Coupling a discrete state to a quasi-continuum: A model quantum mechanical system that interpolates between Rabi oscillations and decay-revival dynamics

TL;DR

This paper introduces a quantum model with a discrete state coupled to a quasi-continuum, unifying various well-known quantum optical models and demonstrating diverse dynamical behaviors through semi-analytical solutions.

Contribution

The authors develop a unified quantum system model that interpolates between multiple established models, providing semi-analytical solutions and exploring its rich dynamical regimes.

Findings

System exhibits Rabi oscillations, decay, and revivals.

Semi-analytical solutions reduce to known models in limits.

Numerical simulations confirm diverse dynamical behaviors.

Abstract

We formulate a quantum mechanical system consisting of a single discrete state coupled to an infinite ladder of equally-spaced states, the coupling between the two being given by a Lorentzian profile. Various limits of this system correspond to well-known models from quantum optics, namely, the narrow resonance limit gives the Rabi system, the wide resonance limit gives the Bixon-Jortner system, the wide resonance, true continuum limit gives the Wigner-Weisskopf system, and the fixed resonance, true continuum limit gives a system that is typically studied by methods developed by Fano. We give a semi-analytical solution of the eigenvalue problem by reducing it to a transcendental equation, and demonstrate the aforementioned limiting behaviors. We then study the dynamics of the initial discrete state numerically, and show that it gives a wide range of behaviors in various limiting cases as predicted by our asymptotic theory including exponential decay, revivals, Rabi oscillations, and damped oscillations. The ability of this system to interpolate between such a rich set of behaviors and existing model systems, and the accessibility of a semi-analytical solution, make it a useful model system in quantum optics and related fields.