Time-Dependent Multiphoton Theory of Phase Delays

Introduction: Attosecond science has opened the way to probe and control electronic dynamics in matter on their natural timescales. Pump–probe techniques combining attosecond extreme-ultraviolet (XUV) pulses with near infrared (NIR) or visible laser fields provide access to phase and timing information encoded in photoelectron wave packets. The reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) has become the cornerstone of attosecond chronoscopy of photoionization processes in atoms [1].

Methods: We present a time-dependent non-perturbative (respective to the NIR laser intensity, up to 1014 W/cm2) theory of RABBIT for photoelectron emission from atoms encompassing multiphoton transitions. The laser pulse involves a fundamental frequency in the NIR and several harmonics in the XUV. Within the strong-field approximation (SFA), we employ a semiclassical model based on the saddle-point-approximation to gain a better understanding of the physics involved [2].

Results: We derive analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interferences between trajectories born within the same optical cycle and those born in different cycles. We identify the contributions from trajectories born within each cycle, or within each half-cycle (depending on the considered emission angle), as the mechanism governing attosecond phase delays in the RABBIT protocol. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation (TDSE) confirm the accuracy of the semiclassical description.

Conclusions: The present theory thus provides a unified framework for describing attosecond chronoscopy in different emission geometries, for laser intensities covering the entire range from perturbative values up to the non-perturbative domain.

References:

[1] Isinger M, et al., Science ;358(6365):893-896 (2017). doi: 10.1126/science.aao7043

[2] S. D. López, M. L. Ocello, and D. G. Arbó, Phys. Rev. A 110, 013104 (2024) DOI: https://doi.org/10.1103/PhysRevA.110.013104