Classical analogue of the continuous transition between the Weisskopf-Wigner exponential decay and the Rabi oscillation

TL;DR

This paper demonstrates a classical mechanical analogue of the quantum transition between exponential decay and Rabi oscillations by studying coupled oscillators with damping, revealing a continuous transition between these regimes.

Contribution

It introduces a classical mechanical system that mimics the quantum transition between decay and oscillation regimes, highlighting the analogy through damping and coupling variations.

Findings

Classical oscillators exhibit a transition similar to quantum decay and Rabi oscillations.

Varying damping and coupling controls the transition between regimes.

The classical model provides insight into quantum dynamical phenomena.

Abstract

When a discrete state is coupled to a continuum, the dynamics can be described either by the Weisskopf-Wigner exponential decay or by the Rabi oscillation, depending on the relative magnitudes of the continuum width and of the Rabi frequency. A continuous transition between these two regimes exists, as demonstrated in 1977 by C. Cohen-Tannoudji and P. Avan. Here, we describe a fully analogous transition in classical mechanics, by studying the dynamics of two coupled mechanical oscillators in the presence of damping. By varying the relative magnitudes of the damping and coupling terms, we observe a continuous transition between a regime analogous to the Rabi oscillation and a regime analogous to the Weisskopf-Wigner exponential decay.