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arXiv:1309.1911 · Physical Review B

Dual-channel lock-in magnetometer with a single spin in diamond

Naufer Nusran, M. V. Gurudev Dutt

Published Dec 23, 2013• 14 citations
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Abstract

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.

DOI
10.1103/physrevb.88.220410

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arXiv:1008.4395•Physical Review Letters•Feb 24, 2011•209 citations
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.
Precision measurements of weak magnetic fields with nanoscale spatial resolution is an outstanding challenge in many fields including medicine, biology, material science and physical science. It has already been demonstrated that a single electronic spin formed by a defect color center in diamond, known as the nitrogen-vacancy (NV) center, can serve as a highly sensitive magnetometer with nanoscale resolution, even under ambient conditions. However, standard quantum sensing methods have significant drawbacks. These include the limited dynamic range due to quantum phase ambiguity, the non-linearity in sensitivity over the detectable field range, the requirement of prior knowledge of a working point for accurate deconvolution, etc. This thesis explores novel quantum control techniques such as the use of phase estimation algorithms (PEA) for magnetic field detection to address these issues. Unlike in the standard approach, PEA readout is linearly dependent on the field being sensed. PEA employed on oscillating (AC) magnetic fields can not only detect unknown field amplitudes but also allows detection of the field phase. The thesis also compares the performance of nonadaptive-PEA (NAPEA) with that of adaptive-PEA (QPEA) and conclude that NAPEA is superior to QPEA due to (a) better sensitivity on average, (b) consistency in sensitivity throughout the full field range, (c) comparatively less demanding measurement fidelity, and (d) for simplicity in its experimental realization. The techniques developed here can potentially have broad applicability to a wide variety of solid-state quantum systems and in the field of quantum control and measurement.
We demonstrate an absolute magnetometer based on quantum beats in the ground state of nitrogen-vacancy centers in diamond. We show that, by eliminating the dependence of spin evolution on the zero-field splitting D, the magnetometer is immune to temperature fluctuation and strain inhomogeneity. We apply this technique to measure low-frequency magnetic field noise by using a single nitrogen-vacancy center located within 500 nm of the surface of an isotopically pure (99.99% 12C) diamond. The photon-shot-noise limited sensitivity achieves 38 nT/sqrt[Hz] for 4.45 s acquisition time, a factor of sqrt[2] better than the implementation which uses only two spin levels. For long acquisition times (>10 s), we realize up to a factor of 15 improvement in magnetic sensitivity, which demonstrates the robustness of our technique against thermal drifts. Applying our technique to nitrogen-vacancy center ensembles, we eliminate dephasing from longitudinal strain inhomogeneity, resulting in a factor of 2.3 improvement in sensitivity.
A key challenge of magnetometry lies in the simultaneous optimization of magnetic field sensitivity and maximum field range. In interferometry-based magnetometry, a quantum two-level system acquires a dynamic phase in response to an applied magnetic field. However, due to the 2π periodicity of the phase, increasing the coherent interrogation time to improve sensitivity reduces field range. Here we introduce a route towards both large magnetic field range and high sensitivity via measurements of the geometric phase acquired by a quantum two-level system. We experimentally demonstrate geometric-phase magnetometry using the electronic spin associated with the nitrogen vacancy (NV) color center in diamond. Our approach enables unwrapping of the 2π phase ambiguity, enhancing field range by 400 times. We also find additional sensitivity improvement in the nonadiabatic regime, and study how geometric-phase decoherence depends on adiabaticity. Our results show that the geometric phase can be a versatile tool for quantum sensing applications.
We propose a protocol to estimate magnetic fields using a single nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales inversely with time, $\ensuremath{\delta}B~1/T$, rather than the square-root of time, $\ensuremath{\delta}B~1/\sqrt{T}$. The method is based on converting the task of magnetometry into phase estimation, performing quantum phase estimation on a single N-V nuclear spin using either adaptive or nonadaptive feedback control, and the recently demonstrated capability to perform single-shot readout within the N-V [P. Neumann et al., Science 329, 542 (2010)]. We present numerical simulations to show that our method provides an estimate whose precision scales close to  ~ 1/T1/T1/T (T T~T  the total estimation time), and moreover will give an unambiguous estimate of the static magnetic field experienced by the N-V. By combining this protocol with recent proposals for scanning magnetometry using an N-V, our protocol will provide a significant decrease in signal acquisition time while providing an unambiguous spatial map of the magnetic field.
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.
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.