We developed time-domain interferometry (TDI) using (57)FE nuclear resonant scattering and applied to the study of the dynamics of ionic liquid 1-buty1-3-methylimidazolium iodide (BmimI). By using a multi-element avalanche photo diode as a detector, four TDI time spectra reflecting different momentum transfers were obtained at 250 K. By considering additional Gaussian broadening of resonant energy in stainless steel foils, the relaxation times of the density correlation in super-cooled BmimI were successfully obtained. The momentum transfer dependence of those relaxation times was confirmed to follow the Gaussian behaviour. Moreover, we discussed the trends of the TDI development in the future.