Abstract
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.
Highlights
It was Dirac who first discovered a relativistic wave equation for electron, which is known as the Dirac equation today [1]
The Dirac equation admits infinitely negative energy states. This looks problematic because any state may fall into lower and lower energy states by emitting photons and there seem no stable states. This problem was resolved by Dirac himself by reinterpreting that negative energy states are all occupied in our physical vacuum (Dirac sea picture) [2]
Dirac’s interpretation suggests that our vacuum is not vacant space, but can be regarded as something like a semiconductor with gap energy characterized by the electron mass scale. This implies that our vacuum exhibits nontrivial responses when exposed to external fields whose characteristic physical scale is larger than the gap energy, as semiconductors do
Summary
It was Dirac who first discovered a relativistic wave equation for electron, which is known as the Dirac equation today [1]. We shall show that a QED analog of the Franz-Keldysh effect takes place, and nontrivial changes in the perturbative production number appear such as excess below the gap energy, and an oscillating behavior above the gap energy These changes are found to be suppressed only weakly by powers of the critical field strength. Based on our perturbation theory, we derive an analytical formula (without any approximations such as the WKB approximation) for the number of produced particles for this particular field configuration With this formula, we explicitly demonstrate how a QED analog of the Franz-Keldysh effect and the interplay between the nonperturbative and the perturbative particle production occur. The Dirac equation for a fermion field operator ψreads
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