Unveiling nonperturbative factors in the resonant photoionization time delay

Atomic photoionization time delay is a vital component of attosecond metrology for investigating the ultrafast electron dynamics in atomic systems on their natural time scale. Here, we probe the factor which leads to the nonperturbative characteristics of resonant photoionization time delay (RPTD) of atomic hydrogen by numerically solving the time-dependent Schrödinger equation (TDSE) and the strong-field nonperturbation theory (SFNPT) with considering the population depletion and ac-Stark energy shift of ground state. RPTD can be retrieved from the energy-resolved optical phase of a bicircular two-color field corresponding to the maximal asymmetry of photoelectron angular distribution even in the nonperturbative regime. Our results reveal that as laser intensity increases the RPTD shows a remarkable difference of energy-dependent behaviors. At lower intensity, the absolute value of RPTD displays a smooth drop with increasing electron energy, however, at higher intensity its absolute value exhibits an obvious enhancement. Given the agreement between TDSE and SFNPT, we clearly elucidate the physical origin of nonperturbative characteristics, i.e., the population depletion of ground state plays a crucial role rather than ac-Stark energy shift. More specifically, the population depletion severely affects the Fourier transformation of the laser envelope, which is an important phase component of transition amplitude. Our work clarifies the physical mechanism of atomic photoionization time delay in nonperturbative environments, advancing the comprehensive understanding of time in attosecond science.