Stable Collective Dynamics of Two-Level Systems Coupled by Dipole Interactions

TL;DR

This paper investigates the non-linear dynamics of dipole-coupled two-level systems under Rabi driving, revealing conditions for stable collective oscillations despite interactions.

Contribution

It provides a comprehensive analysis combining numerical, Floquet, and analytical methods to identify regimes of stable collective Rabi oscillations in dipolar two-level systems.

Findings

Dipole interactions often cause instabilities disrupting Rabi oscillations.

Stable collective Rabi oscillations are possible within specific parameter regimes.

Analytical high Rabi coupling limit confirms numerical stability conditions.

Abstract

We study the dynamics of a set of two-level systems coupled by dipolar interactions under a resonant external Rabi drive. The two-level systems are prepared initially in a coherent product state, and we ask how the non-equilibrium conditions caused by the drive affect this coherence. We study the full non-linear dynamics of the coupled two-level systems within a classical approximation by analysing numerically the equations of motion and determining the stability of the collective coherent state within classical Floquet theory. We establish the behaviour analytically in the high Rabi coupling limit by employing a Magnus expansion and spin wave analysis. Our results show that, typically, the dipole interactions between the two-level systems lead to instabilities that cause a breakdown of the collective Rabi oscillations. However, we identify parameter regimes for which the two-level systems undergo collective coherent Rabi oscillations even in the presence of the dipole interactions.