Resonant generation of electromagnetic modes in nonlinear electrodynamics: Quantum perturbative approach

• URL: http://arxiv.org/abs/2304.10209v2
• Date: Thu, 19 Oct 2023 09:53:11 GMT
• Title: Resonant generation of electromagnetic modes in nonlinear electrodynamics: Quantum perturbative approach
• Authors: Ilia Kopchinskii and Petr Satunin
• Abstract summary: 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. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 ($3 \to 1$ process) as well as the scattering of two cavity mode quanta ($2 \to 2$ 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 $2 \to 2$ scattering is a crucial elementary process for the generation of a quantum of a high-order harmonics with frequency $2\omega_1 - \omega_2$ in an interaction of two coherent states of cavity modes with frequencies $\omega_1$ and $\omega_2$. 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.

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