Optical Bloch equations: Informal motivation without the Schrödinger equation

Abstract

We briefly review the classical model of a Lorentz atom interacting with an optical field. We then ask how the equations describing the atom’s behavior should be modified to include atomic energy level quantization. Simply discussing what modifications make sense provides a strong plausibility argument for the optical Bloch equations. Contrasted with the standard derivation, this argument is less rigorous but has a certain pedagogical appeal: It simply assumes two atomic states with energy difference ℏω, rather than invoking the Schrödinger equation. Also, because our goal is more-or-less to guess the correct equations with minimal formalism, this discussion focuses on the physical meaning of the Bloch equations.