Direct probing of tunneling time in strong-field ionization processes by time-dependent wave packets

We propose a straightforward approach to directly probe the tunneling time by observing the transition of photoelectron wave packets in strong-field ionization processes, where Coulomb potentials do not affect the results. A circularly polarized laser pulse is used to avoid the impact of scattering electrons on the direct ionization electrons, and a pure transmission photoelectron wave packet can be obtained. Then, a positive tunneling time is extracted. The results demonstrate that the tunneling time is dominated mainly by the laser frequency in some laser intensity range. At the same time, we also investigate the tunneling time by analyzing the instantaneous ionization rate, and the consentaneous results are obtained.