We study the tunneling of virtual matter-antimatter pairs from the quantum
vacuum in the presence of a spatially uniform, time-dependent electric
background composed of a strong, slow field superimposed with a weak, rapid
field. After analytic continuation to Euclidean spacetime, we obtain from the
instanton equations two critical points. While one of them is the closing point
of the instanton path, the other serves as an Euclidean mirror which reflects
and squeezes the instanton. It is this reflection and shrinking which is
responsible for an enormous enhancement of the vacuum pair production rate. We
discuss how important features of two different mechanisms can be analysed and
understood via such a rotation in the complex plane. a) Consistent with
previous studies, we first discuss the standard assisted mechanism with a
static strong field and certain weak fields with a distinct pole structure in
order to show that the reflection takes place exactly at the poles. We also
discuss the effect of possible sub-cycle structures. We extend this reflection
picture then to weak fields which have no poles present and illustrate the
effective reflections with explicit examples. An additional field strength
dependence for the rate occurs in such cases. We analytically compute the
characteristic threshold for the assisted mechanism given by the critical
combined Keldysh parameter. We discuss significant differences between these
two types of fields. For various backgrounds, we present the contributing
instantons and perform analytical computations for the corresponding rates
treating both fields nonperturbatively. b) In addition, we also study the case
with a nonstatic strong field which gives rise to the assisted dynamical
mechanism. For different strong field profiles we investigate the impact on the
critical combined Keldysh parameter. [...]Comment: 54 pages, 23 figures, revised, restructured to improve readability,
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