Effects of Lorentz Symmetry Violation in the Spectra of Rare-Earth Ions in a Crystal Field

TL;DR

This paper shows that measuring transition energies of rare-earth ions in crystals can detect violations of Lorentz symmetry, providing a new way to test fundamental physics principles.

Contribution

It introduces a method to calculate frame-dependent energy shifts in rare-earth ions due to Lorentz symmetry violation within the Standard Model Extension framework.

Findings

Transition energies are highly sensitive to Lorentz violation.

Calculated energy shifts depend on the dopant and crystal environment.

Potential for experimental tests of fundamental symmetries.

Abstract

We demonstrate that experiments measuring the transition energies of rare-earth ions doped in crystalline lattices are sensitive to violations of Local Lorentz Invariance and Einstein's Equivalence Principle. Using the crystal field of LaCl$_{3}$ as an example, we calculate the frame-dependent energy shifts of the transition frequencies between low-lying states of Ce$^{3+}$, Nd$^{3+}$, and Er$^{3+}$ dopants in the context of the Standard Model Extension, and show that they have high sensitivity to electron anomalies that break rotational invariance.