and low magnetic fields, in a regime often referred to as Spin-Exchange Relaxation-Free (SERF), these devices reach record-level sensitivities enabling the measurement of very weak magnetic signals originating from a wide variety of sources in applications ranging from navigation to magnetocardiography. Their recent miniaturization has opened attractive perspectives for their deployment in applications such as non-invasive bio-magnetic imaging of the brain, attitude control in space based missions, and non-destructive testing for manufacturing, and even wearable devices for personalized health-care diagnosis. To fully unleash their potential in real world applications a number of open fundamental and technological challenges need to be addressed. One fundamental problem is quantum noise, which limits the best attainable sensitivity δB of these devices to scale with sensor volume V as δB ~ V-1/2. For this reason, the sensitivity of these devices degrades as they are further miniaturized. Moreover, to reach their highest sensitivity optical magnetometers sacrifice temporal resolution; as a result, fast-varying signals have remained outside their reach. A promising approach to overcome these limitations relies on Quantum Optics tools, such as quantum-non-demolition (QND) measurements and squeezed light that allow ultra-sensitive measurements, increased device bandwidth, and the enhancement of physical systems beyond their classical limits. To date, in a proof-of-principle way, QND and squeezed light have been used to improve the performance of optical magnetometers independently but not within the same device. Their simultaneous use remains an open challenge.

The overall objective of the project Quantum-Enhanced Optical Magnetometers QUTEMAG was to combine QND and squeezed light to magnetometry at large atomic densities in a regime where spin-exchange collisions dominate the spin dynamics. This regime is of particular interest for the implementation of high-sensitivity, miniaturized, and high-bandwidth magnetometers as described above. The tools developed during QUTEMAG will find application to enhance current technology most suitable to address challenges in the real world.
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.
QUTEMAG has made progress beyond the state of the art in two ways. First, while Kalman filtering techniques are well known in the engineering community their use in atomic sensors has not been fully explored. The experimental work of QUTEMAG represents the first demonstration of these techniques to track both the state of the atoms and external fields coupled to them. Not only these results show the capability of tracking waveforms beyond the intrinsic resolution of an atomic sensor but also the capability to track waveforms whose dynamics are not known prior to the measurement. One potential use of the latter is the ability to perform system identification, “learn” the sensor’s environment, in real time. For instance, in magnetic field sensing Kalman filtering with atomic sensors may enable in the future the precise mapping of the magnetic field environment as measurements are taken. Such maps can then be used for navigation in unknown environments. Second, our results in Kalman filtering also go beyond the state of the art in the field of measurement-induced entanglement with applications to sensing. Particularly, quantum-enhanced sensing requires the simultaneous estimation of the physical parameter of interest as well as its uncertainties. A natural approach to achieve this is Kalman filtering, which is also optimal for linear systems. Our results show how to track the state of atomic spins with minimum uncertainty, thus generating entanglement-type correlations in real time. Finally, while the work in QUTEMAG has focused on optical magnetometry the tools developed here may impact other atomic sensors where many-body interactions play a key role, such as co-magnetometers and accelerometers that are of interest in inertial navigation, and in applications where real time estimation is required, such as in quantum control.
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