Calibration-Free Vector Magnetometry Using Nitrogen-Vacancy Center in Diamond Integrated with Optical Vortex Beam

Suppressing Thermal Noise to Sub-Millikelvin Level in a Single-Spin Quantum System Using Realtime Frequency Tracking

A single nitrogen-vacancy (NV) center in a diamond can be used as a nanoscale sensor for magnetic field, electric field or nuclear spins. Due to its low photon detection efficiency, such sensing processes often take a long time, suffering from an electron spin resonance (ESR) frequency fluctuation induced by the time-varying thermal perturbations noise. Thus, suppressing the thermal noise is the fundamental way to enhance single-sensor performance, which is typically achieved by utilizing a thermal control protocol with a complicated and highly costly apparatus if a millikelvin-level stabilization is required. Here, we analyze the real-time thermal drift and utilize an active way to alternately track the single-spin ESR frequency drift in the experiment. Using this method, we achieve a temperature stabilization effect equivalent to sub-millikelvin (0.8 mK) level with no extra environmental thermal control, and the spin-state readout contrast is significantly improved in long-lasting experiments. This method holds broad applicability for NV-based single-spin experiments and harbors the potential for prospective expansion into diverse nanoscale quantum sensing domains.

Deep polarization of the ensemble nitrogen-vacancy centers in diamonds induced by an Airy beam with a long focal depth

Solid-state spin systems with nitrogen-vacancy (NV) centers in diamonds constitute an increasingly popular platform for quantum sensing. However, most existing platforms designed with ensemble NV centers exhibit a sensitivity that is significantly less than the theoretical maximum. This low sensitivity limits the expansion of the experimental results and application areas. In this study, the sensitivity is improved by increasing the pumping depth of the excitation beam to increase the number of particles involved in spin polarization at a given laser intensity. Compared with the proposed Airy beam with a long focal depth (25.46 λ) and the widely utilized Gauss beam pumping ensemble NV centers, the spin resonance factor fSR can be improved by 10.02%. This sensitivity-optimized approach enhances the functionality of sensors with NV centers.

Four-Order Power Reduction in Nanoscale Electron-Nuclear Double Resonance with a Nitrogen-Vacancy Center in Diamonds

Detecting nuclear spins using single nitrogen-vacancy (NV) centers is of particular importance in nanoscale science and engineering but often suffers from the heating effect of microwave fields for spin manipulation, especially under high magnetic fields. Here, we realize an energy-efficient nanoscale nuclear-spin detection using a phase-modulation electron-nuclear double resonance scheme. The microwave field can be reduced to 1/250 of the previous requirements, and the corresponding power is over four orders lower. Meanwhile, the microwave-induced broadening to the line-width of the spectroscopy is significantly canceled, and we achieve a nuclear-spin spectrum with a resolution down to 2.1 kHz under a magnetic field at 1840 Gs. The spectral resolution can be further improved by upgrading the experimental control precision. This scheme can also be used in sensing microwave fields and can be extended to a wide range of applications in the future.

Optically polarized selective transmission of a fractional vector vortex beam by the polarized atoms with external magnetic fields

We investigate the role of external magnetic fields and linearly polarized pump light, especially when their directions are parallel or vertical, on the propagation of the fractional vector vortex beams (FVVBs) through a polarized atomic system. Herein, the different configurations of external magnetic fields lead to various optically polarized selective transmissions of FVVBs with different fractional topological charge α caused by the polarized atoms, which is theoretically demonstrated by the atomic density matrix visualization analysis and experimentally explored by Cesium atom vapor. Meanwhile, we find that the FVVBs-atom interaction is a vectorial process due to the different optical vector polarized states. In this interaction process, the atomic optically polarized selection property provides potential for the realization of the magnetic compass based on warm atoms. For the FVVBs, due to the rotational asymmetry of the intensity distribution, we can observe some transmitted light spots with unequal energy. Compared with the integer vector vortex beam, it is possible to obtain a more precise magnetic field direction by fitting the different "petal" spots of the FVVBs.

Orientation of the NV centers are determined using the cylindrical vector beam array

The determination of nitrogen-vacancy centers plays an important role in quantum information sensing. Efficiently and rapidly determining the orientation of multiple nitrogen-vacancy center s in a low-concentration diamond is challenging due to its size. Here, we solve this scientific problem by using an azimuthally polarized beam array as the incident beam. In this paper, the optical pen is used to modulate the position of beam array to excite distinctive fluorescence characterizing multiple and different orientations of nitrogen-vacancy centers. The important result is that in a low concentration diamond layer, the orientation of multiple NV centers can be judged except when they are too close within the diffraction limit. Hence, this efficient and rapid method has a good application prospect in quantum information sensing.

Edge-Machine-Learning-Assisted Robust Magnetometer Based on Randomly Oriented NV-Ensembles in Diamond

Quantum magnetometry based on optically detected magnetic resonance (ODMR) of nitrogen vacancy centers in nano- or micro-diamonds is a promising technology for precise magnetic-field sensors. Here, we propose a new, low-cost and stand-alone sensor setup that employs machine learning on an embedded device, so-called edge machine learning. We train an artificial neural network with data acquired from a continuous-wave ODMR setup and subsequently use this pre-trained network on the sensor device to deduce the magnitude of the magnetic field from recorded ODMR spectra. In our proposed sensor setup, a low-cost and low-power ESP32 microcontroller development board is employed to control data recording and perform inference of the network. In a proof-of-concept study, we show that the setup is capable of measuring magnetic fields with high precision and has the potential to enable robust and accessible sensor applications with a wide measuring range.

An integrated and scalable experimental system for nitrogen-vacancy ensemble magnetometry

Nitrogen-vacancy (NV) centers in diamond are extremely promising solid-state spin quantum sensors for magnetic field in recent years. The rapid development of NV-ensemble magnetometry has put forward higher requirements for high-speed data acquisition, real-time signal processing and analyzing, etc. However, the existing commercial instruments are bulky and expensive, which brings extra complexity to the weak magnetic field detection experiment and hinders the practicality and miniaturization of NV-ensemble magnetometry. Here, we report on an integrated and scalable experimental system based on a field-programmable-gate-array (FPGA) chip assisted with high-speed peripherals for NV-ensemble magnetometry, which presents a compact and compatible design containing high-speed data acquisition, oscilloscopes, signal generator, spectrum analyzer, lock-in amplifier, proportional-integral-derivative feedback controller, etc. To verify its applicability and reliability in experiments, various applications, such as optical magnetic resonance detection, optical cavity locking, and lock-in NV magnetometry, are conducted. We further realize the pump-enhanced magnetometry based on NV center ensembles using the optical cavity. Through the flexible FPGA design approach, this self-developed device can also be conveniently extended into atomic magnetometer and other quantum systems.

Realization of high-dynamic-range broadband magnetic-field sensing with ensemble nitrogen-vacancy centers in diamond

We present a new magnetometry method integrating an ensemble of nitrogen-vacancy (NV) centers in a single-crystal diamond with an extended dynamic range for monitoring a fast changing magnetic-field. The NV-center spin resonance frequency is tracked using a closed-loop frequency locked technique with fast frequency hopping to achieve a 10 kHz measurement bandwidth, thus allowing for the detection of fast changing magnetic signals up to 0.723 T/s. This technique exhibits an extended dynamic range subjected to the working bandwidth of the microwave source. This extended dynamic range can reach up to 4.3 mT, which is 86 times broader than the intrinsic dynamic range. The essential components for NV spin control and signal processing, such as signal generation, microwave frequency control, data processing, and readout, are integrated in a board-level system. With this platform, we demonstrate a broadband magnetometry with an optimized sensitivity of 4.2 nT Hz^-1/2. This magnetometry method has the potential to be implemented in a multichannel frequency locked vector magnetometer suitable for a wide range of practical applications, such as magnetocardiography and high-precision current sensors.

Sensitivity-enhanced magnetometry using nitrogen-vacancy ensembles via adaptively complete transitions overlapping

Nitrogen-vacancy (NV) centers in diamond are suitable sensors of high-sensitivity magnetometry, which have attracted much interest in recent years. Here, we demonstrate sensitivity-enhanced ensemble magnetometry via adaptively complete transitions overlapping with a bias magnetic field equally projecting onto all existing NV orientations. Under such conditions, the spin transitions corresponding to different NV orientations are completely overlapped, which will bring about an obviously improved photoluminescence contrast. We, furthermore, introduce particle swarm optimization into the calibration process, to generate this bias magnetic field automatically and adaptively using computer-controlled Helmholtz coils. By applying this technique, we realize an ∼1.5 times enhancement and obtain a magnetic field sensitivity of 855pT/Hz by utilizing a group of completely overlapped transitions, compared to the 1.33nT/Hz obtained utilizing a single transition in continuous-wave magnetometry. Our approach can be conveniently applied in direction-fixed magnetic sensing and to obtain the potentially maximum sensitivity of ensemble-NV magnetometry.

Synchronized time tagger for single-photon detection in one- and two-dimension quantum experiments

We report a synchronized time tagger based on a field-programmable-gate-array chip for one- or two-dimensional quantum experiments that require precise single-photon detections. The time tagger has a 9.2 ps single-shot root-mean-square precision and is equipped with a 1 GB dynamic memory for data storage. Because the relationship between the control parameter and acquired data is guaranteed by using hardware synchronization, the experiment can be performed much faster than conventional schemes that are based on software synchronization. With this technique, an improvement of up to 61.3% in efficiency is observed in a typical nitrogen-vacancy center quantum experiment. We further show advanced optical features of the center using the detected high-resolution photon-arrival information and provide detailed electrical benchmarking of the device. This technique could be easily extended to other quantum control systems.

Atomic Compass: Detecting 3D Magnetic Field Alignment with Vector Vortex Light

We describe and demonstrate how 3D magnetic field alignment can be inferred from single absorption images of an atomic cloud. While optically pumped magnetometers conventionally rely on temporal measurement of the Larmor precession of atomic dipoles, here a cold atomic vapor provides a spatial interface between vector light and external magnetic fields. Using a vector vortex beam, we inscribe structured atomic spin polarization in a cloud of cold rubidium atoms and record images of the resulting absorption patterns. The polar angle of an external magnetic field can then be deduced with spatial Fourier analysis. This effect presents an alternative concept for detecting magnetic vector fields and demonstrates, more generally, how introducing spatial phases between atomic energy levels can translate transient effects to the spatial domain.

Mixed-signal data acquisition system for optically detected magnetic resonance of solid-state spins

We report a mixed-signal data acquisition (DAQ) system for optically detected magnetic resonance (ODMR) of solid-state spins. This system is designed and implemented based on a field-programmable-gate-array chip assisted with high-speed peripherals. The ODMR experiments often require high-speed mixed-signal data acquisition and processing for general and specific tasks. To this end, we realized a mixed-signal DAQ system that can acquire both analog and digital signals with precise hardware synchronization. The system consisting of four analog channels (two inputs and two outputs) and 16 optional digital channels works at up to 125 MHz clock rate. With this system, we performed general-purpose ODMR and advanced lock-in detection experiments of nitrogen-vacancy (NV) centers, and the reported DAQ system shows excellent performance in both single and ensemble spin cases. This work provides a uniform DAQ solution for the NV center quantum control system and could be easily extended to other spin-based systems.

Nanoscale Vector AC Magnetometry with a Single Nitrogen-Vacancy Center in Diamond

Detection of AC magnetic fields at the nanoscale is critical in applications ranging from fundamental physics to materials science. Isolated quantum spin defects, such as the nitrogen-vacancy center in diamond, can achieve the desired spatial resolution with high sensitivity. Still, vector AC magnetometry currently relies on using different orientations of an ensemble of sensors, with degraded spatial resolution, and a protocol based on a single NV is lacking. Here we propose and experimentally demonstrate a protocol that exploits a single NV to reconstruct the vectorial components of an AC magnetic field by tuning a continuous driving to distinct resonance conditions. We map the spatial distribution of an AC field generated by a copper wire on the surface of the diamond. The proposed protocol combines high sensitivity, broad dynamic range, and sensitivity to both coherent and stochastic signals, with broad applications in condensed matter physics, such as probing spin fluctuations.

A flexible nitrogen-vacancy center probe for scanning magnetometry

The key component of the scanning magnetometry based on nitrogen-vacancy centers is the diamond probe. Here, we designed and fabricated a new type of probe with an array of pillars on a (100 µm)² × 50 µm diamond chip. The probe features high yield, convertibility to be a single pillar, and expedient reusability. Our fabrication is dramatically simplified by using ultraviolet laser cutting to shape the chip from a diamond substrate instead of additional lithography and time-consuming reactive ion etching. As an example, we demonstrate the imaging of a single magnetic skyrmion with nanoscale resolution. In the future, this flexible probe will be particularly well-suited for commercial applications.

Design of coaxial coils using hybrid machine learning

A coil system to generate a uniform field is urgently needed in quantum experiments. However, general coil configurations based on the analytical method have not considered practical restrictions, such as the region for coil placement due to holes in the center of the magnetic shield, which could not be directly applied in most of the quantum experiments. In this paper, we develop a coil design method for quantum experiments using hybrid machine learning. The algorithm part consists of a machine learner based on an artificial neural network and a differential evolution (DE) learner. The cooperation of both learners demonstrates its higher efficiency than a single DE learner and robustness in the coil optimization problem compared with analytical proposals. With the help of a DE learner, in numerical simulation, a machine learner can successfully design coaxial coil systems that generate fields whose relative inhomogeneity in a 25 mm-long central region is ∼10^-6 under constraints. In addition, for experiments, a coil system with 0.069% inhomogeneity of the field, designed by a machine learner, is constructed, which is mainly limited by machining the precision of the circuit board. Benefitting from machine learning's high-dimension optimization capabilities, our coil design method is convenient and has potential for various quantum experiments.