Tunneling Time in Attosecond Experiments and Time Operator in Quantum Mechanics

Abstract

Attosecond science is of a fundamental interest in physics. The measurement of the tunneling time in attosecond experiments, offers a fruitful opportunity to understand the role of time in quantum mechanics (QM). We discuss in this paper our tunneling time model in relation to two time operator definitions introduced by Bauer and Aharonov–Bohm. We found that both definitions can be generalized to the same type of time operator. Moreover, we found that the introduction of a phenomenological parameter by Bauer to fit the experimental data is unnecessary. The issue is resolved with our tunneling model by considering the correct barrier width, which avoids a misleading interpretation of the experimental data. Our analysis shows that the use of the so-called classical barrier width, to be precise, is incorrect.

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

“…However, because L is the distance traveled by the particle (in our case the barrier region) and due to the adiabaticity, we can take on the right-hand side of Equation (17) a mean value p (with m = m e = 1 au). As discussed in [45], see below Section 3, we have p = 4Z e f f and we take the potential difference in the barrier region to obtain the time T corresponding to the deflection angle ∆φ [43] while tunneling. For its interpretation as macroscopic quantity, see [43].…”

“…When the electron interacts with the field, we can assume the quasistatic (adiabatic) dynamics tunneling model (QSTM). The electron moves through the barrier region adiabatically with a mean momentum p = 4Z e f f , which, as discussed in [45], can be seen from…”

“…Hence, no time operator exists in QM in line with the well known Pauli theorem. However, the later point has been clarified and the list of references is too large to be specified; see, for example, [11][12][13][37][38][39]45,[64][65][66][67] and the references therein. The present work is a step in this direction.…”

“…Furthermore, the electron becomes a free particle at the exit point, when it gains the energy through the nonadiabaticity. It is then less affected by the tail of the Coulombic potential, which is screened by the field [45]. Otherwise, we do have to rely on the adiabatic tunneling picture, where our real T-time model, together with the statistical or probabilistic time interpretation as discussed above, offers a reasonable picture in which the nonadiabatic effects are small and not crucial to the ACOA or the T-time.…”