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arXiv:2203.05849 · npj Quantum Information

A neural network assisted 171Yb+ quantum magnetometer

Yan Chen, Yue Ban, Ran He, Jin‐Ming Cui, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo, Jorge Casanova

Published Dec 29, 2022• 12 citations
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Abstract

Abstract A versatile magnetometer must deliver a readable response when exposed to target fields in a wide range of parameters. In this work, we experimentally demonstrate that the combination of 171 Yb + atomic sensors with adequately trained neural networks enables us to investigate target fields in distinct challenging scenarios. In particular, we characterize radio frequency (RF) fields in the presence of large shot noise, including the limit case of continuous data acquisition via single-shot measurements. Furthermore, by incorporating neural networks we significantly extend the working regime of atomic magnetometers into scenarios in which the RF driving induces responses beyond their standard harmonic behavior. Our results indicate the benefits to integrate neural networks at the data processing stage of general quantum sensing tasks to decipher the information contained in the sensor responses.

DOI
10.1038/s41534-022-00669-2

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Abstract A versatile magnetometer must deliver a readable response when exposed to target fields in a wide range of parameters. In this work, we experimentally demonstrate that the combination of 171 Yb + atomic sensors with adequately trained neural networks enables us to investigate target fields in distinct challenging scenarios. In particular, we characterize radio frequency (RF) fields in the presence of large shot noise, including the limit case of continuous data acquisition via single-shot measurements. Furthermore, by incorporating neural networks we significantly extend the working regime of atomic magnetometers into scenarios in which the RF driving induces responses beyond their standard harmonic behavior. Our results indicate the benefits to integrate neural networks at the data processing stage of general quantum sensing tasks to decipher the information contained in the sensor responses.
Abstract Artificial neural networks (NNs) bridge input data into output results by approximately encoding the function that relates them. This is achieved after training the network with a collection of known inputs and results leading to an adjustment of the neuron connections and biases. In the context of quantum detection schemes, NNs find a natural playground. In particular, in the presence of a target (e.g. an electromagnetic field), a quantum sensor delivers a response, i.e. the input data, which can be subsequently processed by a NN that outputs the target features. In this work we demonstrate that adequately trained NNs enable to characterize a target with (i) minimal knowledge of the underlying physical model (ii) in regimes where the quantum sensor presents complex responses and (iii) under a significant shot noise due to a reduced number of measurements. We exemplify the method with a development for 171 Yb + atomic sensors. However, our protocol is general, thus applicable to arbitrary quantum detection scenarios.
Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an 171Yb+ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.
Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.
Efficient unsupervised optimisation of atomic magnetometers is a requirement in many applications, where direct intervention of an operator is not feasible. The efficient extraction of the optimal operating conditions from a small sample of experimental data requires a robust automated regression of the available data. Here we address this issue and propose the use of general regression neural networks as a tool for the optimisation of atomic magnetometers which does not require human supervision and is efficient, as it is ideally suited to operating with a small sample of data as input. As a case study, we specifically demonstrate the optimisation of an unshielded radio-frequency atomic magnetometer by using a general regression neural network which establishes a mapping between three input variables, the cell temperature, the pump beam power and the probe beam power, and one output variable, the AC sensitivity. The optimisation results into an AC sensitivity of 44 fT/Hz at 26 kHz.
Multiparameter sensing such as vector magnetometry often involves complex setups due to various external fields needed in explicitly connecting one measured signal to one parameter. Here, we propose a paradigm of indirect encoding for vector atomic magnetometry based on machine learning. We encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals associated with the optical rotation of a laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 fT/√Hz and angular sensitivities of about 100∼200μrad/√Hz (for a magnetic field of around 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing.
Quantum-enhanced sensing typically relies on preparing specific entangled states. However, engineering these states in scalable many-body systems remains challenging due to the difficulty of designing robust preparation protocols and accounting for realistic noise. We show that evolving a simple product state under native time-independent Hamiltonian dynamics in Rydberg atom arrays generates complex many-body correlations that can potentially enable quantum-enhanced parameter estimation reaching the Heisenberg limit (HL). The key challenge is then shifted to extracting the metrological information encoded in spatial correlations of measurement patterns. We introduce a neural correlation learning framework that combines Bayesian inference with neural networks trained on calibration data. Operating in a two-stage calibration-and-sensing protocol, we numerically demonstrate that this framework effectively extracts many-body correlations to saturate the Cramér--Rao bound dictated by the classical Fisher information. Consequently, it achieves quantum-enhanced sensitivity surpassing the standard quantum limit (SQL). Furthermore, the learned estimator is robust to realistic noise, and remains accurate in the absence of rare measurement patterns. Our results establish a hardware-efficient and scalable paradigm for quantum sensing in interacting many-body systems without requiring engineered entangled states.