Tunneling in attosecond optical ionization and a dynamical time operator

TL;DR

This paper explores the concept of time in quantum mechanics, particularly in attosecond optical ionization, by examining a dynamical time operator in relativistic quantum mechanics and its relation to tunneling measurements.

Contribution

It introduces a self-adjoint dynamical time operator in Dirac's RQM and analyzes its connection to laboratory time and tunneling delay in attosecond experiments.

Findings

The dynamical time operator provides an internal time perspective.

Relation between internal and laboratory time is established.

Implications for interpreting tunneling delay times in experiments.

Abstract

The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ioniza- tion experiments. The parameter status of time in the time dependent Schr\"odinger equation (TDSE) is supported by the well-known Pauli's ob- jection as well as by its interpretation as an emerging property of entangle- ment with a classical environment. On the other hand, the introduction of a self-adjoint dynamical time operator in Dirac's formulation of elec- tron's relativistic quantum mechanics (RQM), yields an additional system observable that represents an internal time. In the present paper the re- lation of this internal time with the parametric (laboratory) time and its relevance to the tunneling measurements in these experiments is examined within the standard framework of RQM.