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Spectro-temporal processing is essential in reaching ultimate per-photoninformation capacity in optical communication and metrology. In contrast to thespatial domain, complex multimode processing in the time-frequency domain ishowever challenging. Here we propose a protocol for spectrum-to-positionconversion using spatial spin wave modulation technique in gradient echoquantum memory. This way we link the two domains and allow the processing to beperformed purely on the spatial modes using conventional optics. We present thecharacterization of our interface as well as the frequency estimationuncertainty discussion including the comparison with Cram\'er-Rao bound. Theexperimental results are backed up by numerical numerical simulations. Themeasurements were performed on a single-photon level demonstrating low addednoise and proving applicability in a photon-starved regime. Our results holdprospects for ultra-precise spectroscopy and present an opportunity to enhancemany protocols in quantum and classical communication, sensing, and computing.

Spectrum-to-position mapping via programmable spatial dispersion implemented in an optical quantum memory