Physicists are perfectly aware that the microscopic behaviour of electrons cannot be understood without the laws of quantum theory. Nevertheless, when scientists trace the dynamics of subatomic phenomena, they like to ask questions that are motivated by a classical, non-quantum perspective. In this spirit, Shafir et al.1 report on page 343 the exact times at which electrons 'exit' atoms that are irradiated by a short flash of laser light. The existence of such an exit time is seemingly counter-intuitive, given that electrons are described by wavefunctions that extend smoothly from the inside to the outside of atoms — part of the electron is always outside the atom. In the presence of a laser field, however, there is a continuous outward flow of electron density, which Shafir and colleagues have decomposed into different electron trajectories, assigning each trajectory an experimentally determined starting time.
The emission of electrons from atoms in Shafir and colleagues' experiments is a consequence of quantum tunnelling. The applied laser field changes the potential-energy profile experienced by the electron, forming a finite barrier that is impenetrable to classical Newtonian particles, but which can be tunnelled across by electrons. A similar process forms the basis of scanning tunnelling microscopy: electrons tunnel between the surface of the object under study and the tip of the microscope. Tunnelling occurs because electron wavefunctions encompass both sides of a potential barrier (Fig. 1a); so what is the meaning of an exit time?
