Quantum-memory-enabled optical spectrum to position converter for optimal spectro-temporal processing

Spectral analysis of optical pulses plays an essential role in classical and quantum optics. The ability to reconstruct the spectral profile of the light pulse or to perform an optimal measurement in the spectro-temporal domain is the basic tool in spectroscopy, classical and quantum communication, or even astronomy. In particular, the decomposition of the input signal into a set of orthogonal modes can be used to achieve ultimate precision in estimating a certain parameter of the light source, or in communication, where it can lead to an increase in the channel capacity, especially in the photon starved regime. One of the approaches to such mode sorting, allowing further processing is to perform the spectrum-to-position mapping. Here, we propose how to achieve such mapping using gradient echo quantum memory protocol (GEM). The memory utilizes a two-photon Raman transition to map signal pulses onto atomic coherence. During the write-in process, the atoms are placed in the magnetic field with a constant gradient allowing for frequency-to-position mapping along the propagation axis, thus different frequencies are absorbed into different parts of the atomic cloud. By utilizing the ac-Stark shift we can impose a spectral phase onto stored optical pulse, making different frequencies be emitted at different angles, thus separating them in the far field of the ensemble and allowing spectrally resolved detection using a simple camera. We numerically simulate the protocol and carefully discuss its experimental implementation and possible limitations.