Limits on Violations of Lorentz Symmetry and the Einstein Equivalence Principle using Radio-Frequency Spectroscopy of Atomic Dysprosium

Abstract

We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of 10(-17), matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to 10(-8). With some enhancements, our experiment may be sensitive to Lorentz violation at the level of 9 × 10(-20).

Limiting superluminal electron and neutrino velocities using the 2010 Crab Nebula flare and the IceCube PeV neutrino events

“…From the fact that photons have been observed with energies E γ ≥ 80 TeV from the Crab nebula [41], we deduce for this case that E max ≥ 80 TeV, or that the magnitude of the negative value for |δ e | is less than 8 × 10 −17 . This value is comparable to the constraint given in [39].…”

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

“…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.…”

“…For a terrestrial laboratory, the lab-frame values of the tensor's dominant spatial components c lab jk depend upon the orientation of the lab with respect to the SCCEF, and thus modulate with characteristic frequency Ω ≃ 2 × 2π/(23 h 56 min), or twice every sidereal day. The value of the anomalous tensor in the lab-frame can be related to that in the SC-, where Λ α µ is the standard Lorentz boost plus rotation from the SCCEF to the lab frame [7,10,18]. Thanks to the Earth's orbital velocity, the boost Λ α µ mixes the time and spatial components of c SCCEF αβ into the spatial components of c lab µν .…”

“…The LLI-violating change in the transition energy between bound states with the same n and different J is therefore expected to scale as δω nm ≃ C (0) 0 (6 × 10 13 Hz). This, combined with the comparatively small range of variation in U/c 2 accessible to a terrestrial laboratory (∼ 10 −10 in the Sun's potential over a year), implies this ion could serve as a stable reference standard to compare against a more sensitive transition (such as those offered by dysprosium [7]) in a null-redshift test of EEP.B. Several valence electrons: Nd 3+ and Er 3+ ions in LaCl3.…”

Highly charged ions for atomic clocks and search for variation of the fine structure constant

“…This may have many technical applications but also clock transitions in HCI can be used to study fundamental problems of modern physics such as variation of fundamental constants [3], local Lorentz invariance violation [4,5], search for dark matter [6], etc. Having extremely high accuracy of the clocks is crucial for these studies.…”