1.CAS Key Laboratory of Microscale Magnetic Resonance, Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China 2.Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China 3.Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Fund Project:Project supported by the National Key R&D Program of China (Grant Nos. 2018YFA0306600, 2016YFA0502400), the National Natural Science Foundation of China (Grant Nos. 81788101, T2125011, 31971156), the Chinese Academy of Scineces (Grant Nos. GJJSTD20170001, QYZDY-SSW-SLH004, YIPA2015370), the Initiative in Quantum Information Technologies of Anhui Province, China (Grant No. AHY050000), and the USTC Research Funds of the Double First-Class Initiative, China (Grant No. YD2340002004)
Received Date:23 July 2021
Accepted Date:06 September 2021
Available Online:11 September 2021
Published Online:05 November 2021
Abstract:Characterizing the properties of matter at a single-molecule level is highly significant in today’s science, such as biology, chemistry, and materials science. The advent of generalized nanoscale sensors promises to achieve a long-term goal of material science, which is the analysis of single-molecule structures in ambient environments. In recent years, the nitrogen-vacancy (NV) color centers in diamond as solid-state spins have gradually developed as nanoscale sensors with both high spatial resolution and high detection sensitivity. Owing to the nondestructive and non-invasive properties, the NV color centers have excellent performance in single-molecule measurements. So far, the NV centers have achieved high sensitivity in the detection of many physical quantities such as magnetic field, electric field, and temperature, showing their potential applications in versatile quantum sensors. The combination with the cross measurements from multiple perspectives is conducible to deepening the knowledge and understanding the new substances, materials, and phenomena. Starting from the microstructure of NV sensors, several detections under the special magnetic field condition of zero field, including zero-field paramagnetic resonance detection and electric field detection, are introduced in this work. Keywords:nitrogen-vacancy color center/ single spin/ zero-field paramagnetic resonance/ electric field detection
3.纳米尺度零场顺磁共振目前NV量子传感器应用最为广泛的是磁信号测量, 其中一个重要的方向就是自旋信号的探测[38], 即磁共振检测. 磁共振根据有无电子自旋的参与分为顺磁共振和核磁共振. 传统的核磁共振已经是结构生物学的重要方法之一[39], 而顺磁共振相对于核磁共振的特点是能够解析生物大分子的长程结构和快动力学信息[40]. 这些信息能够从电子的精细和超精细相互作用中提取出来, 但谱线的展宽则影响了最终得到超精细相互作用的精度. 对样品本身而言, 决定谱线展宽的因素有两种: 一种是外磁场作用下引起的非均匀展宽, 另外一种则是电子本身自旋态退相干时间限制. 第一个问题的主要原因是分子内部存在各向异性的超精细相互作用. 外磁场大小以及和分子主轴的夹角共同决定了谱峰的位置, 如图2(a)所示. 通常情况, 分子主轴的方向是随机无法确定的. 对于传统顺磁共振, 解决非均匀展宽的策略是尽可能地加高磁场, 利用g因子的各向异性, 将不同方向的分子信号在谱线上拉开, 达到类似准晶的效果, 从而降低非均匀展宽. 但是高场设备往往昂贵而复杂, 具有很高的技术壁垒. 相对而言, 零场是一个解决问题的好方法. 当塞曼劈裂项消失, 分子的能级结构可以在主轴坐标系下完全定义, 不再受主轴方向的影响, 达到类似晶体的效果(图2(b)). 因此零场对于解析分子内部相互作用有着先天优势. 图 2 非零场(a)和零场(b)方法对比. θ是分子主轴和外磁场的夹角. 非零场下, 谱峰位置随角度变化, 但是零场谱位置始终保持不变 Figure2. Comparison of non-zero-field (a) and zero-field (b) methods. θ is the angle between the principle axis of the molecule and the external magnetic field. The position of the spectral peak varies with the angle in the non-zero field, but is always constant in the zero field.
其中$\text {δ}\varOmega_1 $表示驱动场$ \varOmega_1 $的波动程度. 结合(1)式和(9)式, 可以分析微波驱动下的能级结构. 在近似条件$D \gg \varOmega_1;\;\varOmega_1 \gg |\gamma {\boldsymbol{B}}|, \;d_{\perp}E_{\perp},\; \varOmega_2;\; \varOmega_2 \gg \text {δ}\varOmega_1$下, 总的哈密顿量经过两次旋转变换之后(见图8)简化为 图 8 上方是相位调制微波的波形示意图. 下面是NV自旋态在不同表象下的能级结构. 蓝色虚线表示电场作用产生的能量偏移 Figure8. Top is a schematic of the waveform of the phase-modulated microwave. Below is the energy structures of the NV center in the different frames by continuous phase-modulated microwave driving. The blue dashed line indicates the energy shift resulting from the electric field effect
而电场会引起缀饰态$ |\pm1\rangle_{\text{d}} $的能级发生偏移$\delta = $$ \pm\dfrac{1}{2}(d_{//}E_z+3 d_{\perp}E_x)$. 微波功率的波动被调制频率$ \varOmega_2 $压制, 而$ \varOmega_2 $的精度取决于任意波发生器的时钟精度, 可以到赫兹级别. 实验中制备缀饰态$ |0\rangle_{\text{d}} $和$ |-1\rangle_{\text{d}} $的叠加态, 通过测量Ramsey振荡来表征电场引起能级移动. 振荡的相对频率大小反映了电场强度, 而振动幅度的衰减速率则说明了电场噪声的强度. 图9(a)给出了不同磁场和电场下信号的频率偏移, 可以看到随着磁场增大, 信号频率几乎不变, 但是对于电场, 信号是线性依赖的. 图 9 (a)频率偏移量随着亥姆霍兹线圈电流和电极电压的变化[28]; (b)不同电介质覆盖下, NV缀饰态的Ramsey振荡衰减[28]; (c)图(b)中曲线的拟合的衰减速率, 黑色实线表示(12)式的拟合曲线, 橙色虚线示意反比的关系[28] Figure9. (a) Variation of frequency shift with Helmholtz coil current and electrode voltage[28]. (b) Decay of Ramsey oscillations in the NV dressed states with different dielectric coverings[28]. (c) Decay rate of the fitted curve in panel (b). The solid black line indicates the fitted curve of Eq. (12), and the dashed orange line shows the inverse relationship[28]