Wavelet-based fast time-resolved magnetic sensing with electronic spins in diamond

Abstract

Time-resolved magnetic sensing is of great importance from fundamental studies to applications in physical and biological sciences. Recently the nitrogen-vacancy (NV) defect center in diamond has been developed as a promising sensor of magnetic field under ambient conditions. However the methods to reconstruct time-resolved magnetic field with high sensitivity are not yet fully developed. Here, we propose and demonstrate a novel sensing method based on spin echo, and Haar wavelet transform. Our method is exponentially faster in reconstructing time-resolved magnetic field with comparable sensitivity over existing methods. Further, 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 nano-scales. Sensing of weak signals with high spatial resolution is of great importance in diverse areas ranging from fundamental physics and material science to biological sciences. NV center in diamond has recently emerged as one multifunctional sensor with high sensitivity and nano-scale spatial resolution under ambient conditions. It is applied for sensing magnetic fields [1][2][3][4][5][6][7][8], electric fields[9], temperature [10][11][12] and magnetic resonance imaging [13][14][15][16][17].For NV based magnetic sensing applications, the basic idea is measuring magnetic field, for example, via Ramsey interferometry [18]: the electron spin is first prepared in an equal superposition of eigenstates |0 and |1 and obtains a relative phase in an external field b(t). After an acquisition time T the accumulated phase T 0 γb(t)dt results in a frequency shift that is measured optically where γ is gyromagnetic ratio. This scheme is often called DC sensing scheme which could in principle extract the complete dynamics of the field required by general applications. By a successive monitoring of the resonance energy, either through increasing the acquisition period or sequential small acquisition steps, we can reconstruct the temporal magnetic field and extract its dynamics. However these reconstruction schemes are inefficient in sampling rate and also suffer from the electron spin's short coherence time (i.e., T * 2 ) which limits the measurement sensitivity. Dynamical decoupling sequences [19][20][21][22][23], acting as a controllable frequency band-pass filter, could be used to enhance the coherence time by filtering out a large part of the noise [24][25][26]. High sensitivity of constant oscillating magnetic fields is achieved based on this method. But the temporal field's reconstruction is not straightforward.To deal with this problem, recently Cooper et.al designed a group of decoupling sequences associated with the Wash functions [27]. While protecting against dephasing noise, each Walsh decoupling sequence is measuring a Wash transform coefficient of temporal magnetic field on the correspon...

Quantum sensing

“…which can be shown to satisfy lim N →∞ V N (t ) = V (t ). A similar result can be obtained using different basis functions, such as Haar wavelets, as long as they can be easily implemented experimentally (Xu et al, 2016). An advantage of these methods is that they provide protection of the sensor against dephasing, while extracting the desired information.…”

Reconstruction-Free Quantum Sensing of Arbitrary Waveforms

“…1(d): By inserting two π pulses at times t and t+t int relative to two consecutive waveform triggers, we selectively acquire phase from the time interval [t, t+t int ] while canceling all other phase accumulation. A similar scheme of partial phase cancellation has been implemented with digital Walsh filters [22] and Haar functions [23] via a sequence of π rotations. The linear recombination of sensor outputs in such waveform sampling, however, is prone to introducing errors, especially for rapidly varying signals whose detection requires many π pulses [21].…”

“…This method, however, is limited to strong signals because the spectral resolution inversely scales with the time resolution. Other approaches include pulsed Ramsey detection [20], Walsh dynamical decoupling [21,22], and Haar wavelet sampling [23], discussed below. These methods use coherent control of the sensor to achieve competitive sensitivities, but require some form of waveform reconstruction.…”

First- and second-order gradient couplings to NV centers engineered by the geometric symmetry

“…Because utilizing the existing quantum platforms or quantum methods, people can greatly improve the accuracy, resolution or sensitivity in comparison with the original measurements [1,[9][10][11][12][13]. To our knowledge, the optomechanical system [14][15][16][17], cold atoms system [8,18], solid-state spins, et al [19][20][21][22][23], have made the important contributions to the QPM [24,25]. Through the analysis and comparison of the above typical quantum systems, we note solid-state spins may be the more promising choice, owing to its unique superiorities, i.e., convenient preparation and applications but without complex trap, optical addressing and readout, easy manipulations even at room temperature, high sensitivity to electromagnetic fields or strain, and long coherence time, and so on [26][27][28][29].…”