Electron-positron pair production in an oscillating Sauter potential is investigated in the framework of the computational quantum field theory. It is found that for a Sauter potential well with oscillating width and depth simultaneously, the phase difference between them has a great impact on the number of created electron-positron pairs. Optimal values of the phase difference corresponding to different oscillation frequencies are obtained. The optimal phase difference has a strong nonlinear dependence on oscillating frequency. When the potential well changes slowly, our results can be explained by the instantaneous bound states. For the higher frequency case, however, multiphoton effect is enhanced and the Pauli blocking effect has a strong inhibitory effect on pair creations. These results can provide a theoretical reference for the experimental creation of the electron-positron pairs.

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