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Results of dynamical sensitivity control. (a) Experimental results showing the dependence of state population P 0 as a function of B RF and ϕ for N = 20. (b) Simulations showing the P 0 as a function of B RF and ϕ for N = 20 matching the experiments shown in (a). (c) Experimental results showing S(ζ), the dynamical sensitivity β(ϕ), and its dependence on the 4 · π-pulse unit phase angle ϕ for N = 160. (d) The simulation results of S(ζ) dependence on ϕ obtained matching the experimental conditions shown in (c).
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The Nitrogen-Vacancy (NV) defect in diamond is a unique quantum system that offers precision sensing of nanoscale physical quantities at room temperature beyond the current state-of-the-art. The benchmark parameters for nanoscale magnetometry applications are sensitivity, spectral resolution, and dynamic range. Under realistic conditions the NV sen...
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Context 1
... sensitivity. We obtain the relation between the phase control and the sensitivity of the sensor employing N = 160 of the 4 · π-pulse units and measuring the state occupancy P 0 (ϕ, B RF ) for ϕ ∈ [0, π]. As the signal P 0 (ϕ, B RF ) is harmonic in the B RF range, we show its corre- sponding Fourier transform S(ζ) for every value of ϕ ∈ [0, π] in Fig. 2(c) (experiment). Thus, the sensitivity dependence of the DYSCO sequence can be deduced from the experimental data as ...
Context 2
... RF In the following, we denote β(ϕ) as the 'dynamical sensitivity' , given that this quantity can be continuously varied in analog manner as desired through the phase angle ϕ of the 4 · π pulse units. Figure 2(c) and (d) illustrates the significance of the function β(ϕ) in the context of magnetometery. The value β = 0 denotes a phase condition ϕ = 0 that sets a DYSCO unit insensitive (or minimally sensitive) to external B RF field while β = 1 defines a con- dition that makes a DYSCO unit most sensitive (high sensitivity) to the B RF field. ...
Citations
... They also, however, experience decoherence due to this same environment, which limits their sensitivity in practice. Techniques to suppress decoherence, without equally suppressing the signal, are therefore of central importance in quantum sensing [2][3][4][5][6][7][8][9]. Quantum error correction (QEC) is currently emerging as an important technique to this end, and has attracted substantial theoretical and experimental interest of late [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. ...
... The derivative of the naïve Eq. (5) with respect to ω is straightforward and its |δω| is thus equal to Eq. (13). For the proposed solution given in Eq. (6), this derivative is however more complicated due to the form of q. It is given by the following expression and ...
... An aspect not discussed in the main text is the precision of the proposed solution with respect to a simulation of the protocol. Fig. 6(a) shows the root-mean-square deviation (RMSE) of the proposed function given in Eq. (6) from the simulated with QuTiP [36] function. We note that the error is consistently below 0.2% indicating that the function is an equally accurate solution of the non-corrected and error-corrected problems. ...
The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side-effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally-motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.
... For quantum-sensing applications, nitrogen-vacancy (NV) centres in diamond have attracted considerable attention due to their exceptional quantummechanical properties 1,2 , including long spin-coherence times 3,4 , and due to their great potential for far-field optical nanoscopy [5][6][7][8] . Furthermore, an increase in sensitivity can be gained for alternating current (AC) field sensing by prolonging the NV spin coherence with dynamical decoupling of the centre's spin from its environment 2,3,[9][10][11][12] . Therefore, AC field sensing is applied in various areas of physics, chemistry and biology: to detect single spins [13][14][15] , for nuclear magnetic-resonance of tiny samplevolumes [16][17][18][19][20] , for nanoscale magnetic-resonance imaging 13,[21][22][23] and to search for new particles beyond the standard model 24,25 . ...
... Their improvement of the dynamic range compared to a sequence with 16 π-pulses was about 26, and they explored the effect of the phase of the measured field in depth. Besides, one of the advantages of the previously reported dynamical sensitivity control 11 was the increase in the range by 4000 times, up to a theoretical maximum of 5000 times. Their uncertainty for a single measurement was about double that of a similar standard measurement, while the required multi-measurement for the large range worsened the sensitivity further (which is the uncertainty times ffiffiffiffiffiffiffiffiffiffi ffi T meas p ) by ffiffiffiffiffiffi N ϕ p with N ϕ the number of phases applied in their method (the more phases, the larger the range, but each phase requires an additional measurement). ...
Quantum sensors are highly sensitive since they capitalise on fragile quantum properties such as coherence, while enabling ultra-high spatial resolution. For sensing, the crux is to minimise the measurement uncertainty in a chosen range within a given time. However, basic quantum sensing protocols cannot simultaneously achieve both a high sensitivity and a large range. Here, we demonstrate a non-adaptive algorithm for increasing this range, in principle without limit, for alternating-current field sensing, while being able to get arbitrarily close to the best possible sensitivity. Therefore, it outperforms the standard measurement concept in both sensitivity and range. Also, we explore this algorithm thoroughly by simulation, and discuss the T ⁻² scaling that this algorithm approaches in the coherent regime, as opposed to the T −1/2 of the standard measurement. The same algorithm can be applied to any modulo-limited sensor.
... [31][32][33][34][35][36] One of the most attractive applications of NV centers is for high sensitivity magnetometers. [11][12][13][14][15][16][17][18][19][20][21][22][23] A single NV center allows nanoscale magnetometry with a reasonably high sensitivity (∼nT= Hz 1=2 ), 2,3,11,12) making it possible to perform nano-NMR. 13) For a sensor with a size of about a micron, where magnetoencephalography and magnetocardiogram applications are possible, an ensemble of NV centers has a high sensitivity proportional to the square root of the number of NV centers. ...
... Dynamical decoupling schemes are based on π pulse trains which command the spin precession abruptly. Recently, dynamical sensitivity control (DYSCO) has been proposed, aiming to provide smooth and analog sensitivity modulation [25]. In this control method, |2π| ambiguities are removed without sacrificing accuracy. ...
The nitrogen-vacancy (NV) center is a point defect in diamond with unique properties for use in ultra-sensitive, high-resolution magnetometry. One of the most interesting and challenging applications is nanoscale magnetic resonance imaging (nano-MRI). While many review papers have covered other NV centers in diamond applications, there is no survey targeting the specific development of nano-MRI devices based on NV centers in diamond. Several different nano-MRI methods based on NV centers have been proposed with the goal of improving the spatial and temporal resolution, but without any coordinated effort. After summarizing the main NV magnetic imaging methods, this review presents a survey of the latest advances in NV center nano-MRI.
... Here, we investigate the potential of noise spectroscopy based on three microwave (MW) driving sequences: the CPMG sequence post-processed by spectral decomposition (CPMG SD) [10,12], and the two recently introduced sequences: DYnamic Sensitivity COntrol (DYSCO) and a modified DYSCO scheme with a Gaussian envelope (gDYSCO) [17]. The properties of the sequences are studied analytically and numerically in terms of accessible bandwidth, frequency resolution and gain as well as their implications for the reconstruction of noise spectra. ...
... The DYSCO pulse sequence was first presented by Lazariev et al. [17] as a means for selective radiofrequency (RF) spectroscopy using NV centres. Contrary to spin-flipping sequences, DYSCO allows for control of the instantaneous sensitivity of the spin-sensor by precise pulse phase handling. ...
... Σ is a measure of how much the coherence curve is affected by the presence of noise around the sensed frequency. While Σ varies slightly as a function of frequency f 0 , overall for DYSCO it is approximately 60 % [17] of the CPMG gain Σ CPMG , and for Gaussian DYSCO it is about 20 %. CPMG has a clear advantage in terms of bandwidth, or dynamic range. ...
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. While quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits and trapped ions, traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes.Here, we compared several methods for noise spectroscopy: spectral decomposition based on the CPMG sequence, the recently presented DYSCO sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO).The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth and sensitivity, revealing a supremacy of gDYSCO to reconstruct non-trivial features.Utilizing an ensemble of nitrogen-vacancy centres in diamond coupled to a high density 13C nuclear spin environment, we experimentally confirm our findings.The combination of the presented schemes offers potential to record high quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.
The sensitivity of force transducers can be calibrated by traceable measurement of dynamic force. It is usually considered as a static parameter in industrial measurement. However, the force transducer will generate inaccurate outputs when the static sensitivity (SS) is used for dynamic measurement with changed frequencies. To overcome this problem, the dynamic sensitivity (DS) is investigated by evaluating its calibration error based on a Gray Bootstrap Model (GBM). First, the force transducer is dynamic calibrated by periodic force to build an error model. Second, the calibration errors are rolling predicted by gray model to generate a sequence matrix. Third, the confidence intervals are solved for the calibrated force in time history by bootstrap sampling from the rolling sequence matrix. Forth, the optimal sensitivities at different frequencies are evaluated by probability density function and fitted by the least square method. The experimental result shows that Relative Errors (RE) are quite small as 0.2% at 160 Hz, -0.1% at 315 Hz, and -0.3% at 1000 Hz. The Degree of Reliability (DR) are great enough and approximately equal, which reveals that the DS of force transducers is superior to SS when it comes to dynamic measurement of force.
Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.
The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.
Solid-state spin systems including nitrogen-vacancy (NV) centers in diamond constitute an increasingly favored quantum sensing platform. However, present NV ensemble devices exhibit sensitivities orders of magnitude away from theoretical limits. The sensitivity shortfall both handicaps existing implementations and curtails the envisioned application space. This review analyzes present and proposed approaches to enhance the sensitivity of broadband ensemble-NV-diamond magnetometers. Improvements to the spin dephasing time, the readout fidelity, and the host diamond material properties are identified as the most promising avenues and are investigated extensively. This analysis of sensitivity optimization establishes a foundation to stimulate development of new techniques for enhancing solid-state sensor performance.
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. Quantum-noise spectroscopy has been used in various quantum systems, such as superconducting qubits, nitrogen-vacancy centers, and trapped ions. Traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and nonmonotonous, thus posing a challenge to existing noise-spectroscopy schemes. Here we compare several methods for noise spectroscopy: spectral decomposition based on the Carr-Purcell-Meiboom-Gill sequence, the recently presented dynamic sensitivity control (DYSCO) sequence, and a modified DYSCO sequence with a Gaussian envelope (gDYSCO). The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth, and sensitivity, revealing a supremacy of gDYSCO to reconstruct nontrivial features. Using an ensemble of nitrogen-vacancy centers in diamond coupled to a high-density C13-nuclear-spin environment, we experimentally confirm our findings. The combination of the schemes presented offers potential to record high-quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.
