Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima

We study the photoionization of molecule ${\mathrm{H}}_{2}^{+}$ in an XUV pulse by numerically solving the time-dependent Schr\"odinger equation simulation and focus on a zeptosecond birth time delay of a photoelectron from the different cores. We propose a simple and robust method to extract accurately the zeptosecond birth time delay with double-slit interference minima. Based on this extraction method, our results show that the birth time delay is strongly affected by the initial bound-electron wave function due to the deviation of the electron emission position from the central core. Furthermore, an experimental scheme is also proposed to testify this wave-function-dependent zeptosecond birth time delay. Our study sheds more light on the ultrafast molecular photoionization dynamics on the zeptosecond timescale.