Tunneling Ionization Time Resolved by Backpropagation

We determine the ionization time in tunneling ionization by an elliptically polarized light pulse relative to its maximum. This is achieved by a full quantum propagation of the electron wave function forward in time, followed by a classical backpropagation to identify tunneling parameters, in particular, the fraction of electrons that has tunneled out. We find that the ionization time is close to zero for single active electrons in helium and in hydrogen if the fraction of tunneled electrons is large. We expect our analysis to be essential to quantify ionization times for correlated electron motion.