The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

TL;DR

This paper demonstrates how the Dirac-Moshinsky oscillator relates to quantum optics models, extends it with external fields while maintaining solvability, and explores entanglement and its quantum optical analogs.

Contribution

It provides a detailed mapping of the Dirac-Moshinsky oscillator to the Jaynes-Cummings model and introduces an external field coupling, preserving solvability and enabling entanglement analysis.

Findings

Mapping of Dirac-Moshinsky oscillator to Jaynes-Cummings model

Conditions for solvability with external field coupling

Analysis of entanglement in relativistic and quantum optical systems

Abstract

The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.