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IEEE Access

Quantum Sensing of Fast Time-Varying Magnetic Field With Daubechies Wavelets

Chou-Wei Kiang, Jian–Jiun Ding, Jean‐Fu Kiang

Published Jan 1, 2024• 4 citations
Publisher

Abstract

A quantum sensing protocol is proposed to apply continuous-wave microwave sequences modulated by Daubechies wavelets to control quantum sensors. The Daubechies wavelet coefficients thus extracted are used to reconstruct a fast time-varying magnetic field with higher smoothness, mitigating square-shaped artifacts as Haar wavelets or Walsh functions are used for modulation. The relations between the qubit readout, the accumulated phase of the quantum state, and the wavelet coefficients are derived based on an intuitive model represented on the Bloch sphere. The efficacy and accuracy of the proposed waveform reconstruction method under various conditions are evaluated by simulations.

DOI
10.1109/access.2024.3364817

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A quantum sensing protocol is proposed to apply continuous-wave microwave sequences modulated by Daubechies wavelets to control quantum sensors. The Daubechies wavelet coefficients thus extracted are used to reconstruct a fast time-varying magnetic field with higher smoothness, mitigating square-shaped artifacts as Haar wavelets or Walsh functions are used for modulation. The relations between the qubit readout, the accumulated phase of the quantum state, and the wavelet coefficients are derived based on an intuitive model represented on the Bloch sphere. The efficacy and accuracy of the proposed waveform reconstruction method under various conditions are evaluated by simulations.
Time-resolved magnetic sensing is of great importance from fundamental studies to applications in physical and biological sciences. Recently, the nitrogen-vacancy defect center in diamond has been developed as a promising sensor of magnetic fields under ambient conditions. However, methods to reconstruct time-resolved magnetic fields with high sensitivity are not yet fully developed. Here, we propose and demonstrate a sensing method based on spin echo and Haar wavelet transformation. Our method is exponentially faster in reconstructing time-resolved magnetic fields with comparable sensitivity than existing methods. It is also easier to implement in experiments. Furthermore, the wavelet's unique features enable our method to extract information from the whole signal with only part of the measuring sequences. We then explore this feature for a fast detection of simulated nerve impulses. These results will be useful to time-resolved magnetic sensing with quantum probes at nanoscale.
Nitrogen-vacancy (NV) ensembles are viable magnetometers to be implemented on nanosatellites for monitoring geomagnetic fluctuations, which are credible precursors for predicting earthquakes at short notice. In this work, a Haar wavelet-based quantum sensing method is proposed to reconstruct the time-varying waveform of geomagnetic fluctuations in the very low frequency band. To collect different frequency components of fluctuations waveform at once, we propose a schematic to employ multiple NV ensembles (NVEs), with each controlled by an independent microwave source. Berry sequences are applied on one set of NVEs to extract the scaling coefficients from accumulated geometric phases to reconstruct near-dc components of a waveform. Spin-echo sequences are applied to another set of NVEs to extract the Haar wavelet coefficients from the dynamic phases to reconstruct high-frequency components. The efficacy of the proposed sensing protocol implemented on multiple NVEs is validated by reconstructing a waveform of geomagnetic fluctuations from a DEMETER satellite dataset through simulations. Each NVE is assumed to containN=108N = 10^{8}N=108uncorrelated NV centers. The application of a Berry sequence to each NVE can achieve the maximum detectable magnetic field of over460 μ460 \ \mu460 μT, resolving the issues of phase ambiguity and hyperfine-induced detuning if conventional Ramsey sequence were applied. The feasibility of the proposed simulation scenario considering spin-bath noise within an NVE is justified by simulations. The effects of wavelet scales, Rabi frequency in Berry sequence, and number of NV centers in each NVE are analyzed. The proposed NVE quantum sensors operated with the proposed sensing protocol can be installed on nanosatellites to monitor global geomagnetic fluctuations, with sub-μ\muμs temporal resolution in the near future.
Coherently controlled quantum systems have lately emerged as precision sensors, especially on small length scales. In this study the authors present a sensing protocol that enables direct detection of time-dependent magnetic fields, without the need to reconstruct the signal, effectively turning their quantum sensor into a sort of oscilloscope. This scheme will be useful for investigating e.g.e.g.e.g. the nanoscale dynamics of photocurrents or magnetic domain walls. While it is demonstrated using N-VVV centers in diamond, the authors' method is applicable to any qubitlike sensor.
We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen-vacancy center in diamond and up to 10 000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6-ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2-ns hardware sampling. We apply the method for the detection of external ac magnetic fields and nuclear magnetic resonance signals of ^{13}C spins with high spectral resolution. Our method is simple to implement and especially useful for quantum applications that require fast phase gates, many control pulses, and high fidelity.
A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.
Abstract We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the autocorrelation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain, from which the autocorrelation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by sampling and discretization in the time domain and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the autocorrelation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues to further improve the reconstruction accuracy.