Frequency super-resolution with quantum environment engineering in a weakly coupled three-nuclear-spin system

Optical super-resolution has been widely employed to beat the spatial diffraction limit, which is often stated by Abbe-Rayleigh criterion. Analogously, we propose a frequency super-resolution method, which beats conventional frequency spectral resolution limit often approximated by the full width at half maximum of the spectral peak, Γ. This method utilizes recently developed quantum environment engineering technique. With numerical simulations and experiments, we demonstrate, as a proof-of-concept, the frequency super-resolution method in a three-nuclear-spin system (Trifluoroiodoethylene) by successfully decomposing a thermal state spectrum of the spin [Formula: see text] into four peaks of engineered pseudo-pure states of the quantum environment. The ultimate frequency resolution reaches [Formula: see text]. This method is potentially useful in spectral decomposition of weakly coupled small-size nuclear spin systems.