Defining the semiclassical limit of the quantum Rabi Hamiltonian

TL;DR

This paper develops a formalism to rigorously derive the semiclassical limit of the quantum Rabi Hamiltonian, clarifying the quantum-to-classical transition in light-matter interaction models.

Contribution

A new method to obtain the semiclassical model directly from the quantum Hamiltonian using a displaced Fock-state basis.

Findings

Resolves discrepancies between coherent-state dynamics and semiclassical Rabi oscillations.

Provides a framework for studying the quantum-to-classical transition.

Applicable to standard and ultrastrong coupling regimes.

Abstract

The crossover from quantum to semiclassical behavior in the seminal Rabi model of light-matter interaction still, surprisingly, lacks a complete and rigorous understanding. A formalism for deriving the semiclassical model directly from the quantum Hamiltonian is developed here. Working in a displaced Fock-state basis $\lvert \alpha, n \rangle$, the semiclassical limit is obtained by taking $\lvert \alpha \rvert \to \infty$ and the coupling to zero. This resolves the discrepancy between coherent-state dynamics and semiclassical Rabi oscillations in both standard and ultrastrong coupling/driving regimes. Furthermore, it provides a framework for studying the quantum-to-classical transition, with potential applications in quantum technologies.