Fig. 1: Illustration of the setup.

a Overview of experimental energy diagram. Probe and coupling laser beams excite the atoms at ground state \(|5{S}_{1/2}\rangle \) to the Rydberg state \(|51{D}_{3/2}\rangle \). Multifrequency microwave (MW) electric fields couple the Rydberg states \(|51{D}_{3/2}\rangle \) and \(|50{F}_{5/2}\rangle \). b Schematic of Rydberg atom-based antenna and mixer interacting with multifrequency signals. A 795 nm laser beam is split into two beams, which then propagate in parallel through a heated Rb cell (length: 10 cm, temperature: 44.6 ^∘C, atomic density: 9.0 × 10¹⁰ cm⁻³)⁴⁶. One is the probe beam, which counterpropagates with the coupling laser beam exciting atoms to Rydberg states to reduce Doppler broadening. The other is the reference beam, which does not counterpropagate with the coupling laser beam. The beams are detected using a differencing photodetector (DD) to obtain the probe transmission spectrum (inset). Multifrequency MW fields transmitted by a horn are applied to the atoms, with a radiated direction that is perpendicular to the laser beam propagation direction. The multifrequency MW fields are modulated using a phase signal such that the phase differences between the reference bin and the other bins carry the messages. The probe transmission spectrum is fed into a well-trained neural network to retrieve the variations of the phases with time. c–e Schematics of the neural network. The network consists of c a one-dimensional convolution layer, d a bi-directional long–short-term memory layer and e a dense layer; for further details about these layers, see the “Methods” section.