Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model

TL;DR

This paper presents an exactly solvable quantum model for electro-optic light modulation involving finite optical modes, analyzing the interaction with microwave fields and exploring conditions for semiclassical approximation validity.

Contribution

It introduces a novel exactly solvable multimode quantum model for electro-optic modulation, utilizing Lie algebra techniques to analyze mode interactions and approximation regimes.

Findings

Analytical solutions for mode interactions using Jordan mappings

Conditions for the validity of semiclassical approximation

Effects of modulation on photon counting rate

Abstract

We theoretically study electro-optic light modulation based on the quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and, in the semiclassical approximation where the microwave field is treated as a classical mode, can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. We also establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field.