Effects of Lorentz-symmetry violation on the spectra of rare-earth ions in a crystal field

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 LaCl3 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.PACS numbers: 03.30.+p, 11.30.Er, 11.30.Cp, 32.30.Jc Most of our day-to-day experiences are mediated by light and charged particles, and in particular its interaction with electrons. To the best of our knowledge, the physics of a system of photons and electrons is independent of the velocity and orientation of that system in absolute space, nor is it locally dependent upon where that system lies in a gravitational potential. These symmetries, respectively described as local Lorentz invariance (LLI) and Einstein's equivalence principle (EEP), are fundamental to our modern understanding of the standard model and general relativity. It is possible, however, that these symmetries are not exact at experimentally accessible energy scales, thanks to spontaneous symmetry breaking or other physics at high energy scales [1,2]. This possibility has driven many experimental tests of LLI and EEP [3], and motivated the development of phenomenological frameworks that can quantitatively describe the effect of LLI-and EEP-violation on known particles and fields. One such framework is provided by the standard model extension (SME) [4,5], which has been used to analyze a wide range of experiments [6]. The SME augments the standard model Lagrangian with all combinations of known particles and fields that are not invariant under Lorentz transformations, but which preserve gauge invariance, energy and translational invariance, and the invariance of the total action [4,5]. These terms are parameterized by Lorentz tensors that are collectively known as LLI-and EEP-violating coefficients, and are further subdivided into 'sectors' that deal with terms involving a particular particle. In this Letter, we focus on tests of the electron-sector c µν tensor, which modifies the inertial energy of electrons according to their direction of motion.Spectroscopy of neutral dysprosium atoms has already led to one of the world's most sensitive tests of electronic LLI and EEP [7]. More recently, a still more sensitive measurement of the electron c µν coefficients was obtained by engineering the quantum state of a pair of trapped Ca + ions [8], extending precision tests of electronic LLI past the electroweak (relative to the Planck mass) scale. Both of these experiments operate at or near the interrogation-time-of-flight or atom (ion) shot-noise limit. In this Letter, we consider the possibility of using rare earth ions doped in a crystalline lattice to perform similar measurements of the electronic c µν . Rare-earth ion...

Measuring the stability of fundamental constants with a network of clocks

“…Note that in general, and especially for systems based on heavy atoms or ions where relativistic corrections can be large, intrinsically relativistic methods, starting from solving the Dirac-Hartree-Fock equations, are used to obtain the electronic wave functions used in Eq. ( 31) to accurately capture the effects of the c-type coefficients [213,[215][216][217][218][219][220]. Relativistic analogues of the momentum-space matrix elements, e.g.…”

Search for New Physics with Atoms and Molecules

“…Another interesting future possibility is measuring transition energies of rare-earth ions doped in crystalline lattices, which can be highly sensitive to the electron SME parameters (Harabati et al, 2015).…”

Overview of the Phenomenology of Lorentz and CPT Violation in Atomic Systems

“…Since the early years of the SME, models for atomic systems in the presence of Lorentz and CPT violation have been proposed [11][12][13][14][15]. Based on these models, experimental bounds on coefficients for Lorentz violation have been reported [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The original SME, referred to as the minimal SME, only considered the contributions from Lorentz-violating operators of mass dimensions three and four [9,10].…”