https://doi.org/10.1140/epjd/s10053-024-00850-6
Regular Article - Quantum Optics
Resonant generation of electromagnetic modes in nonlinear electrodynamics: quantum perturbative approach
1
Faculty of Physics, Moscow State University, Leninskiye Gory, 119991, Moscow, Russia
2
Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312, Moscow, Russia
Received:
27
February
2024
Accepted:
17
April
2024
Published online:
9
May
2024
The paper studies resonant generation of higher-order harmonics in a closed cavity in Euler-Heisenberg electrodynamics from the point of view of pure quantum field theory. We consider quantum states of the electromagnetic field in a rectangular cavity with conducting boundary conditions and calculate the cross section for the merging of three quanta of cavity modes into a single one (
process) as well as the scattering of two cavity mode quanta (
process). We show that the amplitude of the merging process vanishes for a cavity with an arbitrary aspect ratio and provide an explanation based on plane wave decomposition for cavity modes. Contrary, the scattering amplitude is nonzero for specific cavity aspect ratio. This scattering is a crucial elementary process for the generation of a quantum of a high-order harmonics with frequency 
in an interaction of two coherent states of cavity modes with frequencies 
and 
. For this process, we calculate the mean number of quanta in the final state in a model with dissipation, which supports the previous result of resonant higher-order harmonics generation in an effective field theory approach (Kopchinskii and Satunin in Phys Rev A 105:013508, 2022).
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