Temporal imaging and sub-Fourier spectroscopy for ultra narrowband single-photon systems

Manipulation and detection of photonic spectro-temporal modes via light-matter interfaces play a crucial role in quantum information processing and metrology. Feasible implementations of protocols merging the flexibility of atomic systems and spectro-temporal processing capabilities inherently require an ability to manipulate and detect temporal photonic modes with a spectral and temporal resolution matched to the narrowband atomic emission. Here we employ cold-atoms-based Gradient Echo Memory combined with novel ac-Stark spin-wave manipulation technique to demonstrate far-field temporal imaging achieving <20kHz spectral resolution and 1MHz bandwidth. Moreover, inspired by the real-space sub-Rayleigh imaging techniques we adjust our setup to implement a time inversion interferometer and demonstrate a sub-Fourier spectrometer that leads to a ten-fold improvement in spectral resolution while compared to the conventional (direct detection) approach.