  We studied a QED analog of the Franz-Keldysh effect, and the interplay
between the non-perturbative (the Schwinger mechanism) and the perturbative
particle production mechanism from the vacuum in the presence of a strong slow
field superimposed by a weak field. We found that the Franz-Keldysh effect
significantly affects the particle production: (i) the perturbative particle
production occurs even below the threshold energy; (ii) the perturbative
production becomes the most efficient just above the threshold energy; and
(iii) an oscillating behavior appears in the production number above the
threshold energy. These non-trivial changes are suppressed only weakly by
powers of the critical field strength of QED. A relation to the dynamically
assisted Schwinger mechanism and implications to experiments are also
discussed.
