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

Spectrotemporal processing is essential in reaching ultimate per-photon information capacity in optical communication and metrology. In contrast to the spatial domain, multimode processing in the time-frequency domain is, however, challenging. Here, we propose a protocol for spectrum-to-position conversion using the spatial spin wave modulation technique in gradient echo quantum memory. This way we link the two domains and allow the processing to be performed purely on the spatial modes using conventional optics. We present the characterization of our interface as well as the frequency estimation uncertainty discussion, including comparison with the Cramer-Rao bound. The experimental results are backed up by numerical simulations. The measurements were performed on a single-photon level demonstrating low added noise and proving applicability in a photon-starved regime. Our results hold prospects for ultraprecise spectroscopy and present an opportunity to enhance many protocols in quantum and classical communication, sensing, and computing.