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

Abstract

Tunneling time in attosecond and strong-field experiments is one of the most controversial issues in current research, because of its importance to the theory of time, the time operator and the time–energy uncertainty relation in quantum mechanics. In Kullie (2015 Phys. Rev. A 92 052118) 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, the classical view of the time measurement and our tunneling time relation(s). We draw some conclusions concerning the validity and the relation between the different types of the tunneling time with the hope that they will help to answer the question put forward by Orlando et al (2014 J. Phys. B 47 204002, 2014 Phys. Rev. A 89 014102): tunneling time, what does it mean? However, as we will see, the important question is a more general one: how to understand the time and the measurement of the time of a quantum system? 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, and consequently (perhaps only) classical Newtonian time remains as a parametric type of time.