Tunneling time in attosecond experiment for hydrogen atom

Ossama Kullie

doi:10.1088/2399-6528/aac797

Abstract

Tunneling and tunneling time are hot debated and very interesting issues because of their fundamental role in the quantum mechanics. The measurement of the tunneling time in today’s attosecond and strong field (low-frequency) experiments, despite its controversial discussion offers a fruitful opportunity to understand the time measurement and the role of time in quantum mechanics. In previous work Kullie (2015 Phys. Rev. A 92, 052118), we suggested a model and derived a simple relation to calculate the tunneling time, which showed a good agreement with the experimental result for He-atom. In the present work we analyze and discuss our model considering the experimental result for H-atom, which is obtained recently by Satya Sainadh et al (2017 arXiv:1707.05445). In the tunneling region, we find that our model shows a good agreement with their experimental result (similar to the He-atom in our previous work), and with the accompanied time-dependent Schrödiger equation simulations. However, Sainadh et al use a different picture of the tunneling, in which tunneling time becomes an imaginary quantity. Whereas our model represents a real tunneling time picture, precisely a delay time with respect to the ionization time at the atomic field strength. Moreover, even though the above-threshold-ionization is beyond the tunneling regime, we still see that the actual ionization time is related to our model. However, crucial points arise and keep some questions open especially on the experimental side.

Highlights

The advent of attophysics opens new perspectives in the study of time resolved phenomena in atomic and molecular physics [1,2,3,4], the tunneling process and the tunneling time (T-time) in atoms and molecules [5,6,7,8,9]
We find that our model shows a good agreement with their experimental result, and with the accompanied time-dependent Schrödiger equation simulations
In previous work [10, 11] we presented a tunneling model by exploiting the time-energy uncertainty relation (TEUR), precisely that time and energy are conjugate pair

Summary

Introduction

The advent of attophysics opens new perspectives in the study of time resolved phenomena in atomic and molecular physics [1,2,3,4], the tunneling process and the tunneling time (T-time) in atoms and molecules [5,6,7,8,9]. For more details we refer to the tutorials [19, 20] (and the above mentioned.) A key quantity is the Keldysh parameter [9, 21], g= K. where e, me are the charge and mass of the electron, Ip the ionization potential of the system (atom or molecule), ω0 is the central circular frequency of the laser pulse or the laser wave packet and F, throughout this work, stands (unless it is clear) for the peak electric field strength, and τK denotes the Keldysh time. In this region for long wave laser, tunneling process is usually recognized and the contribution form multiphoton ionization are or assumed to be small. For pulses used in the experiment is inside a region called ‘Tunnel Oasis’ by Reiss [23], where according to Reiss tunneling models can be applied successfully without concern for the broader limitations of the tunneling approximation

The tunneling time

The time

The Hydrogen atom

Ip for figure

Conclusion