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Abstract
To solve the problem of static magnetic field detection accuracy and consistency, we prepared an array of single NV centers for static magnetic field vector and gradient detection using the femtosecond laser direct writing method. The prepared single NV centers are characterized by fewer impurity defects and good stress uniformity, with an average spatial positioning error of only 0.2 µm. This array of single NV centers can achieve high accuracy magnetic field vector and gradient measurement with GBZ≈-0.047 µT/µm in the Z-axis. This result provides a new idea for large-range, high-precision magnetic field vector and gradient measurements.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nitrogen-vacancy (NV) center, a stable defect in diamond consisting of an N impurity atom and vacancy could emit bright fluorescence, which benefits from the characteristic level structure [1]. Because of its micrometer-level spatial resolution in magnetic field detection and non-need for cryogenic and biased magnetic fields, the NV center has become a competitive technical solution for precision magnetic field sensing even in high-pressure environments [2]. In particular, The NV ensembles, due to the advantages of easy preparation [3] and high sensitivity [4], are used widely in scenarios such as sensor probes [5,6], and vector AC/DC magnetic field detection [7].
In contrast, single NV centers have not received sufficient attention in magnetic field sensing, not only because of the weaker shot-noise-limited sensitivity to the ensemble-NV but also because a single NV center can't achieve vector magnetic field detection. However, single NV centers have the following advantages over ensemble-NV: (i) higher readout fidelity [8], (ii) longer dephasing time T2* as an important parameter to optimize sensitivity [9], and (iii) better consistency, particularly the spatial localization accuracy. Therefore, the array constituted by the single NV centers is hopeful for the application of magnetic field vector and gradient detection, which requires high accuracy and consistency.
In recent years, researchers have realized the preparation of single NV centers or NV ensembles by chemical vapor deposition [10], electron beam radiation [11], and ion beam injection [12] methods. However, the spatial positioning accuracy of NV centers prepared by these methods is low, and introduced many impurity defects, resulting in a broadening of the ESR spectral line width and poor magnetic field detection accuracy and consistency. Since the femtosecond laser direct writing method can prepare NV centers at the desired spatial location and combine them with waveguide structures, etc., it has become a hot method for preparing NV centers [13–15]. However, this method requires high accuracy and stability of the optical path, which limits the preparation and application of single NV center arrays.
In this study, an array of single NV centers was successfully prepared under the near-surface of diamond using an NV center integrated processing and test system, and femtosecond laser direct writing method. The average positioning error of the prepared single NV centers is only 0.2 µm, and the zero-field splitting deviation is less than 0.66 MHz, demonstrating good consistency. Finally, the high-precision static magnetic field vector measurement based on the single NV center array was achieved, and the magnetic field gradient with GBZ≈-0.047 µT/µm in the z-axis was measured.
2. System structure and single NV center preparation
2.1 NV center integrated processing and test system
The NV center integrated processing and test system contains four subsystems: processing light path, excitation light path, fluorescence confocal light path, and spin control system, as shown in Fig. 1(a). For processing the NV center, the 1030 nm femtosecond laser is multiplied to 515 nm and then focused on the diamond surface at a depth of 10 µm. The spatial light modulator (SLM) and the 4f lens could shorten the length of the laser focus inside the diamond and obtain extremely high instantaneous energy only at the processing position. 100x magnification, 1.25 numerical aperture oil immersion objective helps to reduce the refractive index difference and improve the fluorescence collection efficiency. A 532 nm CW laser modulated by an acousto-optic modulator (AOM) is designed to excite the NV centers. The excited fluorescence is collected in fiber by the fluorescence confocal system. Photons are equally distributed into two single-photon detectors (APD), and the pulse signals are counted by the TCSPC and microwave (MW) system for photon time-correlation and optical detection magnetic resonance (ODMR) measurements.
Fig. 1. (a) Block diagram of NV center integrated processing and test system. (b) Rendering of the core optical platform selected in the dashed box in Fig. 1 (a). (c) The figure of the core optical platform of NV center integrated processing and test system.
The marble optical platform designed and simulated by SOLIDWORKS software, as shown in Fig. 1(b), could guarantee the 4f lens-to-objective distance error of less than 1 mm. The compact layout makes it possible to achieve the function within 620 mm * 350 mm * 410 mm size while ensuring optical stability and shading effect. The time sequence controller with 6 ns timing accuracy was developed using FPGA as the kernel of the MW system. It controls the high-speed MW switch and AOM to realize NV coherent spin manipulation, and counts the reference and signal light under internal gating. The MW system can amplify the MW signal power up to 30 dBm and apply the MW field to the NV centers through the 20 µm copper wire antenna. The final system figure is shown in Fig. 1 (c).
2.2 Femtosecond laser prepares single NV centers
The bulk diamond sample was prepared using the CVD growth method from Element Six Company. The nitrogen doping concentration of the sample was less than 5 ppb, and the oriented surface was {100}. Before processing the NV centers, we put the diamond into the acid solution (95% concentrated sulfuric acid and 30% hydrogen peroxide in a ratio of 3:1) configured for acid cooking, and water cleaned the diamond repeatedly. Then fix the cleaned diamond on the sample platform, and loaded the hologram used to correct aberrations on the SLM. Set up the combined displacement platform through LabVIEW software to position the laser focus at the correct depth and starting position. Femtosecond lasers with a single pulse energy of 21.0 nJ were used as seed pulses to produce a nonlinear absorption effect with the diamond, creating vacancies at the target location [16]. Repeat 25 times to achieve a set of 5*5 processed arrays with 5 µm pitch. Annealed the diamond at 800° temperature for 12 hours, and the NV centers formed randomly during the thermal diffusion of vacancies.
3. NV center array characterization
3.1 NV center array fluorescence characterization
To verify the effectiveness of femtosecond laser preparation of NV center arrays, the annealed sample was excited by the 532 nm CW laser with a power of 0.7 mW. The results verified the high positioning accuracy and preparation efficiency demonstrated by femtosecond laser direct writing in the preparation of single NV centers, as shown in the fluorescence scan image in Fig. 2(a). A total of 25 NV centers were verified in four 5 × 5 µm dot pitch arrays by measuring g(2)(τ) for all fluorescence centers [17]. Among them, 22 single NV centers, 2 double NV centers and 1 triple NV center (No. 5 in Fig. 2(a)) were checked. The yield of single NV center is 22%, which is close to the Gaussian distribution probability. Since the energy threshold required for the generation of vacancies is extremely close to the energy for diamond graphitization, the remaining fluorescence centers shown in the image are graphitized spots, which are without numbers. In combination with the fluorescence confocal system and high numerical aperture objective, the fluorescence image of the processed array is clear, with a maximum contrast ratio of 125 between the processed and blank positions. In particular, the fluorescence scan for a single NV center, as shown in Fig. 2(b), and the profile exhibits a good fit for the Gaussian distribution of fluorescence intensity [18]. This means that there is no damage outside the processed area, which results are outperforming ion or electron beam injection methods [19]. The resulting graphitized dots, such as Fig. 2(c), are generally non-regularly shaped in the fluorescence scan images, although they are similar to single NV centers in size and fluorescence count rate. No NV centers were found near the graphitization sites of the array. This may be related to the fact that the majority of the energy is used to expand the graphitized structure at the moment of its creation, and no vacancies can be created.
Fig. 2. (a) Femtosecond laser preparation of NV center array fluorescence scan image. (b) Single NV center fluorescence scan image. (c) Graphitized spot fluorescence scan image. (d) g(2)(τ) measurement curves for single NV center and dual NV centers.
The mix of additional impurities and structures in the vicinity of the NV center will further reduce the NV center's dephasing times T2*, which will seriously affect the sensitivity and consistency of the magnetic field detection [20]. To verify that no graphitized spots are generated around the NV center, the layered fluorescence scanning image was performed to obtain the results shown in Fig. 3(a). It can be seen that regular circular fluorescence images are shown at a detection depth of 10.00 µm, and the fluorescence count rate decreases rapidly after the depth changes beyond the center ±0.25 µm, clearly show that no other fluorescence spots in different layers. The preparation of single NV centers without the mix of impurities can provide an effective means for a variety of ideal devices used for magnetic sensing, temperature sensing, pressure sensing, and even single-photon source arrays [21]. While showing the good processing and detection performance of the integrated processing and test system, it also reflects the good spatial resolution of the fluorescence confocal system. As shown in Fig. 3(b) and 3(c), by positioning the NV centers and comparing them with the theoretical processing positions, the 25 NV centers in the array have a spatial positioning accuracy of ±0.3 µm, and average linear distance errors are 0.2 µm.
Fig. 3. (a) Single NV center layered fluorescence scan images at 0.25 µm intervals. (b) Spatial positioning deviation distribution and 95% confidence interval range of the NV centers. (c) Histogram of the deviation of the straight-line distance between the NV centers and the target processing point in 3D space.
The spatial positioning error is generated mainly for the following reasons: (i) the vacancy will move near the processing point during the annealing process, and a distance of about 50-100 nm will cause a spatial positioning error [13]. (ii) the FWHM of the fluorescence curve is about 0.3 µm, and the selection of a smaller detection pinhole can help improve the positioning accuracy of the fluorescence center, but the rapidly decreasing fluorescence count rate will seriously affect the ODMR detection. (iii) Since the processing path and the fluorescence scanning path may exist angular deviation, it is necessary to rotate the whole fluorescence scanning image by a certain angle to obtain the actual coordinates matching the processing coordinates. Therefore, the selection of the rotation reference NV center and the trigonometric operation will also bring a small calculation error.
3.2 NV center spin characterization
In addition to the good spatial positioning accuracy, the stress environment of single NV centers prepared with the femtosecond laser is also better uniform. Too close to the diamond surface, such as NV centers in NDs [22], or interstitial defects around NV centers will generate extra stresses to the NV centers [20]. This stress manifested in the spin ground state, where the zero-field splitting Dgs between the electron spin-spin coupling increases and decrease dephasing time. Under the applied magnetic field, which makes the spin state ms = ±1 produces the Zeeman splitting, and the average value of the Pulsed-ODMR(P-ODMR) resonance peaks of the six single NV centers in the array of Fig. 2(a) are measured separately. With a minimum value of 2871.36 MHz and a maximum value of 2872.02 MHz, the average frequences have a standard deviation σ ≈ 0.244. The reason for the deviation from 2870 MHz is the static magnetic field perpendicular to the NV axial direction. On the other hand, as shown in Fig. 4 (a), the single NV center dephasing time T2* ≈ 2 µs [4,23]. It is not only demonstrates the advantage of the femtosecond laser preparation of single NV centers in the stress environment, but also ensures the high consistency of the parameters of each NV center in the array.
Fig. 4. (a) Femtosecond laser-prepared single NV center Ramsey curve and dephasing time T2*. (b) The P-ODMR curve of the single NV center with a contrast of about 31%. As shown in the inset, the detection pulse sequence was repeated 40 thousand times for each frequency.
The single NV center has a higher readout fidelity and is denoted by F = 1/σR, where σR quantifies the additional noise from incomplete readouts, and σR = 1 corresponds to readout at the spin-projection limit. It is possible to calculate σR
where a and b are the average number of photons obtained in a single readout for a single NV center at the spin state ms = 0 and ms=±1, respectively [8]. The microwave control system was used to sweep the frequency near 2.87 GHz and drive the electron spin state into ms=±1. After 400,000 repeated readouts, the P-ODMR curve shown in Fig. 4(b) was obtained. σR≈40.12 results demonstrate the good readout fidelity of the system and the single NV center without additional means such as diamond surface modification, cavity coupling, and spin-to-charge conversion [24]. Due to the high readout fidelity and long dephasing time, the P-ODMR-based shot-noise-limited sensitivity is about 2∼3 µT/√Hz, which lays the foundation for precision magnetic field gradient measurements [25].4. NV center array static magnetic field measurement
In recent years, NV centers have made great progress in the field of magnetic field sensing. This is due to the good optical stability of NV centers, the spin-triplet state of both ground and excited states, and the Zeeman splitting effect under the magnetic field [26,27]. Compared with Hall devices, NV centers not only have higher detection sensitivity but also better spatial resolution. The magnitude of the applied static magnetic field along the NV axial direction can be calculated by measuring the resonance peak spacing of the ODMR curve [28]. To measure the magnetic field vector, the coordinate system should be established based on the NV axes.
4.1 NV center coordinate system establishment
NV centers exist in four orientation distributions within the diamond lattice, as shown in Fig. 5(a). Taking the NV1 axial direction as the x-axis, a Cartesian coordinate system is established [7]. The projection of the magnetic field B in the x-y plane in any direction in Fig. 5(b), can be calculated separately
Fig. 5. (a) Cartesian coordinate system along the NV1 and (110) crystal planes. (b) Projected components of the magnetic field in different quadrants along the NV2 and y-axis. (c) Projected components of the magnetic field in different quadrants along the NV3 and Bxy axis. (d) Projection of magnetic field B in the direction of Bxy.
Eventually, when magnetic field B lies in quadrants 1 and 3 or 2 and 4 on the (110) crystal plane, depending on the quadrant in which B is projected on the x-y plane, it needs to be calculated by Eqs. (6) and 7, respectively
Based on the known Bx, By, and Bz, when magnetic field B lies in quadrants 1 and 3 on the (110) crystal plane, the magnitude of the magnetic field B can be calculated as
Correspondingly, when magnetic field B is located in quadrants 2 and 4 on the (110) crystal plane
4.2 Static magnetic field vector measurements
The combination of NV centers with different orientations enables the measurement of magnetic field magnitude and direction, as well as the measurement of magnetic field gradient distribution at the specific axis. Taking the NV center array in Fig. 2(a) as an example, the single NV center is first determined by the g(2)(τ) measurement. Secondly, the fluorescence count rates of single NV centers with different excitation polarization states are classified into two types of directions: “in-plane” and “out-of-plane" [13]. Finally, the orientation of each NV center was accurately determined by the Zeeman splitting and the diamond cut crystal plane under different directions and positions of the external static magnetic field. The results were obtained for NV1 orientation for centers No. 3 and No. 7, NV2 orientation for centers No. 1 and No. 6, and NV3 orientation for centers No. 2 and No. 4. As shown in Fig. 6(a), a static magnetic field B generated by an elongated NdFeB magnet is applied to one side of the NV center array, which is characterized by suitable intensity, uniform distribution, and small background noise, and the direction is located in the 2nd quadrant of the x-y plane and the 1st quadrant of the (110) crystal plane. The fine energy-level coupling from the NV center to the surrounding 14N and 13C nuclear spins (natural abundance of 1.1%) is precisely measured to significantly reduce the half-peak width of the resonance peak of the ODMR spectrum, as a way to precisely determine the resonance frequency when the spin state ms = 0 turns to ms=±1.
Fig. 6. (a) Schematic diagram of the NV center arrays in different axes and the applied static magnetic field B. (b) Reduced half-peak width by coupling with 14N and 13C nuclear spins while ensuring high spectral contrast. (c) Magnetic field intensity and gradient variation curves near 40.5 mm by COMSOL simulation.
Three typical P-ODMR spectra of the NV center nuclear spin couplings are shown in Fig. 6(b). Under the premise of appropriately reducing the microwave power to avoid the ODMR spectrum broadening, a microwave time τ of about 500-1000 ns is chosen to allow the NV center electron spin to couple with the 14N nuclear spin and even the more distant 13C nuclear spin. The contrast of the ODMR spectrum can be maintained at about 15% while the FWHM is greatly reduced, which is especially important for high-sensitivity magnetic field detection systems. The exact values of each NV center’s resonance peak were determined by fitting a Gaussian to the finely coupled ODMR spectra of the nuclear spins as shown in Table 1.
Table 1. ODMR resonance frequency of each NV center and magnetic field intensity along each axial direction under the action of static magnetic field B
Since the distance of each NV center does not exceed 15µm, the three axial NV centers are considered at the same position. The static magnetic field strength |B|=1.105 mT at the NV center array can be calculated according to Eq. (8), where Bx = 667.25 µT, By = 331.70 µT, and Bz = 815.72 µT. By COMSOL simulation, it is consistent with the magnetic field strength of the selected NdFeB of BMN-35 material at 40.5 mm. The digital Gauss meter also verifies this measurement.
The individual NV centers exhibit differences in the measurement of each axial magnetic field component due to the slight difference in distance from the magnet (Table 1). Since the NV centers displacement in direction of No. 2 and No. 4 coincide with the direction of the z-axis magnetic field component, the gradient of the magnetic field in the z-axis direction can be calculated approximately GBz ≈ -0.047 µT/µm based on the theoretical distance of 5 µm between them, which is similar to the gradient GB ≈ -0.072 µT/µm in the z-axis direction derived from the simulation. The distribution between NV1 and NV2 centers does not strictly follow the coordinate axis direction, so the axial magnetic field gradient cannot be calculated accurately. In the future, a 3D spatially distributed array of single NV centers may be able to solve this problem well.
In this work, the following methods are used to improve the accuracy of the measurement results. (i). The use of ms=±1 peak frequency difference measurements of the axial magnetic field magnitude avoids the effects of absolute frequency errors of the signal source and the vertical NV axial magnetic fields on the energy level spacing between ms=±1 and ms = 0. (ii). Using nuclear spin coupling to reduce the FWHM of the fitted curve to improve the peak position fitting accuracy. (iii). The curve contrast of about 10%-15% makes the fitting more accurate at the maximum slope during the Gaussian curve fitting and improves the peak position fitting accuracy. However, errors may be generated from the following. (i). In P-ODMR measurements, the frequency step accuracy and the number of P-ODMR probing cycles directly affect the accuracy of the measurement results, although the Gaussian fitting curve enhances the frequency resolution, it is also affected by the error introduced by the raw data. (ii) The baseline for the Gaussian fit must be close to the peak position of the P-ODMR curve, and different choices of baseline may bring about a frequency error of ±0.25 kHz.
5. Conclusion
The integrated NV center processing and test system using femtosecond laser have successfully achieved high-quality single NV center array processing at 10 µm under the diamond surface. The yield of the prepared single NV center reached 22%, and the high-quality and low defects of the NV centers processed by the femtosecond laser were verified by the layered fluorescence scan images. The single NV center array has high positioning accuracy and internal stress uniformity. The readout fidelity of about 40.12 and the decoherence time of 2µs ensure that the shot-noise-limited sensitivity can reach 2∼3 µT/√Hz, laying the foundation for the magnetic field gradient measurement.
By establishing a Cartesian coordinate system for the NV centers, the magnetic field intensity is calculated with the NV center array as a whole. The NV center pairs with spacing between 5, 10, and 15 µm can clearly distinguish the weak magnetic field intensity variation along the NV axis, and the calculated magnetic field gradient along the Z-axis direction is about 0.047 µT/µm, realizing the calculation of magnetic field gradient with extremely small spacing and high accuracy. In the future, by further reducing the NV center spacing and preparing a three-dimensional NV center array, it is expected that large size, high accuracy, and high consistency of static magnetic field vector and gradient measurement can be realized.
Funding
National Natural Science Foundation of China (61825502, 61827826, 62131018); National Key Research and Development Program of China (2021YFF0502700); Strategic Priority Research Program of CAS (XDC07030303); Jilin Scientific and Technological Development Program (20220301001GX); China Postdoctoral Science Foundation (2019M651200) .
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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