A Hardware Measurement Platform for Quantum Current Sensors ^†

Abstract

A concept towards current measurement in low and medium voltage power distribution networks is presented. The concentric magnetic field around the current-carrying conductor should be measured using a nitrogen-vacancy quantum magnetic field sensor. A bottleneck in current measurement systems is the readout electronics, which are usually based on optically detected magnetic resonance (ODMR). The idea is to have a hardware that tracks up to four resonances simultaneously for the detection of the three-axis magnetic field components and the temperature. Normally, expensive scientific instruments are used for the measurement setup. In this work, we present an electronic device that is based on a Zynq 7010 FPGA (Red Pitaya) with an add-on board, which has been developed to control the excitation laser, the generation of the microwaves, and interfacing the photodiode, and which provides additional fast digital outputs. The T1 measurement was chosen to demonstrate the ability to read out the spin of the system.

1. Introduction

1.1. Current Measurement

In power grids, the choice of current sensors is critical for optimizing the efficiency, safety, and reliability of electrical energy transmission and distribution [1]. Measurement principles can be tailored to specific network needs, improving various aspects of power system management [2]. Shunt resistors provide accurate and direct measurements, but they require a direct circuit connection and have energy losses. Current transformers, based on Faraday’s law of induction, are essential in high-voltage applications, enabling high AC currents to be safely converted to manageable levels for effective monitoring and control in substations and along transmission lines. Magnetic field sensors, such as Hall effect devices, provide non-contact measurement capabilities that are critical in high-voltage environments and measure the fluctuations in decentralized energy generation of modern smart grids through real-time DC and AC monitoring. Optical sensors utilizing the Faraday effect provide robust electrical isolation and superior immunity to electromagnetic interference, enhancing data integrity in extreme conditions. Each sensor type is strategically selected to meet the unique requirements of a power network’s operational, environmental, and technological context, supporting the seamless integration of renewable energy and advanced grid technologies, and contributing to grid resilience and sustainability.

The category of magnetic field sensors can be expanded to include the nitrogen-vacancy (NV) sensor. A NV sensor is a quantum system that is sensitive to magnetic fields. The charge movement inside the conductor leads to a surrounding magnetic field, which is measured by the NV sensor.

1.2. Nitrogen-Vacancy Centers

NV centers in diamond represent a very sensitive sensor for magnetic fields [3,4,5,6]. Furthermore, temperature [7,8,9,10] and voltage [11,12] can also be measured with this type of sensor. Most research focuses on the physics of the NV center and sensitivity optimization. Applications [13,14] drive developments from the laboratory to industry, enabling rapid market acceptance of NV centers in sensing.

A NV center is a defect within a diamond lattice, characterized by the substitution of a carbon atom with a nitrogen atom and the absence of an adjacent carbon atom. Figure 1a illustrates the diamond lattice structure, highlighting the four orientations of the NV center. These centers facilitate the formation of a localized electronic spin, which can be controlled using resonant microwaves and detected optically.

Figure 1b shows an energy level diagram of the NV center. The electron spin can be manipulated by microwave radiation at frequencies around 2.87 GHz within the ground state ³A₂. When a magnetic field is present at the NV center, the sublevels $m_{\mathrm{s}}=+1$ and $m_{\mathrm{s}}=-1$ are shifted by the Zeeman effect by $2\gamma B_i$, where $\gamma =28\mathrm{GHz}/\mathrm{T}$ is the gyro magnetic ratio and $B_i$ is the projected magnetic field on the NV center symmetry axis. Additionally to the projected parallel magnetic field, there is an orthogonal part of the magnetic field, which results in a non-linear part of the frequency shift that can be neglected in most cases [15].

A pump light with a wavelength of 520 nm excites the state from ³A₂ to ³E. There are two possible decay paths from the ³E state to the ³A₂ state, with a spin-dependent probability. The first decay path is the direct one, which is chosen with a high probability, when the spin state is $m_{\mathrm{s}}=0$. The second decay path uses the intermediate singlet state ¹A₁, which is non-radiant in the visible spectrum. It is chosen with a high probability if the spin state is $m_{\mathrm{s}}=\pm 1$. Unlike the first decay path, the second decay path is not spin-conserving. In the absence of a resonant microwave, the spin can be initialized to the $m_{\mathrm{s}}=0$ state by irradiation with the pump light. Each of the four possible NV center orientations can have a different magnetic projection, which results in four different Zeeman splits. These four splits lead to eight resonance frequencies. When the microwave (MW) frequency is swept around 2.87 GHz, up to eight dips can be seen in an optically detected magnetic resonance (ODMR) spectrum. Figure 1c shows such an ODMR spectrum.

1.3. T1 Measurement

The T1 measurement for NV centers in diamonds refers to the measurement of the longitudinal relaxation time. This is the time it takes for the system to return to its thermal equilibrium state after excitation. This is an important measure of the time that the system can maintain its polarization before it decays due to interactions with its environment. For NV centers, the T1 time is measured by preparing the spin population in an excited state and observing how this population returns to the ground state over time. The NV centers are initialized to a defined spin state by optical excitation. Laser light is used for this purpose, which brings the electrons in the NV centers into a known state. After initialization, the system is allowed to relax for a variable period of time. After the waiting time, the system is read out by a further optical excitation and measurement of the fluorescence. By varying the waiting time and recording the fluorescence signal, the relaxation curve of the system can be plotted. The T1 time is then determined by exponential fitting of these data, which describe the time in which the spin polarization has exponentially dropped by half.

2. Methods

This chapter describes the setup and the methods used. First, the optical setup is explained. Second, the electronics, which replace expensive scientific instruments, are reviewed. Finally, the implementation of the T1 measurement in the FPGA is discussed.

2.1. Optical Setup

The optical setup is shown in Figure 2. We used an excitation laser PLT5 520B (Osram, Premstaetten, Austria) with a power of 70 mW at a driving current of 170 mA, measured at the input of a multimode fiber (MF) FG105UCA (Thorlabs, Newton, NJ, USA). As shown in Figure 2, the laser beam is adjusted by two mirrors and passes a dichroic beam splitter (DBS) DMSP567 (Thorlabs, Newton, NJ, USA) to a collimator lens F950FC-A (Thorlabs, Newton, NJ, USA). The collimated light is then fed into a MF and guided to the NV diamond MDNV150umHi30mg (Adamas, Raleigh, NC, USA), which is glued to the MF with optical adhesive NOA61 (Norland, Jamesburg, NJ, USA). The fluorescence of the diamond is then guided through the MF back to the collimator and reflected by the DBS to a longpass filter FELH0600 (Thorlabs, Newton, NJ, USA), which blocks unwanted excitation light. Finally, a collimation lens LA1951-AB (Thorlabs, Newton, NJ, USA) focuses the filtered fluorescence onto the photodiode (PD) S5971 (Hamamatsu, Shizuoka, Japan). The photocurrent is amplified by $7.5 \mathrm{k}\mathsf{\Omega }$ with a transimpedance amplifier, followed by an amplifier with a gain of 19. The antenna for spin driving from [3] is used.

2.2. Electrical Setup

An electronic system was developed, as shown in Figure 3. It is stacked on top of a Red Pitaya board. Since the Red Pitaya board does not have the necessary interfaces for the laser, the photodiode, and the microwave, this add-on board is necessary. There is also a power supply and fast outputs for optional synchronization with external components on the board. This chapter describes the main interfaces.

Laser Driver

The laser is controlled by an iC-NZN from iC-Haus GmbH (Bodenheim, Germany). This device embeds a current mirror with a ratio of 1:240 and a semiconductor switch for modulating the laser, up to 155 MHz. There are several possible configurations for controlling the laser.

One possible option would be to control the output power of the laser using feedback of the photodiode inside the laser module. The feedback control uses a gated control, where only the on state of the current is used for control. This solution is limited to a frequency of 4 MHz.

Another feedback control option is the averaging mode, where the average power from the photodiode is used for the control. The disadvantage is the dependence on the duty of the modulation.

We chose to use constant current control of the laser, where the laser is supplied with a precise constant current that can be adjusted in the range of 30 mA to 200 mA. Figure 4 shows the main parts of the laser controller. On the right side is the controllable constant current source circuit. The reference current generated here is fed to pins IMON and IC of the ic-NZN. The circuit generates a mirrored current with a ratio of 1:240, which feeds the reference current to the laser diode with 240 times amplification. The differential laser control inputs EP and EN are directly connected to the FPGA.

3. Programmable Logic for T1 Measurement

We use the T1 measurement [16] to demonstrate the ability to read out the spin of the system. The pulse generator for the laser driver is implemented in Red Pitaya’s FPGA. A synchronized data acquisition engine samples the analogue voltage from the photodetector and is also implemented in the FPGA. A transmission control protocol/internet protocol (TCP/IP) connection with an first-in-first-out (FIFO) queue to the computer is used to process the data.

3.1. Laser Pulse Generation

The generation of laser pulses is shown in Figure 5 and is managed by a counter that starts at zero and increases to a specified adjustable value T_PERIOD. This counter is 32 bits wide and is driven by the internal 125 MHz clock. Actions are triggered based on specific comparisons within the counter. When the counter is at a value of 0, it initiates the readout pulse, activating the laser and producing an output trigger for ADC sampling. Once the counter reaches the value of T_STOP_R, the laser is switched off and remains off until the counter reaches T_START_I. The laser is then switched on for the initialization, where the sampling is not required until T_STOP_I.

3.2. Data Acquisition and Measurement

The ADC is triggered by the pulse generator and clocked by the internal 125 MHz clock. We used a sample buffer with a length of 32768 samples, resulting in an acquisition time of $t_{\mathrm{aquisition}}\approx 262 \mathsf{\mu }\mathrm{s}$. The readout time $T_{\mathrm{readout}}$ and initialization time $T_{\mathrm{init}}$ were equal to the acquisition time of $\approx 262 \mathsf{\mu }\mathrm{s}$. The period of the signals was $100 \mathrm{m}\mathrm{s}$. With this setup, we swept the $t_{\mathrm{delay}}$ from $1 \mathsf{\mu }\mathrm{s}$ to $10 \mathrm{m}\mathrm{s}$ and captured the photoluminescence signal from the photodiode with the Red Pitaya. Each captured signal, shown in Figure 6, was post-processed with a normalization and averaging by a factor of 10. For the normalization we used an average of the photoluminescence signal from $200 \mathsf{\mu }\mathrm{s}$ to $240 \mathsf{\mu }\mathrm{s}$.

The normalized photoluminescence signal was averaged from $400 \mathrm{n}\mathrm{s}$ to $800 \mathrm{n}\mathrm{s}$. The averaged signals were plotted against $t_{\mathrm{delay}}$ and a fit function was then applied, which is shown in Figure 7.

$$P{L}_{\mathrm{evaluated}}=A+B{e}^{-{\displaystyle \frac{t_{\mathrm{delay}}}{T_1}}}$$

(1)

This resulted in $T_1=651 \mathsf{\mu }\mathrm{s}$, which is comparable to other results with the same diamonds [3,17].

4. Conclusions and Outlook

This project highlights a significant advancement in the study of diamond properties and electromagnetic interactions using accessible technology. By employing an add-on board for the Red Pitaya, we successfully demonstrated the ability to modulate lasers at high frequencies, to measure the T1 relaxation time in diamonds. Building on previous work [18], which showed that microwaves could be synthetically generated using an IQ modulator to excite multiple resonances, the project aims to enhance this capability by focusing future efforts on the automatic tracking of these multiple resonances. Both technologies will soon enable precise current measurements to be taken using inexpensive sensor systems, allowing time series to be created and analyzed for increased observation detail.