Tunneling time in attosecond experiments, Keldysh, Mandelstam-Tamm and intrinsic-type of time

TL;DR

This paper explores various concepts of tunneling time in attosecond experiments, comparing different theoretical approaches and proposing a quantum clock-based estimation that aligns well with experimental data.

Contribution

It introduces a new estimation of tunneling time using the time-energy uncertainty relation and compares it with existing approaches like Keldysh and Mandelstam-Tamm times.

Findings

The proposed tunneling time estimation agrees with experimental measurements.

Different approaches to tunneling time are analyzed and contrasted.

The paper classifies quantum mechanical time into intrinsic and external types.

Abstract

Tunneling time in attosecond and strong field experiments is one of the most controversial issues in today's research, because of its importance to the theory of time, the time operator and the time-energy uncertainty relation in quantum mechanics. In [1] we derived an estimation of the (real) tunneling time, which shows an excellent agreement with the time measured in attosecond experiments, our derivation is found by utilizing the time-energy uncertainty relation, and it represents a quantum clock. In this work, we show different aspects of the tunneling time in attosecond experiments, we discuss and compare the different views and approaches, which are used to calculate the tunneling time, i.e. Keldysh time (as a real or imaginary quantity), Mandelstam-Tamm time and our tunneling time relation(s). We draw some conclusion concerning the validity and the relation between the different types of the tunneling time with the hope, it will help to answer the the question put forward by Orlando et al [2] tunneling time, what does it mean?. In respect to our result, the time in quantum mechanics can be, in more general fashion, classified in two types, intrinsic dynamically connected, and external dynamically not connected, to the system.