Control of free induction decay with quantum state preparation in a weakly coupled multi-spin system

Nuclear magnetic resonance (NMR) has been a widely used tool in various scientific fields and practical applications, with quantum control emerging as a promising strategy for synergistic advancements. In this paper, we propose a novel approach that combines NMR and quantum state preparation techniques to control free induction decay (FID) signals in weakly coupled spin systems, specifically Trifluoroiodoethylene $C_2F_3I$. We investigate the FID signal of the three-spin system and compare the differences between the FID signals in the thermal state and the pseudo-pure state (PPS), where the latter is generated using quantum state preparation techniques. Our approach aims to demonstrate a single exponentially decaying FID in weakly coupled spins, in which oscillatory FID signals are often observed. We validate our findings through numerical simulations and experimental measurements, and justify the validity of the theory. Our method opens a door to advancing spin system research and extending the capabilities of NMR with current quantum technologies in various scientific and practical fields.