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arXiv:1008.4395 · Physical Review Letters

Single-Spin Magnetometry with Multipulse Sensing Sequences

G. de Lange, Diego Ristè, V. V. Dobrovitski, Ronald Hanson

Published Feb 24, 2011• 209 citations
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Abstract

We experimentally demonstrate single-spin magnetometry with multipulse sensing sequences. The use of multipulse sequences can greatly increase the sensing time per measurement shot, resulting in enhanced ac magnetic field sensitivity. We theoretically derive and experimentally verify the optimal number of sensing cycles, for which the effects of decoherence and increased sensing time are balanced. We perform these experiments for oscillating magnetic fields with fixed phase as well as for fields with random phase. Finally, by varying the phase and frequency of the ac magnetic field, we measure the full frequency-filtering characteristics of different multipulse schemes and discuss their use in magnetometry applications.

DOI
10.1103/physrevlett.106.080802

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We experimentally demonstrate single-spin magnetometry with multipulse sensing sequences. The use of multipulse sequences can greatly increase the sensing time per measurement shot, resulting in enhanced ac magnetic field sensitivity. We theoretically derive and experimentally verify the optimal number of sensing cycles, for which the effects of decoherence and increased sensing time are balanced. We perform these experiments for oscillating magnetic fields with fixed phase as well as for fields with random phase. Finally, by varying the phase and frequency of the ac magnetic field, we measure the full frequency-filtering characteristics of different multipulse schemes and discuss their use in magnetometry applications.
We present an experimental method to perform dual-channel lock-in magnetometry of time-dependent magnetic fields using a single spin associated with a nitrogen-vacancy color center in diamond. We incorporate multipulse quantum sensing sequences with phase estimation algorithms to achieve linearized field readout and constant, nearly decoherence-limited sensitivity over a wide dynamic range. Furthermore, we demonstrate unambiguous reconstruction of the amplitude and phase of the magnetic field. We show that our technique can be applied to measure random phase jumps in the magnetic field, as well as phase-sensitive readout of the frequency.
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.
We discuss multipulse magnetometry that exploits all three magnetic sublevels of the S=1 nitrogen-vacancy center in diamond to achieve enhanced magnetic field sensitivity. Based on dual frequency microwave pulsing, the scheme is twice as sensitive to ac magnetic fields as conventional two-level magnetometry. We derive the spin evolution operator for dual frequency microwave excitation and show its effectiveness for double-quantum state swaps. Using multipulse sequences of up to 128 pulses under optimized conditions, we show enhancement of the SNR by up to a factor of 2 in detecting NMR statistical signals, with a 4× enhancement theoretically possible.
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.
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.
We show how nitrogen-vacancy centers can be used to determine the amplitude, phase, and frequency of unknown weak monochromatic and multichromatic oscillating magnetic fields using only the periodic dynamical decoupling and Carr-Purcell-Meiboom-Gill sequences. The effect of decoherence on the measurement of the magnetic field parameters is explicitly analyzed, and we take into account the fact that different pulse sequences suppress decoherence to different extents. Since the sensitivity increases with increasing sensing time while it decreases due to decoherence and limited photon detection efficiency, we use the Fisher information matrix in order to optimize the number of pulses that should be used.