Tunneling time in attosecond experiment for hydrogen atom

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.

Time Operator, Real Tunneling Time in Strong Field Interaction and the Attoclock

“…In previous works [1][2][3], we presented a tunneling model and a formula to calculate the tunneling time (T-time) by exploiting the time-energy uncertainty relation (TEUR), precisely that time and energy are a (Heisenberg) conjugate pair. Our T-time is in good agreement with the attosecond (angular streaking) experiment for He-atom [1] with the experimental finding of Eckle et al [4][5][6], and for hydrogen atoms [7] with the experimental finding of Sainadh et al [8]. Our model presents a real T-time picture or a delay time with respect to the ionization time at atomic field strength F a (see below, compare Figure 1).…”

“…Hence, they support the point of view that T-time, i.e., the time to traverse the barrier region, is an imaginary quantity. In [7], we found that the measured data in the experiment with H-atom of Sainadh et al and the accompanied NITDSE [8,49] fits very well to our real T-time picture (Equation (7)). Solely the factor of (1/2) is still unclear; it is absent in the experimental data of Sainadh et al [8,49], unlike the data of Landsman et al [4] for the He atom, as discussed in Sections 3 and 4.…”

“…Taking a second 1/2 factor by symmetrization (anti-symmetrization) as done in Equations (24)-(27) (and (28)) corresponds to forward, backward scattering. In our view, this again shows that the result of Landsman et al [4] for He-atom [1], is more reliable than the result of Sainadh et [49] for H-atom [7] (which lacks a factor 1/2), as already mentioned in Section 3.…”

“…Thus far, we see that our real T-time picture is highly consistent and fundamental. However, we have to add in regard to imaginary tunneling picture that it is common (rather fundamental) in QM that two pictures exist for a QMal physical process or phenomena [7]. Indeed, the debate continues and a complete picture of the T-time is not reached so far.…”

“…which is the relation given in Equation (7). With the symmetry consideration, or changing exit, entrance points (forward, backward process), we carry out the same procedure and obtain τ T,i , and hence the total time τ total , see Equation (7).…”