Research on optical fiber current transducer using nv center in diamond

Diamond nitrogen-vacancy (NV) center has been widely employed in experimental magnetic field measurement using continuous wave optical detection magnetic resonance (ODMR), which makes it possible for current sensing. An optical fiber current transducer prototype using an NV center is built for electric power application. The DC measurement with an error of less than 4% within 500 A is realized, in which the error of 50 A to 450 A is better than 2%, and the low-frequency AC measurement is preliminarily realized. In this essay, the accuracy of low current measurement is primarily affected by system noise, while the accuracy of heavy current is mainly affected by the width of the ODMR resonance peak. Optimizing the optical path as well as sensing structure meanwhile updating the demodulation algorithm of the measured data is the following work to improve the measurement accuracy.


Introduction
As the construction of a new power system accelerates, the composition of the power system includes a high proportion of renewable energy and power electronic equipment.The equilibrium of complicated energy supply and demand requires maximum access to the information about each system node.However, the existing measurement methods, precision materials, and core devices cannot be effectively adapted to the complex measurement signals for the new power system.It is necessary to apply new technology to the measurement of power systems [1,2] .
Quantum precision measurement based on diamond nitrogen-vacancy (NV) center is a technology that uses single-spin quantum interference and quantum transition phenomenon to accurately measure physical quantities, which can achieve extremely high detection accuracy and nanoscale spatial resolution in room temperature atmospheric environment [3] .Diamond NV Center has exceptional qualities like nonfluorescent scintillation, non-fluorescent bleaching, stable physical state, etc., making it a burgeoning research field [4] .In the nearly decade of development, nanoscale weak magnetic field detection, temperature detection, electric field detection, and single spin magnetic resonance detection have been achieved based on NV center in the laboratory [5] .At present, the engineering application based on quantum sensing is still in the ascendant, and the current measurement based on NV center provides a promising way to meet the demand for panoramic perception for the new power system.as shown in Figure 1.The NV centers described in this article are all related to the NV -charge state, which is best for sensing within three possible charge states for the NV center: NV -, NV 0 , and NV + [6] .

Theory
Figure 2. Energy level structure of NV center.The ground state 3 A2 and the excited state 3 E of the NV center are both spin-triplet states [7] , as demonstrated in Figure 2. The external magnetic field  will cause the splitting of   = ±1.The splitting energy level difference Δ between   = +1 and   = −1 is linear with the magnetic field, which can be described as Δ = 2  , where   = 2.87 MHz/Gs is a gyromagnetic ratio.Under 532 nm laser pumping, the NV center transitions from the ground state to the excited state.The NV center in   = 0 will directly transition back to the ground state and emit photons, while part of the NV center in   = ±1 return to the ground state through the intersystem crossing (ISC) process and emit 1042 nm infrared light [8] .By analyzing the process of energy level change, the spin state of the NV center can be normalized to   = 0 after a long time of laser irradiation, and Rabi Oscillation between   = 0 and   = ±1 occurs under the microwave at 2.87 GHz.By this time, the transition process and the oscillation process are in dynamic equilibrium, and the intensity of fluorescence emitted by the NV center decreases macroscopically [9] .Hence, by continuous laser irradiation and microwave frequency scanning, the optical detection magnetic resonance (ODMR) spectrum of the NV center can be obtained, which is vital for magnetic field measurement based on the NV center.
To understand how the external magnetic field affects the spin energy levels and causes shifts in the electron spin resonance frequency, it is necessary to inspect the NV center's spin Hamiltonian [10] : Where ℎ = 6.626 × 10 −34 J•s is Planck constant,   ≈ 2.0 is Lande factor,   = 9.274 × 10 −24 J/T is Bohr magneton,   , ,   Are the operators that describe the electron spin resonance, the NV center's main axis is along the z-axis,  is the zero-field splitting, and B is the external magnetic field.The Hamiltonian component parallel to the main axis is denoted as  ∥ = ℎ    2 +         , while the Hamiltonian component perpendicular to the main axis is denoted as  ⊥ =     (    +     ).By adjusting the direction between the external magnetic field and the NV center sample, the electron spin resonance frequency  ± Can be expressed by the following formula when  ∥ >  ⊥ : Figure 3. Relationship between external magnetic field and resonance frequency difference Under an external magnetic field, the energy level of the NV center will split according to the Zeeman effect, as illustrated in Figure 3, and the magnetic field is proportional to the resonance frequency difference, that is: Hence, the NV center can be utilized for current measurement in accordance with the Ampere circuital theorem.

Experimental method
Figure 4. Experimental schematic diagram of the magnetic measurement system based on NV center.The structure of the NV center magnetic measurement system is shown in Figure 4.The microwave is output by the source, then passes through the power amplifier, 1×4 splitter, and circulator, and is finally radiated to the NV center sample by the antenna.The 532 nm laser is emitted by a fiber laser and then passes through the single-mode polarization-maintaining fiber to the 1×4 optical fiber splitter.There are four exactly same light paths with identical structures and devices.Taking one of the light paths as an example, the 532 nm laser enters the multi-mode fiber optic circulator through Port 1 after exiting the splitter and leaves the circulator at Port 2. Transmitted via multi-mode fiber, the 532 nm laser is focused on the NV center sample by the compound lenses assembled in the magnetic probe.Under the magnetic field generated by the external current, the microwave radiated by the antenna, and the 532 nm laser, the NV center will radiate red fluorescence transmitted via multi-mode fiber to Port 2 of the circulator.According to the unidirectional passing characteristic of the circulator, only Port 3 can be used for the beam's exit when it enters Port 2. The red fluorescence containing the magnetic field measurement information is emitted from Port 3 of the circulator, passing through the multi-mode fiber to the avalanche photodetector (APD), whose optical receiving port is cladded with a 532 nm notch filter and 650 nm high-pass filter.The four-channel APD signal is processed by the phase-locked amplifier (LIA) and then output to the data acquisition (DAQ).The LIA, DAQ, and microwave source are controlled by the host computer through the pulse generator's TTL signals.As shown in Figure 5, the compound lenses, antenna, NV center sample, and package construction make up the magnetic probe.The collimator is used to lessen the divergence of the fiber's outgoing light, while the aspherical lens and the molded compound parabolic concentrator are utilized to focus the light beam and collect fluorescence.A reflection cavity is arranged inside the package structure, whose internal surface is cladded with reflecting film to improve the collection efficiency of fluorescence as much as possible.The layout of the probes and conductor on the primary side is illustrated in Figure 6.The ampere loop theorem is utilized for current measurement by placing four magnetic probes around the conductor, which are 25 cm away from the conductor and arranged as a spatially symmetrical structure to reduce external interference.The experimental setup adopted in this paper is shown in Figure 7.

Experimental Results and Analysis
Figure 8 illustrates the ODMR spectra of four probes under an external magnetic field generated by a 400 A current, and each ODMR spectrum has four pairs of resonance peaks, which correspond to four crystal orientations in the NV center.The certain resonance peak farthest from the center frequency is selected to obtain the magnetic field value.However, microwave frequency sweeping is necessary to acquire the ODMR spectrum, which greatly extends the duration of a single measurement and further substantially reduces the available sampling rate and frequency of measured current.9 can be obtained by differentiating the ODMR spectra in Figure 8, in which there are linear regions centered on the resonance frequency.The microwave frequency is fixed at the resonance frequency to shorten the single measuring time, and the first-order differential curve of the ODMR spectrum will shift along the frequency axis as the external magnetic field (current) changes, leading to the linear relationship between the output signal and measured magnetic field (current).As can be observed, each measurement point has some degree of system noise, which will raise the measurement error, particularly for the measurement of low current.To improve the measurement accuracy, the measurement time under a single current point can be appropriately extended, or the optical path structure and demodulation algorithm can be optimized.In the case of heavy current measurement, the measurement error occurs because the frequency offset caused by the external magnetic field exceeds the half-width of the resonance peak, and the output signal is no longer linear with the measured magnetic field.At this time, the position of the probe should be adjusted to reduce the measured magnetic field corresponding to the measured current, or the system structure should be optimized to increase the width of the resonance peak.

Conclusion
Based on the quantum sensing of the NV center, an optical fiber current transducer prototype is built.This work realizes the DC measurement with an error of less than 4% within 500 A, in which the error of 50 A to 450 A is better than 2%, and initially realizes the low-frequency AC measurement at 5 Hz, supporting the application of quantum sensing technology in the power system.To further improve the measurement accuracy and range, the optical path and sensing structure will be optimized afterward, and the iterative control demodulation algorithm will be updated.

Figure 1 .
Figure 1.NV centers with different crystal orientations and corresponding ODMR spectrum.Diamond has a body-centered cubic lattice structure, and the NV center is a point defect in diamond, which consists of an N atom and a vacuum close to the lattice.Due to the tetrahedral structure of diamond, there are four different crystal orientations in the NV center, which are [111], [11 ̅ 1 ̅ ], [1 ̅ 11 ̅ ]and [1 ̅ 1 ̅ 1],as shown in Figure1.The NV centers described in this article are all related to the NV -charge state, which is best for sensing within three possible charge states for the NV center: NV -, NV 0 , and NV +[6] .

Figure 5 .
Figure 5. Magnetic probe's structure.As shown in Figure5, the compound lenses, antenna, NV center sample, and package construction make up the magnetic probe.The collimator is used to lessen the divergence of the fiber's outgoing light, while the aspherical lens and the molded compound parabolic concentrator are utilized to focus the light beam and collect fluorescence.A reflection cavity is arranged inside the package structure, whose internal surface is cladded with reflecting film to improve the collection efficiency of fluorescence as much as possible.

Figure 6 .
Figure 6.Arrangement of magnetic probes in current sensing ring.The layout of the probes and conductor on the primary side is illustrated in Figure6.The ampere loop theorem is utilized for current measurement by placing four magnetic probes around the conductor, which are 25 cm away from the conductor and arranged as a spatially symmetrical structure to reduce external interference.The experimental setup adopted in this paper is shown in Figure7.

Figure 8 .
Figure 8. ODMR spectra of four probes under an external magnetic field generated by a 400 A current.The graph in Figure9can be obtained by differentiating the ODMR spectra in Figure8, in which there are linear regions centered on the resonance frequency.The microwave frequency is fixed at the resonance frequency to shorten the single measuring time, and the first-order differential curve of the ODMR spectrum will shift along the frequency axis as the external magnetic field (current) changes, leading to the linear relationship between the output signal and measured magnetic field (current).

Figure 9 .
Figure 9. Differential curves of ODMR spectra in Figure 7.The processed probe data is compared to the current data measured by the standard shunt in order to determine the performance of the current measurement.Following the shunt with 0.02 accuracy class and 200:1 ratio, the current in the measured conductor flows through a 0.2 Ω precise low-temperature bleach resistor, whose voltage represents the standard current.Using the method described in the last paragraph,

Figure 10 .
Figure 10.DC measurement curve based on the NV center.

Figure 11 .
Figure 11.Error and linearity of DC measurement.Figure10displays the measured current waveform based on the NV center when the standard current ranges from 0 to 500 A and increases by 50 A per 10 s.Taking the average of the measured currents within 10 s, Figure11can be obtained, which exposes the error and linearity of DC measurement.The error of measured current is less than 2% in the range of 100 A to 450 A, but it is 3.47% (48.265A) and 3.93% (480.348A) at 50 A and 500 A respectively.Furthermore, AC measurement at a low frequency based on the NV center is preliminarily realized.Figure12displays the measured curves of 100 A, 200 A, and 500 A at 5 Hz.

Figure 10
Figure 11.Error and linearity of DC measurement.Figure10displays the measured current waveform based on the NV center when the standard current ranges from 0 to 500 A and increases by 50 A per 10 s.Taking the average of the measured currents within 10 s, Figure11can be obtained, which exposes the error and linearity of DC measurement.The error of measured current is less than 2% in the range of 100 A to 450 A, but it is 3.47% (48.265A) and 3.93% (480.348A) at 50 A and 500 A respectively.Furthermore, AC measurement at a low frequency based on the NV center is preliminarily realized.Figure12displays the measured curves of 100 A, 200 A, and 500 A at 5 Hz.

Figure 12 .
Figure 12.Low-frequency AC measurement curve based on the NV center.As can be observed, each measurement point has some degree of system noise, which will raise the measurement error, particularly for the measurement of low current.To improve the measurement