Energy quantization and probability density of electron in intense-field-atom interactions

We find that, due to the quantum correlation between the electron and the field, the electronic energy becomes quantized also, manifesting the particle aspect of light in the electron-light interaction. The probability amplitude of Ending electron with a given energy is given by a generalized Bessel function, which can be represented as a coherent superposition of contributions from a few electronic quantum trajectories. This concept is illustrated by comparing the spectral density of the electron with the laser assisted recombination spectrum.