Mixed Quantum-Classical Dynamics Yields Anharmonic Rabi Oscillations

TL;DR

This paper demonstrates that a mixed quantum-classical approach to the quantum Rabi model produces persistent anharmonic Rabi oscillations, closely matching full quantum results in the single-quantum limit, with implications for small quantum systems.

Contribution

It introduces an analytical and numerical study of MQC dynamics in the quantum Rabi model, revealing anharmonic oscillations governed by a Duffing equation, and shows how to approximate quantum results with classical fields.

Findings

MQC approach yields anharmonic Rabi oscillations

Oscillations closely match full quantum results with zero-point energy

Guidance for applying MQC to small quantum systems

Abstract

We apply a mixed quantum-classical (MQC) approach to the quantum Rabi model, involving a classical optical field coupled self-consistently to a quantum two-level system. Under the rotating wave approximation, we analytically show this approach to yield persistent yet anharmonic Rabi oscillations, governed by an undamped and unforced Duffing equation. We consider the single-quantum limit, where we find such anharmonic Rabi oscillations to closely follow full-quantum results once zero-point energy is approximately enforced when initializing the optical field coordinate. Our findings provide guidance in the application of MQC dynamics to classes of problems involving small quantum numbers and far away from decoherence.