Collective Behaviour of Cr$^{3+}$ ions in Ruby Revealed by Whispering Gallery Modes

TL;DR

This paper investigates the collective behavior of Cr$^{3+}$ ions in ruby using microwave whispering gallery modes, revealing superradiant spin-mode doublets and specific interaction rules, modeled with four harmonic oscillators.

Contribution

It introduces a novel observation of collective Cr$^{3+}$ ion behavior in ruby and develops a four oscillator model to explain the interactions with whispering gallery modes.

Findings

Observation of superradiant spin-mode doublets

Interaction rules based on mode wavenumber and azimuthal phase

Validation of a four harmonic oscillator model

Abstract

We present evidence for collective action of Cr$^{3+}$ ion impurities in a highly doped ruby crystal at microwave frequencies. The cylindrical geometry of the crystal allows for the creation of a superradiant, or "spin-mode" doublet, with spatial structure similar to that of microwave whispering gallery modes (WGMs). This results in a strict criteria of selection rules regarding the interaction of resonant WGMs and spin-modes; namely that only modes with the same wavenumber and azimuthal phase may interact. What results is an avoided level crossing between the two, in which both WGM doublet constituents are seen to interact with the spin resonance. We demonstrate that a four harmonic oscillator model is necessary to accurately describe this result.