A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics

TL;DR

This paper develops a relativistic model of a two-level atom using Grassmann variables, extending traditional quantum optics models to a relativistic framework within Minkowski spacetime.

Contribution

It introduces a point-particle representation of a two-level atom with electric dipole in a relativistic setting, including quantization and generalization of key quantum optics Hamiltonians.

Findings

Derived the Poincaré generators for the system.

Quantized the model to obtain a relativistic two-level atom.

Generalized Rabi and Jaynes-Cummings Hamiltonians relativistically.

Abstract

We define a relativistic version of the two-level atom, in which an extended atom is replaced by a point particle carrying suitable Grassmann variables for the description of the two-level structure and of the electric dipole. After studying the isolated system "atom plus the electro-magnetic field" in the electric-dipole representation as a parametrized Minkowski theory, we give its restriction to the inertial rest frame and the explicit form of the Poincar\'e generators. After quantization we get a two-level atom with a spin 1/2 electric dipole and the relativistic generalization of the Hamiltonians of the Rabi and Jaynes-Cummings models.