Quantum Travel Time and Tunnel Ionization Times of Atoms

Time it takes to travel from one position to another, devoid of any quantum mechanical description, has been modeled variously, especially for quantum tunneling. The model time, if universally valid, must be subluminal, must hold everywhere (inside and outside the tunneling region), must comprise interference effects, and must have a sensible classical limit. Here we show that the quantum travel time, hypothesized to emerge with the state vector, is a function of the probability density and probability current such that all the criteria above are fulfilled. We compute it inside and outside a rectangular potential barrier and find physically sensible results. Moreover, we contrast it with recent ionization time measurements of the $\rm He$ as well as the $\rm Ar$ and $\rm Kr$ atoms, and find good agreement with data. The quantum travel time holds good for stationary systems, and can have applications in numerous tunneling-driven phenomena.