A second quantized approach to the Rabi problem

TL;DR

This paper develops a second quantized framework for the Rabi problem, linking quantum, semiclassical, and Jaynes-Cummings models, and extends the approach to matter fields, revealing connections with Maxwell's theory.

Contribution

It introduces a novel second quantization method for the Rabi problem directly in a non-covariant setting, bridging different quantum models and extending to matter fields.

Findings

The second quantization approach is consistent with the semiclassical limit.

The method connects Schrödinger and Maxwell theories through negative energy sectors.

The generalized theory remains strictly quantum and non-relativistic.

Abstract

In the present work the Rabi Problem, involving the response of a spin 1/2 particle subjected to a magnetic field, is considered in a second quantized approach. In this concrete physical scenario, we show that the second quantization procedure can be applied directly in a non-covariant theory. The proposed development explicits not only the relation between the full quantum treatment of the problem and the semiclassical Rabi model, but also the connection of these approaches with the Jaynes-Cummings model. The consistency of the method is checked in the semiclassical limit. The treatment is then extended to the matter component of the Rabi problem so that the Schr\"odinger equation is directly quantized. Considering the spinorial field, the appearance of a negative energy sector implies a specific identification between Schr\"odinger's and Maxwell's theories. The generalized theory is consistent, strictly quantum and non-relativistic.