Deep learning enhanced Rydberg multifrequency microwave recognition

The study addresses how to accurately recognize and decode multifrequency microwave (MW) electric fields using Rydberg atoms despite strong noise and complex inter-bin interference. Rydberg atoms are highly sensitive to MW fields and have been used for amplitude, phase, and frequency measurements, enabling applications in communications and radar. However, their sensitivity also makes them susceptible to environmental and atomic-collision noise, and theoretical decoding via the Lindblad master equation becomes complex when including noise and higher-order effects. The paper proposes integrating a deep learning model with a Rydberg-atom receiver to exploit atomic sensitivity while mitigating noise, enabling direct decoding of frequency-division multiplexed (FDM) digital signals without solving the master equation and scaling to many frequency bins.

Prior Rydberg-atom MW sensing uses electromagnetically induced absorption, electromagnetically induced transparency (EIT), and Autler–Townes splitting to measure field amplitudes, phases, and frequencies with high sensitivity, SI traceability, and wide bandwidth. Such sensors have enabled analog (e.g., audio) and digital communications (e.g., PSK, QAM) and radar applications. A continuously tunable RF carrier has been demonstrated, paving the way for multichannel communication, but multifrequency decoding is hindered by noise and the need for multiple bandpass filters. Deep learning has proven effective in physics tasks such as subwavelength acoustic imaging, stochastic magnetic field estimation, vortex/OAM beam recognition, demultiplexing, and automatic experiment control. Building on these, the authors apply deep learning to Rydberg-based multifrequency MW signal recognition and decoding.

Experimental platform: A two-photon Rydberg-EIT scheme in 85Rb excites |5S1/2, F=2⟩ → |5P1/2, F=3⟩ (probe, ~795 nm) and |5P1/2, F=3⟩ → |51D3/2⟩ (coupling, ~474 nm). Multifrequency MW fields drive the |51D3/2⟩ ↔ |50F5/2⟩ transition with an energy spacing of 17.62 GHz. Probe (Ωp), coupling (Ωc), and MW (Ωm) fields have detunings Δp, Δc, Δm. A 10 cm heated Rb vapor cell at 44.6 °C (atomic density ~9.0×10^10 cm−3) is used. Probe and coupling counterpropagate to reduce Doppler broadening; a reference probe beam does not counterpropagate. A differencing photodetector measures probe transmission (EIT spectra) modulated by continuous MW excitation. The MW horn irradiates perpendicular to the optical beams. MW signal generation and calibration: A signal generator (Ceyear 1465F-V) synthesizes multifrequency MW signals; a horn transmits to the cell. Each bin’s frequency, amplitude, and phase are independently tunable. An antenna and spectrum analyzer (Ceyear 4024F) calibrate field amplitudes at the cell center. The atoms act as an antenna and mixer, down-converting GHz carriers to beat notes in the kHz range observable in probe transmission. More than 20 MW bins can be applied; amplitudes, phases, and frequencies are individually controlled. FDM-2PSK encoding: Demonstration uses four bins detuned from resonance: carriers at 17.62 GHz − 3 kHz, −1 kHz, +1 kHz, +3 kHz (Δf = 2 kHz). One bin serves as phase reference (φ4 = 0); the other three bins carry bits via 2PSK (φ1,2,3 ∈ {0, π}), yielding 3 bits per symbol. To avoid degeneracy due to atomic nonlinearity (identical spectra for distinct bit strings), the reference bin amplitude is set larger than the others (A4 ≫ A1,2,3), which linearizes the phase mapping. With Δf = 2 kHz and four bins, the data rate is (4−1)×2 kHz = 6 kbps; increasing Δf raises the rate. Deep learning model: Input sequences are probe transmission time series T of length 1000 (t = 0 to 0.999 ms, Δt = 1 μs). Labels are 4-element vectors encoding relative phases (last element is fixed 0 for reference). Data are scaled to [0,1] by min–max normalization; labels are dense binary vectors. Architecture: 1D convolutional layer (feature extraction), batch normalization, ReLU, max-pooling, followed by a bidirectional LSTM layer, batch normalization, and a dense output layer producing four values constrained to [0,1] (sigmoid). Batch size is 64. Cross-validation: fourfold; a held-out test set remains untouched; validation sets monitor over/underfitting. Training uses RMSprop; initial learning rate 0.001 with scheduling (×0.1 if validation loss plateaus for 10 epochs). Gaussian noise (μ=0, σ=0.5) is added to training data to enhance robustness. Hyperparameters (kernel length, hidden size, learning rate) tuned with Optuna. Implemented in Keras 2.3.1 (Python 3.6.11). Hardware: NVIDIA GTX 1650 GPU, Intel Core i7-9750H CPU. Noise handling and evaluation: Two noise types considered: systematic (environmental, atomic collisions) present across the dataset and additional injected white noise with controllable standard deviation σ. Because datasets are i.i.d. and shuffled before splits, systematic noise distributions are similar across train/test. The model’s generalization to mismatched train/test noise levels is assessed by varying σ during training and testing. Master equation baseline: For comparison, the Lindblad master equation for the open atomic system is solved in steady state (dp/dt=0) with a rotating-wave atom-light Hamiltonian. Higher-order terms and noise spectrum are not included. The complex susceptibility χ yields the transmission spectrum. Fitting to noisy spectra is performed using Mathematica’s FindFit with default AccuracyGoal and PrecisionGoal. Prediction time per spectrum is recorded for comparison. High-speed scenario and scalability: Two scaling routes are tested: (1) increasing number of MW bins (up to 20) at Δf=2 kHz; only the first 3 of 19 message bits (one reference among 20 bins) are varied for evaluation. (2) Increasing Δf to 200 kHz with four bins (raising data rate), necessitating higher detector bandwidth and introducing more noise; the model is trained with additional epochs to maintain performance.

• Accurate decoding of multifrequency 2PSK signals: With four MW bins at Δf=2 kHz, the deep learning model achieves 99.38% accuracy on a uniformly distributed test set of 160 spectra after ~70 epochs.
• QR code reconstruction: The transmitted QR-coded message is reconstructed with 99.32% accuracy after 35 training epochs (147 bit strings). Earlier epochs yield lower accuracy (3 epochs: 51.02%; 4 epochs: 76.87%).
• Noise robustness and generalization: The model maintains high accuracy when test noise exceeds training noise (generalizes to stronger white noise). Training with too much noise degrades accuracy when the test noise is lower.
• Speed advantage: Inference time is ~1.6 ms per spectrum, versus ~25 s per spectrum for master equation fitting on the same hardware, enabling real-time decoding.
• Superiority over master equation fitting on noisy data: On noisy test sets, the deep learning method consistently outperforms master equation fitting. For 20 bins (Δf=2 kHz) with 8 categories (first 3 bits varied), the master equation attains 20.63% accuracy (near random 1/8), while the deep model reaches 100% on 123 test spectra at epoch 78. For four bins at Δf=200 kHz, the deep model achieves 98.83% accuracy (171 test spectra, epoch 83) versus 60.00% for master equation fitting.
• Throughput scaling: Data rates scale with bins and spacing: four bins at Δf=2 kHz yield 6 kbps; 20 bins at Δf=2 kHz yield 38 kbps ((20−1)×2 kbps). Increasing Δf to 200 kHz with four bins yields 0.6 Mbps ((4−1)×200 kbps).
• Scalability and high-speed viability: The model scales to recognize information in >20 MW bins and remains accurate under increased detector bandwidth and noise when trained appropriately (more epochs).

The results demonstrate that combining a Rydberg-EIT atomic receiver with a deep learning model enables direct decoding of multifrequency MW signals that are otherwise difficult to resolve due to noise and nonlinear interference. By learning from the probe transmission spectra, the model extracts relative bin phases without solving the Lindblad master equation, thus sidestepping complexities introduced by noise and higher-order interactions. The approach is robust to systematic and additional white noise, providing high accuracy and low latency decoding. It eliminates the need for prior knowledge such as carrier frequency and complex multi-band filter banks required by conventional I-Q or lock-in demodulation for multifrequency carriers. The method scales to many bins, supporting higher bandwidth efficiency and transmission rates, and performs well for high-speed signals where detector bandwidth-induced noise would otherwise degrade performance. These capabilities position deep learning-enhanced Rydberg receivers as promising tools for MW communications, potentially approaching quantum-limited channel capacity, and for radar scenarios requiring simultaneous detection of multiple Doppler-shifted targets. The general framework can extend to other modulation formats (FDM-ASK, FDM-QAM) and carrier standards and across carrier frequencies from Hz to THz by tuning laser frequencies rather than antenna dimensions.

The paper demonstrates a deep learning-enhanced Rydberg atomic receiver that decodes multifrequency FDM-2PSK signals with high accuracy, strong noise robustness, and millisecond-level inference speed. It outperforms master equation fitting on noisy data and scales to more than 20 MW bins and higher symbol rates via increased bin spacing. This approach removes the need for complex filter banks or lock-in demodulation and avoids solving the Lindblad master equation, enabling practical, high-throughput, and scalable MW sensing and communications. Future work should increase training data and epochs for further accuracy and robustness, stabilize lasers and temperature to approach the shot-noise limit, integrate advanced architectures (e.g., self-attention) if resources permit, and generalize to additional modulation schemes and real-world communication standards. The technique may also support multi-target radar via multifrequency Doppler signatures and contribute to studies of channel capacity limits in atom-based receivers.

• Proof-of-principle stage: The system has not reached the photon shot-noise limit; further optimization (laser stabilization, linewidth narrowing, temperature stabilization) is needed.
• Noise assumptions: Performance analysis primarily considers i.i.d. noise; non-i.i.d. or test-only noise events may require online learning and inclusion of auxiliary features (e.g., temperature, environment) for robustness.
• Amplitude constraint: Reliable phase decoding requires a strong reference bin (A4 ≫ A1,2,3) to mitigate nonlinear spectral degeneracy, imposing constraints on signal design.
• Re-training needs: Significant changes in operating conditions (e.g., detector bandwidth, noise profile, number of bins, Δf) may necessitate retraining or fine-tuning to maintain high accuracy.
• Master equation comparison: The baseline excludes higher-order terms and noise spectrum; while highlighting the ML advantage under noise, it does not represent the best possible physics-based model with full noise modeling.