According to energy band theory, ground states of a normal conductor and insulator can be obtained by filling electrons individually into energy levels, without any restrictions. It fails when the electron-electron correlation is taken into account. In this work, we investigate dynamic process of building ground states of a Hubbard model. It bases on time-ordered quantum quenches for unidirectional hopping across a central and an auxiliary Hubbard models. We find that there exists a set of optimal parameters (chemical potentials and pair binding energy) for the auxiliary system, which takes the role of electron pair-reservoir. The exceptional dynamics allows the perfect transfer of electron pair from the reservoir to the central system, obtaining its ground states at different fillings. The dynamics of time-ordered pair-filling not only provides a method for correlated quantum state engineering, but also reveals the feature of the ground state in an alternative way.
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