Tunneling in attosecond optical ionization and a dynamical time operator

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.