Self-Supervised Learning with Noisy Dataset for Rydberg Microwave Sensors Denoising

TL;DR

The paper addresses the challenge of denoising Rydberg-based microwave sensor signals under open-environment noise while preserving temporal resolution. It introduces a self-supervised denoising framework trained on two noisy measurements with identical distributions, enabling single-shot denoising that matches $10{,}000$-set averaging and achieves three orders of magnitude faster processing. Through comparisons with Kalman filtering and wavelet methods, and a systematic analysis of Transformer versus U-Net architectures, it demonstrates robust denoising in both time- and frequency-domain data and provides practical guidance for model selection. This work enables real-time, high-sensitivity Rydberg sensing in noisy conditions by leveraging data-driven priors and a label-free training paradigm.

Abstract

We report a self-supervised deep learning framework for Rydberg sensors that enables single-shot noise suppression matching the accuracy of multi-measurement averaging. The framework eliminates the need for clean reference signals (hardly required in quantum sensing) by training on two sets of noisy signals with identical statistical distributions. When evaluated on Rydberg sensing datasets, the framework outperforms wavelet transform and Kalman filtering, achieving a denoising effect equivalent to 10,000-set averaging while reducing computation time by three orders of magnitude. We further validate performance across diverse noise profiles and quantify the complexity-performance trade-off of U-Net and Transformer architectures, providing actionable guidance for optimizing deep learning-based denoising in Rydberg sensor systems.

Figures (7)

• Figure 1: The process of model testing and training. (a) A trained model is capable of generating a clean signal from an input noisy signal including time (upper panel) and frequency domain (lower panel) data. The data are collected from experiment. (b)Experimental setup. The probe light is split into two beams: one counter-propagates with the coupling light inside a cesium vapor cell, while the other outside the cell acts as a reference beam to enable balanced detection. The data set of time domain and frequency domain is collected by a oscilloscope and spectrum analyzer after the balanced detection. The signal electric field $E_{S}$ and local oscillator electric field $E_{L}$ interact with the atoms via parallel-plate electrodes. RM-reflect mirror, DM-dichroic mirror, PD-balanced photo-detector. (c) Energy level diagram. The probe light (Rabi frequency $\Omega_p$) and coupling light (Rabi frequency $\Omega_c$, frequency detuning from resonant $\Delta_c$) excite atoms from the ground state $6S_{1/2}$ to the Rydberg state $60S_{1/2}$ via the intermediate state $6P_{3/2}$. The signal and local fields with amplitude $E_{S}$ and $E_{L}$ and frequency 63 MHz and 63.05 MHz act on the Rydberg state distribution. (d) During training, the input data and their corresponding labels are independent measurement results of the microwave signal from the same Rydberg atom, differing only in identically independent distributed noise.
• Figure 2: Intermediate frequency (IF) frequency-domain signals under different attenuation levels. IF Signal intensities are labeled in the top-right corner of Subfigures (a)–(d). Gray curves: Single-shot measurements of probe beam transmission signals (attenuating from above noise floor to noise floor level). Green curves: Averaged results of 10,000 measurements (noise-free ground truth, not used in model training), showing noise elimination with only IF signal retained (plus IF sidebands and 49 kHz weak signals under weak attenuation in (c)–(d)). Blue curves: Denoising results of Transformer based model (trained solely on noisy signals), achieving performance comparable to multi-measurement averaging and revealing IF signal, IF sidebands, and 49.1 kHz weak signals. The two red boxes in (c) are zoomed-in views of the averaged and deep learning denoising results at frequencies of 50 kHz and 49.1 kHz, respectively, to illustrate the retained submerged signal.
• Figure 3: MSE depends on the size of the training dataset in frequency domain. This panel presents the MSE between the denoised results of the deep learning model and the results of 10000-set averaging, under different voltages applied to the dipole plates from 4.6 mV to 4.9 mV. As the training dataset size increases, the MSE decreases.
• Figure 4: Different denoising models on time-domain signals for Vpp=200 mV (a) and 100 mV (b). Adopted denoising methods include wavelet denoising (green solid line), Kalman filtering (orange solid line), multi-measurement averaging (black dashed line), and the proposed model’s denoising results (blue solid line), all applied to the single-shot measurement result of the probe beam transmission signal (gray solid line). Parameters of wavelet denoising and Kalman filtering were optimized by minimizing the error between their denoising results and the multi-measurement averaging result, as detailed in the main text.
• Figure 5: Denoising results of different deep learning models under the same self-supervised architecture. (a) Denoising results of Transformer (blue solid line) and convolution based U-Net structure (orange solid line), both applied to the single-shot measurement result of the probe beam transmission signal (gray solid line); the averaged result of 10,000 measurements (black dashed line) serves as the Ground truth reference. (b) Denoising results of Transformer (blue solid line) and convolution based U-Net structure (orange dashed line) applied to the frequency-domain data of the single-shot measurement result (gray solid line). The Transformer result exhibits not only the intermediate frequency (IF) signal but also its sidebands and the weak 49.1 kHz signal, and is closer to the averaged result than the U-Net.