Towards ubiquitous radio access using nanodiamond based quantum receivers

Working principles of a diamond receiver

The principle underlying the diamond receiver, which utilizes the diamond with NV centers as an antenna, relies on the optically detected magnetic resonance (ODMR). When the microwave frequency is in resonance with the ground state energy gap between the |0〉 spin state and the two degenerate |±1〉 spin states (Supplementary Fig. 1a), NV centers experience a drop in fluorescence intensity. This drop is characterized by a Lorentzian peak at approximately 2.87 GHz, as shown in Supplementary Fig. 1b (yellow curve). The region around this peak enables the conversion of RF signals into fluorescence signals (Fig. 2a). While a large ensemble of NV centers with random orientations shows a contrast of only a few percent, the FNDs used in our study generally exhibit a contrast of around 10%. Based on this contrast, the sensitivity of our FNDs is 0.735 µT · Hz ^-1/2 when ODMR is applied for detecting the magnetic component of the incident electromagnetic field. A comprehensive discussion on the sensitivity and contrast can be found in Supplementary Note 4. By exploiting the distinct properties of ODMR, it becomes feasible to detect signals, especially those employing prevalent amplitude and frequency modulations (Fig. 2b–d). The contrast of ODMR spectrum exhibits an inverse linear correlation with the power of the incident microwave signal (Fig. 2e), allowing for the detection of the amplitude modulated signals. Moreover, the fluorescence intensity to the right of the Lorentzian peak interval is roughly proportional to the frequency of the incoming microwave signal (Fig. 2f), enabling the effective use of frequency modulation within this specific range. We tested one dimensional audio signals and observed that residual levels in our system are below 0.4% for both amplitude and frequency modulations (Fig. 2h, i). This indicates that the diamond receiver based on NV centers can effectively detect and demodulate amplitude and frequency modulated signals with high fidelity. Furthermore, we examined the diamond receiver’s capability in terms of joint amplitude and frequency modulation in a digital communication system. The fluorescence intensity is influenced by both the power and frequency of the incident microwave signal, as evidenced by the observation of four distinguishable combinations (Fig. 2g). As shown in Fig. 2j, our analysis of the audio signal showed an insignificant residual, with a maximum absolute value of 0.5%, which indicates that the diamond receiver can effectively handle complex modulation schemes with minimal error. Through these experimental results, the diamond receiver has exhibited exceptional performance in detecting both amplitude and frequency-modulated microwave signals.

a NV center-based RF signal detection: Converting amplitude or frequency modulated microwaves into fluorescence intensities. b Amplitude demodulation illustrates optically detected magnetic resonance (ODMR) near 2.87 GHz with transmission powers P₁ < P₂. c Frequency demodulation places the carrier frequency on the slope, mapping frequency changes onto fluorescence intensities. d Joint demodulation shows four unique combinations of frequencies and power levels. e Amplitude modulation reveals an inverse relationship between fluorescence intensity and microwave power. f Frequency modulation demonstrates a direct correlation between fluorescence intensity and microwave frequency. g Results of 30 experimental repeats. Joint amplitude-and-frequency modulation presents four distinct fluorescence intensity states. h–j Comparison of demodulated fluorescence intensities with expected audio signals, accompanied by respective residuals in histograms, for (h) amplitude, (i) frequency, and (j) joint modulations.

NV centers based multiple access system

The principle of the diamond receiver described above is primarily designed for the point-to-point communication, i.e., a single user scenario, but is not sufficient for serving multiple users simultaneously. In most communication networks, an access point is designed to accommodate multiple users. Hence, for practical implementation in such contexts, a multiple access system needs to be developed to cater to multiple users concurrently. Beyond the use of bulk diamond, an FND containing NV centers can serve as the antenna in the aforementioned receiver, albeit with a slight compromise in signal-to-noise ratio (SNR). When numerous FNDs are randomly distributed on a cover glass, they serve as multiple anisotropic antennas, enabling them to function as a multi-antenna receiver in the multiple access system. This setup facilitates the demultiplexing of signals from different users. This capability stems from three key facts: microwaves from different users encounter distinct wireless channels; spins of FNDs possess varying orientations; and the number of NV centers in FNDs differs. As a result, FNDs exhibit diverse responses to different combinations of incident microwaves, enabling the system to distinguish and process multiple user signals simultaneously.

The operation of a multiple access system with an FND-receiver is outlined as follows. The bit stream of each user is composed of reference bits and data bits, as depicted in Fig. 3a. The reference bits are devised to realize all possible combinations. To enable simultaneous detection of signals from multiple users, the transmission of reference bits takes precedence. These bits generate reference fluorescence images at the FND-receiver’s end. Subsequently, the received fluorescence images from data bits are compared to these reference images for signal demultiplexing. For proof-of-concept, we consider a two-user scenario in our experiments. Each user transmits an image message, with each pixel represented using 8 bits in uint8 format. For digital frequency modulation, we assign bits 0 and 1 to frequencies 2870 MHz and 2900 MHz, respectively. The resultant fluorescence images, induced by the received pairs of reference bits, serve as the basis for bit-pair detection. Due to the diversity of FNDs’ responses, different bit-pairs generate varied reference fluorescence images. This concept is illustrated by the differences between the reference fluorescence images displayed in Fig. 3b. Following the transmission of reference bits, data bits – the bits of the transmitted messages – are sent. To identify the data bit-pair at each sampling point, we compare the received fluorescence images with the reference images, pinpointing the bit-pair that provides the minimum mean squared error (MSE) at each sampling point. This detection process can be mathematically expressed as \(_^=_{||{{{\bf}}}_-{{\bf{R}}}(x,y)||}_{{{\rm{F}}}}^{2},\) where \({(x,y)}_{t}^{\star }\) represents the detected optimal bit-pair at the \(t\)-th sampling point during data transmission, \({{||}\cdot {||}}_{{{\rm{F}}}}\) refers to the Frobenius norm, \({{{\bf{I}}}}_{t}\) denotes the received fluorescence image at the \(t\)-th sampling point, and \({{\bf{R}}}(x,y)\) is the fluorescence image of the corresponding reference bit-pair \((x,y)\). This detection process is conceptually similar to a lookup table, where matching operations are performed to identify the correct bit-pair. By detecting the bit-pair at each sampling point, we can recover the bit for each image message, ultimately reconstructing the two transmitted image messages at the FND-receiver’s end. We tested the transmission of two types of image message: handwritten digit images³⁰ and face images³¹, with the latter requiring a higher communication overhead. Figure 3d illustrates the transmission results for both of them. For frequency-modulated transmission, the BER for handwritten digit images is 0.146%, while for face images, the BER is slightly higher at 0.439%. The associated BEP, taking into account its uncertainty, is estimated at (0.0031 ± 0.0009) at a 95% confidence level. These results highlight the effectiveness and accuracy of the proposed FND-receiver in distinguishing and demodulating the transmitted signals from multiple users in a multiple access system. Moreover, for amplitude-modulated transmission, the system operates at a single frequency of 2870 MHz. For one user, bits 0 and 1 are modulated to power levels of -15 dBm and -7 dBm, while for the other user, they are modulated to power levels of -15 dBm and 0 dBm, respectively. The remaining procedures mirror those of the frequency modulation case. The resultant reference images are depicted in Fig. 3c, and the final recovered images are shown in Fig. 3d, with the BERs being zero for both sets of image message. This indicates that the BEP is less than 0.000069. Furthermore, the digital transmission with joint amplitude and frequency modulation extends the principles and designs for frequency modulation and amplitude modulation discussed above. The results are presented in the Supplementary Fig. 5, showing the capability and adaptability of the FND-receiver in managing complex modulation schemes in a multiple access system.

a Schematic illustration of the fluorescent nanodiamond (FND)-receiver for supporting a multiple access system. Users transmit reference bits followed by data transmission, resulting in reference images, i.e., fluorescence intensity matrix, composed of fluorescence intensity measurements of a region of the plate containing randomly placed FNDs. During data bits transmission, the fluorescence images are compared to the reference images to be demultiplexed using the minimum mean square error (MSE) criterion. b Reference images obtained in the frequency modulation experiment. The baseline corresponds to the fluorescence intensity matrix when both users simultaneously transmit bit “0”. The other three images represent the remaining three-bit combinations, with their differences from the baseline. c Reference images acquired in the amplitude modulation experiment, with the same interpretation as described. d Experiment involving the transmission of (Left) two digit images from MNIST Database³⁰ and (Right) two subsampled face images from Yale Face Database³¹: Image messages transmitted by two users, image messages received during the frequency modulation experiment, and image messages received during the amplitude modulation experiment.

Multi-band receiver and reference-free design

The multiple access system discussed above is not confined to operating near the zero-field splitting (ZFS) frequency but can be extended to other frequency bands, enabling multi-band communication. By applying an external static magnetic field B along the NV axis, the ODMR spectrum comprises two Lorentzian peaks, as shown in Supplementary Fig. 1b (red curve). Each peak corresponds to a ground state spin transition at energy levels D ± γB, where γ = 2.8 MHz/G is the electron spin gyromagnetic ratio of the NV center. Such capability of modifying the frequency range of the peaks by adjusting the magnetic field facilitates the multi-band communication. This means that the system can be tuned to match the receiver’s operating frequency, eliminating the need for distinct antennas as required by traditional radio receivers for different bands. This makes the proposed NV centers based receiver more versatile and efficient, as it can adapt to various frequency bands without the need for antenna changes.

To demonstrate the feasibility of a multi-band receiver, we examine the same communication scenario described in the aforementioned multiple access system. By analyzing the ODMR spectra of FNDs within an 80 μm field of view, we observe that when an external magnetic field is applied, the smallest Lorentzian peak in the ODMR spectra of most FNDs is approximately 2776 MHz. Figure 4a displays the ODMR spectrum of one of the FNDs (marked by a blue circle). In the frequency range from 2700 MHz to 2776 MHz, bits 0 and 1 are respectively mapped to frequencies 2700 MHz and 2776 MHz for digital frequency modulation. The remaining procedures are the same as those in the previously discussed multiple access case. The subsequently recovered image messages are presented in Fig. 4a, with a BER measured as 0.428%. The corresponding BEP, considering its uncertainty, is estimated to be (0.004 ± 0.001) at a 95% confidence level. The current frequency range employed corresponds to the ground state transition |0〉 → |-1〉 of NV centers, while the transition |0〉 → |+1〉 enables an extended operating frequency range exceeding 2870 MHz to meet communication systems’ requirement. Figure 4b demonstrates the capability of operating at higher frequency bands for transmission within the range from 2963 MHz to 3020 MHz, with the recovered image messages presented and a measured BER of 0.123%. The related BEP is specified as (0.0012 ± 0.0006) at a 95% confidence level.

a Lower frequency band (2700 MHz to 2776 MHz) and b higher frequency band (2963 MHz to 3020 MHz). (Left) Optically detected magnetic resonance (ODMR) spectrum of the fluorescent nanodiamond (FND) marked by a blue circle. (Right) The recovered images at the FND-receiver’s end. c Reference-free orthogonal multiple access. (Left) ODMR spectra of the two FNDs labelled by blue and green circles. (Right) The recovered images at the FND-receiver’s end.

Finally, we propose a reference-free design for orthogonal multiple access, addressing the issue of communication overhead caused by the transmission of reference bits. Due to the presence of different axis of randomly distributed FNDs and the existence of magnetic field gradients when an external magnetic field is applied, multiple FNDs can be observed within a certain field of view without their Lorentzian peaks overlapping in the ODMR spectrum. The left curves in Fig. 4c depict the ODMR spectra of two FNDs, labelled by blue and green circles, within an 18 µm field of view. The transitions |0〉 → |+1〉 in one kind of NV centers in two FNDs occur at frequencies of 2946.5 MHz and 2959.5 MHz, respectively. Within this field of view, applying a small static magnetic field leads to magnetic field gradients of around 0.023 G/um, resulting in an ODMR drift of approximately 1 MHz (Supplementary Fig. 7). Consequently, the discrepancy in their Lorentzian peaks primarily arises from the distinct axial orientations of the two FNDs. Orthogonal dual access is achieved by incorporating the two distinct FNDs into the receiver’s cover glass, with both links functioning as parallel connections. The separation between the two FNDs is merely around 10 µm, much smaller than the half-wavelength spacing (around 150 mm) typically required between antenna elements in radio receivers. For digital frequency modulation, bits 0 and 1 of one user map to frequencies 2946.5 MHz and 3000 MHz, respectively, while bits 0 and 1 of the other user map to 2959.5 MHz and 3000 MHz, respectively. The remaining transmission procedures are the same as those in the previously described multiple access scenario. The recovered image messages with a BER of 0.0657% are displayed on the right side of Fig. 4c, validating the feasibility and efficiency of this approach. The estimated BEP, factoring in its uncertainty, is given as (0.0006 ± 0.0004) at a 95% confidence level. Furthermore, although we have demonstrated the transmission for two users in this example, a broader field of view enables the identification of multiple appropriate FNDs. In particular, due to a restricted field of view and limited axial orientations, our FND-receiver in the experiment can accommodate up to 5 users within a 75 µm × 75 µm field of view and magnetic field gradients of approximately 0.023 G/µm, yielding a utilization ratio of 11.1% (5 out of 45) for FNDs. A comprehensive discussion on the number of channels can be found in Supplementary Note 5. The number of channels is determined by the frequency separation of Lorentzian peaks, which is affected by the external magnetic field gradients and field of view. Specifically, an extensive field of view allows for the automatic demultiplexing of signals from a considerable number of users without the need for transmitting reference bits. The scalability of the system to accommodate more users would come with several trade-offs in terms of power, space, and complexity as discussed in Supplementary Note 6.

Implementation of a compact device

To demonstrate the feasibility and practicality of the proposed FND-receiver, we constructed a compact device containing all essential optical components, as illustrated in Fig. 5a, with fabrication details provided in Methods. A photograph of the assembled compact FND-receiver device is displayed in Fig. 5b. The details of the size, weight, and power consumption of our implemented receiver are presented in Methods and Supplementary Note 9. We evaluate the performance of the implemented device by conducting tests following procedures similar to those discussed in the previous section, focusing on the simultaneous detection of two transmitted signals from two distinct users. The experiments involve transmitting two black-and-white images, with the received images presented in Fig. 5c. In the experiment, the BERs are measured as 1.79% and 0.38% for the two received image messages, respectively, and the overall BER is calculated to be 1.08%. The estimated BEP, including its uncertainty, is provided as (0.011 ± 0.005) at a 95% confidence level. Although this value is higher than that obtained in experiments conducted using the laboratory precise facilities, it remains noteworthy given the uncoded transmission adopted in the experiments.

a The schematic shows the components and overall structure of the implemented compact device. It consists of key elements such as a laser, a concave mirror, a dichroic mirror, a CMOS sensor, and an objective lens. b A photograph of the fabricated compact device. c Experiments involving the transmission of two black-and-white images: (Left) the transmitted images; (Right) the received images. d, e The impact of the number of fluorescence spots and laser power on the communication performance measured by the bit error ratio (BER).