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arXiv:1807.00946 · Physical Review Applied

Influence of Dynamical Decoupling Sequences with Finite-Width Pulses on Quantum Sensing for AC Magnetometry

T. Ishikawa, Akio Yoshizawa, Yasunori Mawatari, Hideyuki Watanabe, Satoshi Kashiwaya

Published Nov 27, 2018• 14 citations
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Abstract

Dynamical decoupling sequences of multiple pulses offer filter functions for the time evolution of a qubit superposition state, and thus are indispensable tools for quantum sensing. The authors investigate the effects of sequences of finite-width pulses on ac magnetometry based on nitrogen-vacancy centers in isotopically controlled diamond. This experimental and theoretical study shows that finite pulse width alters the optimum acquisition time, and shows how to correct the resulting frequency shift, providing a guideline for accurate measurement of the frequency, linewidth, and amplitude of an ac field.

DOI
10.1103/physrevapplied.10.054059

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Dynamical decoupling sequences of multiple pulses offer filter functions for the time evolution of a qubit superposition state, and thus are indispensable tools for quantum sensing. The authors investigate the effects of sequences of finite-width pulses on ac magnetometry based on nitrogen-vacancy centers in isotopically controlled diamond. This experimental and theoretical study shows that finite pulse width alters the optimum acquisition time, and shows how to correct the resulting frequency shift, providing a guideline for accurate measurement of the frequency, linewidth, and amplitude of an ac field.
Quantum sensors based on the electron spin states of nitrogen vacancy centers in diamond have found wide application in magnetometry and nuclear spin magnetic resonance measurements. Previously, we have theoretically and experimentally investigated the effect of finite pulse width on quantum sensing for synchronous alternating-current (AC) magnetic fields to dynamical decoupling sequences [T. Ishikawa et al., Phys. Rev. Appl. 10, 054059 (2018)]. However, many biological and condensed-matter systems exhibit fluctuating AC fields over time, and thus, our model needs modifications because of additional non-ideal conditions in practical measurements. Here, we investigate the effects of finite pulse width of multiple-pulse decoupling sequences on quantum sensing for asynchronous AC magnetic fields. For this purpose, we use a spin ensemble of nitrogen vacancy centers in an isotopically purified diamond film. We reveal through experiments that the finite-width pulse causes shifts in AC magnetometry signals in a free-precession-time plot. In addition, our results indicate that the finite-width pulse affects the amplitude of magnetometry signals, implying that the finite-pulse-width effect should be taken into account for realizing accurate measurement of the frequency and amplitude of asynchronous AC magnetic fields.
Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen-vacancy (NV) center in the diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC-field can be generally obtained when the π-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is π/2. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the nonphase-accumulation condition is available for detecting a very small phase shift of an AC-field from its initial phase. Measurements of the real part and the imaginary part of AC impedance require the amplitude and the phase information of an AC-field, and thus, this finding is expected to provide a guide for realizing sensitive measurement of AC impedance in the micrometer and nanometer scales.
Ensembles of nitrogen-vacancy (NV) centers in diamond are widely used as AC magnetometers. While such measurements are usually performed using standard (XY) dynamical decoupling (DD) protocols at room temperature, we study the sensitivities achieved by utilizing various DD protocols, for measuring magnetic AC fields at frequencies in the 10-250 kHz range, at room temperature and 77 K. By performing measurements on an isotopically pure 12^{12}12C sample, we find that the Carr-Purcell-Meiboom-Gill (CPMG) protocol, which is not robust against pulse imperfections, is less efficient for magnetometry than robust XY-based sequences. The concatenation of a standard XY-based protocol may enhance the sensitivities only for measuring high-frequency fields, for which many (>500> 500>500) DD pulses are necessary and the robustness against pulse imperfections is critical. Moreover, we show that cooling is effective only for measuring low-frequency fields (~10 kHz), for which the experiment time apporaches T1T_1T1​ at a small number of applied DD pulses.
Ensembles of nitrogen-vacancy (NV) centers in diamond are widely used as AC magnetometers. While such measurements are usually performed using standard (XY) dynamical decoupling (DD) protocols at room temperature, we study the sensitivities achieved by utilizing various DD protocols, for measuring magnetic AC fields at frequencies in the 10-250 kHz range, at room temperature and 77 K. By performing measurements on an isotopically pure 12^{12}12C sample, we find that the Carr-Purcell-Meiboom-Gill (CPMG) protocol, which is not robust against pulse imperfections, is less efficient for magnetometry than robust XY-based sequences. The concatenation of a standard XY-based protocol may enhance the sensitivities only for measuring high-frequency fields, for which many (>500> 500>500) DD pulses are necessary and the robustness against pulse imperfections is critical. Moreover, we show that cooling is effective only for measuring low-frequency fields (~10 kHz), for which the experiment time apporaches T1T_1T1​ at a small number of applied DD pulses.
Solid-state qubits hold the promise to achieve an unmatched combination of sensitivity and spatial resolution. To achieve their potential, the qubits need, however, to be shielded from the deleterious effects of the environment. While dynamical decoupling techniques can improve the coherence time, they impose a compromise between sensitivity and the frequency range of the field to be measured. Moreover, the performance of pulse sequences is ultimately limited by control bounds and errors. Here we analyze a versatile alternative based on continuous driving. We find that continuous dynamical decoupling schemes can be used for ac magnetometry, providing similar frequency constraints on the ac field and improved sensitivity for some noise regimes. In addition, the flexibility of phase and amplitude modulation could yield superior robustness to driving errors and a better adaptability to external experimental scenarios.