Energy-dependent phases more fundamental than ''attosecond time delays''

Matthias F. Kling

Candong Liu, M. Nisoli

Single-photon ionization of a hydrogen atom irradiated by two time-delayed isolated attosecond pulses is theoretically investigated by numerically solving the fully three-dimensional time-dependent Schr\"odinger equation. It is demonstrated that the analysis of the angular-resolved electron energy spectrum, showing a complex interference pattern, allows one to completely retrieve the difference between the energy-dependent phases of the electron wave packets generated by the two delayed attosecond pulses. Moreover, it is shown that in the case of a pair of excitation pulses with the same chirp rate, the proposed interferometric technique can be used to measure the difference between the carrier envelope phase values of two attosecond pulses.

Xiao‐Yun Zhao, Ming-Qing Liu

Abstract 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.

Alexandra S. Landsman, Ursula Keller

Theodor W. Hänsch

Chuncheng Wang, Xiaokai Li, Xiwang Liu +7 more

Tunnelling lies at the heart of quantum mechanics and is a fundamental process in attosecond science, molecular biology, and quantum devices. Whether tunnelling takes time and how a microscopic particle transits through a barrier have been debated since the early days of quantum mechanics. The time required for an electron to tunnel through an atomic potential barrier has been measured with attosecond angular streaking (attoclock), and a recent work on the hydrogen atom claimed that electron tunnelling is instantaneous. However, the time required for Rb atoms to tunnel through an optical potential barrier has been measured to be on the order of milliseconds with a recent Larmor clock measurement. The essence of electron and atom tunnelling is identical, but the reason for the contradictory conclusions remains unknown. Here, we demonstrate that the sub-barrier potential interaction is the root of the nonzero tunnelling delay time. We reveal that the wave-particle duality of a tunnelling electron must be fully taken into account when decoding the tunnelling delay time from the attoclock measurements. Based on energy-resolved attoclock measurements, we show that the tunnelling delay time of an electron ranges from 24 to 58 attoseconds, and the counterintuitive result that an electron with a lower energy may spend less time in the barrier is consistent with the velocity-dependent tunnelling time of atoms in Larmor clock measurements. Our results unify the tunnelling time of microscopic particles by highlighting the classically forbidden sub-barrier potential interactions of matter waves.