Fig. 1: Energy level diagram and experimental setup.

a The laser at 580.039 nm is resonant with electronic state ⁵D₀ and ⁷F₀ of ¹⁵¹Eu³⁺:Y₂SiO₅, which split into six hyperfine levels respectively in the ZEFOZ magnetic field. \({\left|3\right\rangle }_{{\rm{g}}}\), \({\left|4\right\rangle }_{{\rm{g}}}\), and \({\left|3\right\rangle }_{{\rm{e}}}\) form the Λ system for the long-lived spin-wave AFC storage. Details about the hyperfine structure and the pumping scheme can be found in the Supplementary Note 2. The AFC is prepared in the \({\left|3\right\rangle }_{{\rm{g}}}\) level. The control pulse resonant with the \({\left|4\right\rangle }_{{\rm{g}}}\) and \({\left|3\right\rangle }_{{\rm{e}}}\) transfers the optical coherence into a spin wave and drives the spin wave back to the optical regime. b Schematic of the experimental setup. The probe and pump beam are emitted with single-mode fibers (SMF) and fiber collimators (FC) before entering the cryostat. The two beams are arranged in a non-collinear configuration. Half-wave plates (λ/2) control the polarization of the beams, and two pairs of lenses are used to obtain proper beam widths at the position of the crystal. A BS (beam splitter) with a reflection-to-transmission ratio of 8:92 is employed to efficiently collect the transmitted signal. The probe beam is reflected by the mirror at the bottom of the cryostat and coupled to a SMF for optical heterodyne detection after passing through the BS. A pair of coils placed at the two sides of the sample is driven by an arbitrary waveform generator (AWG) with the output amplified with a 300-W RF amplifier.