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Abstract
In this paper, we propose a method for simultaneously recovering multiple radio wave signals based on nitrogen-vacancy (NV) centers in diamond combining optically detected magnetic resonance (ODMR) spectrum. A controlled magnetic field gradient applied to the laser excitation area on the surface of diamond widens the detectable ODMR bandwidth to 200 MHz. Three different frequency-modulated (FM) signals with distinct carrier frequencies falling within the resonance frequency range are received and demodulated in real-time. Subsequently, the FM signal reception capability of this system is further investigated by measuring baseband signal frequencies ranging from 0.1 Hz to 200 Hz and adjusting the carrier power within a dynamic range from -10 dBm to 30 dBm. This proposal, which accomplishes multi-channel demodulation using a compact and single device, has potential applications in fields such as wireless communication, radar and navigation.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nitrogen-vacancy (NV) centers have become a subject of both fundamental research and practical application in fields like quantum computing, biological [1,2], and particularly in quantum sensing. Their high sensitivity and precision to minute environmental changes make them valuable tools for measuring various physical quantities. In magnetic field detection, NV center-based sensors can achieve sub-$\textrm{pT/}\sqrt {\textrm{Hz}} $ sensitivity in geomagnetic environments, and enable nanoscale spatial resolution in magnetic field imaging [3–5]. In the field of electric field sensing, electric field sensors based on NV centers perform well in the detection of both direct current (DC) and alternating current (AC) electric fields [6,7]. Furthermore, as radio signal sensors, their remarkable sensitivity to microwave frequencies allows them to cover a spectrum bandwidth over gigahertz (GHz) range with a high frequency resolution [8–10].
Further research into NV center-based sensors highlights their potential as valuable candidates for addressing challenges in the traditional communication field [11]. The conventional method of transmitting signals in wireless communication involves modulating the baseband signal, which carries information, onto the carrier wave. This modulation is accomplished by modifying certain properties of the carrier, such as its frequency, amplitude, or phase, to encode the data onto the carrier. At the receiving end, a demodulator is employed to retrieve the original information.
Recent studies have demonstrated that, during the process of enhancing the sensitivity of magnetometers, the optical properties of NV center spin transitions can be utilized for demodulating frequency-modulated (FM) signals. This demodulation process converts frequency deviations centered around the carrier frequency into fluctuations in fluorescence intensity [12,13], which can then be recorded to recover the target signal. Shao et al. achieved the reception of audio signals using NV centers in combination with optically detected magnetic resonance (ODMR) spectrum, and confirmed the operational capability of this device in high-temperature environments [14]. In the same year, they also achieved real-time FM microwave signal detection using a similar principle, facilitated by wide-field optical microscopy [15]. Zheng et al. utilized this principle to record remote heart sounds, reducing interference from the crowded 2.4 GHz frequency band, typically associated with Bluetooth and Wi-Fi in complex environments [16]. However, previous research has primarily focused on single-signal processing or employed sensor arrays for handling multiple signals. Given the practical considerations of signal acquisition efficiency and equipment cost, there is a growing demand for wideband and multi-carrier signal receivers.
In this article, we presented a method for the simultaneously reception and recovery of multiple radio wave signals based on NV centers in diamond. A controllable magnetic gradient is applied on the surface of the diamond to expand the ODMR bandwidth to 200 MHz. Multi-carrier capability is achieved within this bandwidth. We successfully demodulate three different FM signals with distinct carrier frequencies, simultaneously. The experimental results confirmed the ability of this system, with a detectable range for baseband signals spanning from 0.1 Hz to 200 Hz and a carrier dynamic range from -10 dBm to 30 dBm.
2. Principles and experimental setup
The NV center is an atomic defect in diamond constituted of a substitutional nitrogen atom adjacent to a lattice vacancy, which the structure is illustrated in Fig. 1(a). The negatively charged NV center (NV-, simply denoted as NV) consists of two unpaired electrons and possesses an electron spin of 1 [17]. Because of the tetrahedral arrangement in the diamond lattice, the crystal contains four potential orientations for the N-V axis [18].
Fig. 1. (a) Schematic diagram illustrating the NV center structure, with the black sphere representing the C atom, the white sphere denoting the vacancy, and the light blue sphere corresponding to the N atoms. (b) Diagram of NV center energy level.
As shown in Fig. 1(b), the energy levels of the NV center consist of an excited state and a ground state, both of which are spin triplet states. The zero-field splitting (D) between the ground state (${m_s} = 0$) and the two degenerate states (${m_s} ={\pm} 1$) is 2.87 GHz. At room temperature and zero magnetic field, the ${m_s} ={\pm} 1$ sublevels remain degenerate. Optical pumping (at 532 nm) drives the primary deexcitation process, characterized by spin-conserving radiative transitions. This results in a photoluminescence (PL) emission spectrum with a zero-phonon line at 637 nm and a broad electron-phonon band [19]. In addition, a nonradiative intersystem crossing (ISC) links the ${m_s} ={\pm} 1$ excited state sublevels to the ${m_s} = 0$ ground state sublevel through a metastable state, resulting in darker PL for the ${m_s} ={\pm} 1$ sublevels [20]. Upon the application of an external magnetic field, the ${m_s} ={\pm} 1$ state is lifted, for clarity and simplicity, we are exclusively focusing on the interaction between the ${m_s} = 0$ and ${m_s} ={+} 1$ sublevels, the phenomenon known as Zeeman splitting:
where $\gamma $ is the NV center gyromagnetic ratio which is equal to 28 MHz/mT [21], ${B_{NV}}$ is the magnetic field component parallel to the N-V axis, ${V_0}$ is the resonance frequency. These magnetic resonances can be detected by applying a microwave field that induces transitions between the states ${m_s} = 0$ and the states ${m_s} ={+} 1$ [22]. As the microwave frequency scanning over the resonance frequency point, fluorescence intensity exhibits a distinct drop, which called ODMR.In our experimental scheme, A magnetic field gradient is applied on the surface of the diamond, generating ODMR at different resonance frequencies along the magnetic field direction with NV centers. This broadens the detectable bandwidth of resonance frequencies. The ODMR signals are collected using wide-field imaging, as illustrated in Fig. 2(a). Each image corresponds to a different frequency point, detecting variations in grayscale values of pixel points at the same coordinates in the images [23]. In order to enhance the ODMR signal signal-to-noise ratio (SNR) while preserving the resonance information of pixel points along the magnetic gradient direction, vertical pixel binning is applied to all images to obtain row-wise data, as shown in Fig. 2(b). The magnetic field acts on corresponding pixel positions of diamond, with intensity represented by color depth. Each pixel corresponds to information at different frequency points according to Eq. (1). Simply stacking these image data yields the spectrum image within this bandwidth as shown in Fig. 2(c), and Fig. 2(d) illustrates the input of different signals that are modulated onto carriers at various frequencies and transmitted to the diamond. The principle of demodulating multiple FM signals by NV centers is depicted in Fig. 2(e). Typically, an FM signal can be expressed as follows:
where ${A_c}$ is the amplitude of the carrier, ${f_c}$ is the carrier frequency, ${k_{FM}}$ is the frequency-to-amplitude gain, $x(t )$ represent the modulating signal and it can be simply written as: ${A_m}$ and ${f_m}$ respectively represent the amplitude and frequency of the modulated signal. Where the time-dependent frequency of the FM signal can be written as: where ${f_{dev}}$ =${k_{FM}}{A_m}$, is the frequency deviation of the FM signal [24].Fig. 2. (a) A schematic illustrating the working principle of frame-based widefield sensing, where each image corresponds to a specific sweep point, involving the detection of variations in grayscale values of pixels at identical coordinates across these images. Pixel binning is performed on each image by columns. (b) The colors varying from dark (blue) to light (yellow) across different pixels in a single line reflect the changes in magnetic field gradient intensity. (c) Under the magnetic gradient, the ODMR spectrum images are obtained through pixel stitching, where dark lines indicate a decrease in grayscale values at corresponding pixels. (d) Diagram of radio signals input, three different signals modulated onto three distinct carriers and transmitted onto the diamond. (e) Each pixel point extracts the ODMR signal with various colors corresponding to distant resonance frequencies. The instantaneous frequency of the input modulated signal is offset around the carrier frequency, and this frequency offset is dynamically converted into fluctuations in fluorescence intensity. (f) Original signals, which are recovered from modulated signals, remain consistent with signals at the input end.
When the carrier frequency of the FM signal is positioned at one of the two slopes of the ODMR, frequency variations of the signal are converted into changes in the amplitude of the fluorescence. Therefore, identifying the frequency bands where three independent ODMR signals are located and selecting appropriate carrier frequencies within those bands enables the demodulation of multiple FM signals. Figure 2(f) illustrates output signals of the system, and the collected output signals exhibit excellent consistency with the original signals.
In comparison with the more widely used pulsed laser excitation method, we have chosen to employ continuous-wave laser excitation for detecting FM signals [25]. The advantage of this approach is its simplicity in experimental setup, ease of practical application, and continuous detection capability for FM signals. The combination of wide-field imaging mode with ensemble NV centers allows for the mapping of spectral information of the spatial field onto each individual pixel. This forms the foundation for achieving multi-channel sensing of FM signals using NV centers in diamond.
The experimental setup is illustrated in Fig. 3, the core of the system consists of a commercially 3 × 3 × 0.5 mm3 {100} chemical vapor deposition diamond with a doping concentration of NV centers at 100 parts per million. The diamond is pumped by a 532 nm laser from the side, leaving a narrow line as the beam enters the diamond. The PL is collected through an optical microscope objective (Olympus PLN 10 × 0.25 NA), a filter (FLH633-1 Bandpass Filter), and focused onto a commercial complementary metal oxide semiconductor (CMOS) camera (MARS-1231-46G5MC-P) by a 60 mm lens. To minimize data processing costs, the camera only collects PL emitted from the central region of a 2 mm-diameter loop antenna made from 50 µm copper wires (buried beneath a resin-made antenna board), where the microwave field is relatively uniform. Due to limitations imposed by the coil diameter and the beam waist, the final size of region of interest (ROI) is 1090 × 104 $\mathrm{\mu }{\textrm{m}^\textrm{2}}$. We capture images with 1008 × 64 pixels. The spatial resolution of our system is 1.62 $\mathrm{\mu}\textrm{m}$. The computer manages the coordinated control of the microwave generators and the camera, as well as real-time processing of the image data acquired by the camera. All operations on the computer side are performed using Python. We employed three identical microwave generators (Keysight N5181B) as radio signal transmitter and controlled the output of microwave signals through computer. Signals output by the microwave generators converge at the mixer and are transmitted to the surface of the diamond through the antenna coil. A 12.7 mm diameter spherical magnet (Supermagnete K-13-C) is used to provide a sufficiently strong and extensive magnetic field gradient, which is fixed on a three-axis displacement stage (DHC GCM-VC13 M) for precise control of magnetic field direction and distance between the magnet and the diamond. Due to the special crystalline structure of diamond, the angles between each axis are consistent. Therefore, when the magnetic field direction is aligned with an N-V axis, the magnetic field components projected onto the remaining three axes are identical that results in the same Zeeman splitting according to Eq. (1). The magnet placement angle is adjusted until the ODMR spectra from all three non-aligned axes overlap during the experimental process.
Fig. 3. Diagram of the overall experimental setup, where the diamond is continuously pumped by 532 nm laser (green) and the PL (red) from the ROI of camera is collected by the optical microscope and monitored by a CMOS camera. The magnetic field intensity and gradient is sourced from a spherical magnet with the magnetic field direction aligning N-V axes. Three microwave generators (MW1, MW2, MW3) are individually controlled by computer to apply single or multiple distinct microwave signals onto the diamond.
3. Results and discussion
We select a range of magnetic field gradient corresponding to a range of microwave frequencies to characterize their strength and distribution within the ROI on the diamond surface. The applied magnetic field gradient intensity is approximately 205∼265 Gauss (Gs), corresponding to a microwave frequency range of 3.443∼3.612 GHz. Commands are issued from the computer to both MW1 and the camera, enabling coordinated control of MW1 output and camera capture. The exposure time of camera is set to 80 ms, while ensuring minimal overexposure for this experiment. The image data collected by the camera is stored in a three-dimensional matrix {x, y, v}, where the first two dimensions represent the number of pixels in the rows and columns of a single image and the third dimension represents different frequency points corresponding to each image. Each pixel on the image is then fitted by a Lorentzian function with respect to the v dimension information. The fitting function is written as:
where adjusting A (usually set to 1), contrast C, linewidth 2*$w$ to achieve fitting [26]. The fitting error conforms to a 95% confidence interval. Recording the resonant frequency ${v_0}$ corresponding to each pixel and convert it to magnetic field strength using Eq. (1). The fitting results are depicted in Fig. 4(a). The magnetic field exhibits a linear relationship within the ROI. The image pixels at different coordinates reflect varying magnetic field strengths. Different pixels also indicate varying distances on the diamond surface. As the distance from the magnet increases, the magnetic field strength gradually decreases. We performed simulations on the spherical magnet and compared the results with our experimental data, as shown in Fig. 4(b). The simulated and measured data are in good agreement. Subsequently, the data from each image (1008 × 64 pixels) was binned into a single row (1008 × 1 pixels) to enhance the SNR and improve fitting accuracy, thereby increasing the precision of radio signals receive. Data storage transitions from a three-dimensional matrix to a two-dimensional matrix. Within the range of this magnetic gradient, the corresponding frequency spectral image can be generated by simple concatenation of images, as depicted in Fig. 4(c). It can be observed that along the row of pixels, there is a change in the resonant pixels corresponding to the variation in the magnetic field intensity.Fig. 4. (a) Characterization of magnetic field gradient. The x and y axes represent the rows and columns of the image, respectively, while the z axis distinguishes different magnetic field strengths using varying colors. The transition from dark blue to light yellow indicates a gradual decrease in magnetic field strength. (b) The comparison between the simulated and experimental results of the magnetic field gradient intensity distribution at distances ranging from 3.13∼4.22 mm from the spherical magnet. (c) Frequency spectrum within the gradient magnetic field range, with frequencies ranging from 3.443∼3.612 GHz.
Then, the capability of synchronized multi-channel FM signal sense using NV centers within this frequency range is demonstrated. To provide a more intuitive representation of the capability, we present the collected data in the form of images. For the best demodulation performance, ODMR signals are differentiated to identify the points of maximum slope, which are determined as the carrier frequency points of the FM signals. We established three carrier frequency points: 3.439 GHz, 3.527 GHz, and 3.616 GHz, which are assigned as carrier frequencies for MW1, MW2, and MW3 and serve as the three channels for FM signal receive, the signal strength was set to 30 dBm, and the frequency deviation is set to the maximum value of 8 MHz for the best original signal waveform.
To enhance the clarity of distinguishing differences between FM signals across different channels in the image, a uniform data collection time of 3 s is employed. Initially, we configured MW1, MW2, and MW3 to remain inactive, allowing us to acquire fluorescent images as reference data for comparison as depicted in Fig. 5(a). Later, we captured data while only MW2 produced a 4 Hz square wave signal and then synchronized MW1, MW2, and MW3 to simultaneously emit 4 Hz square wave signals, the experimental results are shown in Fig. 5(b) and Fig. 5(c). Next, as shown in Fig. 5(d), MW1, MW2, and MW3 are configured to generate square wave signals at frequencies of 2 Hz, 4 Hz, and 8 Hz, respectively. Furthermore, in Fig. 5(e), we recorded the waveform transition of MW1 and MW3 to triangular waves at 1.55 s. Finally, similar to the previous case, using the 1.55 s mark as the transition point, all three channels simultaneously undergo changes in frequency and signal waveform, which are then captured in the data, as depicted in Fig. 5(f). By analyzing the experimental results above, there are gaps between the channels, and the shape and frequency differences of each waveform within each channel can be clearly observed.
Fig. 5. Detection of multi-channel FM signals using NV centers, simultaneously. (a) Image with no signal. (b) Single-channel 4 Hz square wave signal. (c) Three-channel 4 Hz square wave signals. (d) From left to right: 2 Hz, 4 Hz, and 8 Hz square wave signals. (e) Channel 1 from top to bottom: 2 Hz triangular wave, 2 Hz square wave signal. Channel 2: 4 Hz square wave signal. Channel 3 from top to bottom: 8 Hz square wave, 8 Hz triangular wave. (f) Channel 1 from top to bottom: 2 Hz triangular wave, 4 Hz square wave signal. Channel 2 from top to bottom: 4 Hz square wave, 6 Hz square wave signal. Channel 3 from top to bottom: 6 Hz square wave, 8 Hz triangular wave signal.
In order to explore the frequency range of baseband signals that the system can recognition, we proceeded to measure FM square wave signals at various frequencies at the carrier frequency point of 3.439 GHz. Because of the inherent constraints in the internal modulation signal generation of the microwave generator, with the lowest frequency being 0.1 Hz, and the concern of excessively long data acquisition times at very low frequencies, the minimum achievable data acquisition FM signal of the system is 0.1 Hz, as depicted in Fig. 6 (a). In order to ensure the integrity of the signal waveform, the data acquisition frame for the 0.1 Hz FM signal was set to 2 ms per frame, resulting in an extended data acquisition time. We also measured square wave signals at 1 Hz, 10 Hz, 50 Hz, and 100 Hz are shown in Fig. 6(b)∼(e). With the camera frame rate remaining almost constant, it can be observed that as the signal frequency increases, the waveform of the output signal gradually exhibits slight distortion. The maximum data acquisition frame rate of the system is limited by the frame rate of the camera. Due to the optical demodulation method of radio signals based on the optical readability of the electron spin property of NV center in diamond, which directly converts FM microwave signals into AM fluorescence signals, the maximum detectable baseband signal frequency is determined by the frame rate of the optical signal collection. The camera in this system operates at a frame rate of around 400 frames per second. Consequently, the maximum detectable frequency of FM signals is limited to approximately 200 Hz, as depicted in Fig. 6(f).
Fig. 6. FM signals were detected with different frequencies: (a) 0.1 Hz, (b) 1 Hz, (c) 10 Hz, (d) 50 Hz, (e) 100 Hz and (f) 200 Hz square wave signals.
Next, we will discuss into the dynamic range of carrier signals during the process of receive and demodulation. Under the same experimental conditions, a 4 Hz square wave signal was generated by MW 1. The power is gradually adjusted from -20 dBm to 30 dBm, and the power of the carrier signal directly affects the contrast of the ODMR signal,as shown in Fig. 7(a), leading to a reduction in slope and consequently indirectly impacting the sensitivity of frequency variation to fluorescence intensity change. The process of the signal transitioning from strong to weak and eventually disappearing is observed in Fig. 7(b). When the carrier power is set to -20 dBm, the shape of the output signal disappears completely. At a carrier frequency of -10 dBm, the amplitude of the baseband signal still exhibits a square wave form. As the microwave source equipment has a maximum power limit of 30 dBm, the carrier dynamic range of the system is 40 dBm.
Fig. 7. (a) Impact on ODMR spectra (resonance frequency at 3.439 GHz) of NV centers in diamond under different carrier powers. (b) The shape variations in the 4 Hz square wave signals correspond to different carrier power levels.
4. Conclusion
In conclusion, we demonstrate a novel approach for the reception and demodulation of multiple FM signals based on the capability of NV centers in diamond to convert frequency variations of FM signals into amplitude-changes of fluorescence intensity. By applying a controllable magnetic field gradient on surface of diamond to turn the carrier range and expand the selectable carrier channel bandwidth combined with wide-field image mode. We demonstrate the ability for three-channel synchronized demodulation of FM signals within the detectable frequency range of 0.1 Hz to 200 Hz. The carrier range is from 3.443 GHz to 3.662 GHz with a dynamic range of 40 dBm (-10 to 30 dBm). The bandwidth can potentially be expanded to over a GHz with increased magnetic gradient strength, allowing for more carrier channels. The system could benefit from enhancements by utilizing widefield imaging equipment with a higher frame rate, aiming to further augment the maximum detectable frequency of baseband signals. In response to the increasing demand for frequency band utilization in wireless communication, the real-time FM transmission mode based on quantum sensing with multiple high-frequency carriers may serve well in various professional fields, which is particularly applicable in fields necessitating high reliability and stability, like military communication, aviation radar, and maritime navigation.
Funding
National Key Research and Development Program of China (2022YFC2204104); International Cooperation and Exchange Programme (62220106012); Outstanding Youth Fund of Shanxi Province (202103021221007); International Science and Technology Cooperation Program of Shanxi Province (202204041101015); Key Lab of Quantum Sensing and Precision Measurement, Shanxi. (201905D121001).
Disclosures
The authors declare no conflicts of interest.
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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