Lorentz symmetry is one of the cornerstones of modern physics. However, a number of theories aiming at unifying gravity with the other fundamental interactions including string field theory suggest violation of Lorentz symmetry [1-4]. While the energy scale of such strongly Lorentz symmetry-violating physics is much higher than that currently attainable by particle accelerators, Lorentz violation may nevertheless be detectable via precision measurements at low energies [2]. Here, we carry out a systematic theoretical investigation of the sensitivity of a wide range of atomic systems to violation of local Lorentz invariance (LLI). Aim of these studies is to identify which atom shows the biggest promise to detect violation of Lorentz symmetry. We identify the Yb+ ion as an ideal system with high sensitivity as well as excellent experimental controllability. By applying quantum information inspired technology to Yb+, we expect tests of LLI violating physics in the electron-photon sector to reach levels of $10^{-23}$, five orders of magnitude more sensitive than the current best bounds [5-7]. Most importantly, the projected sensitivity of $10^{-23}$ for the Yb+ ion tests will allow for the first time to probe whether Lorentz violation is minimally suppressed at low energies for photons and electrons.
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 Einsteins 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.
We apply a version of the recently developed approach combining the correlation potential, linearized singles-doubles coupled-cluster, and the configuration interaction methods to the spectra of the heavy alkaline earths barium, radium, and element 120. Quantum electrodynamics radiative corrections are included. We have found unprecedented agreement between ab initio theory and experiment for the spectra of barium and radium, and we make accurate predictions for missing and unreliable data for all three atoms.
Effect of the electric quadrupole moment, $Q$, is studied for positron-atom bound systems. It is demonstrated that for $Q >50$ a.u. the electric quadrupole potential is sufficiently strong to bind positron (or electron) even in the absence of the dipole polarization potential. Such large values of $Q$ are not known for atomic ground states, however, they exist in molecules and excited atoms. In the state $2s2p~^3P^o_2$ of beryllium, the quadrupole contribution makes difference between stable bound state and decay to Be$^+$ ion and positronium. In a majority of atoms the quadrupole contribution is small and can be neglected.
We discuss possible search for optical transitions in Sm13+ and Sm14+ using ab initio calculations of differential dynamic polarizability. We calculate dynamic polarizability for M1 transition between first and second excited states of Sm14+ . Transition amplitudes and energies within optical range for states that contribute to the polarizability of the mentioned transition are presented. Employing simple analytical formula for polarizability data in the vicinity of a resonance and assuming that several values of the polarizability for different laser frequencies will be measured one can find the accurate position of the resonance. Results of similar calculations of amplitudes and energies of states that contribute to the polarizability of the M1 transition between ground and first excited states of Sm13+ are also presented.
The possibility of using neutral and double ionized erbium for atomic clocks of high precision is investigated. In both cases the narrow electric quadrupole clock transition between the ground and first exited state of the same configuration lies in optical region. The estimated ratio of decay width to transition energy is less then 10 20. We demonstrate that this transitions are not sensitive to black body radiation and if other perturbations are also considered the relative accuracy of the clocks can probably reach the level of 10 (pow minus 18) or better.
We propose a novel class of atomic clocks based on highly charged ions. We consider highly-forbidden laser-accessible transitions within the $4f^{12}$ ground-state configurations of highly charged ions. Our evaluation of systematic effects demonstrates that these transitions may be used for building exceptionally accurate atomic clocks which may compete in accuracy with recently proposed nuclear clock.
Level crossings in the ground state of ions occur when the nuclear charge Z and ion charge Z_ion are varied along an isoelectronic sequence until the two outermost shells are nearly degenerate. We examine all available level crossings in the periodic table for both near neutral ions and highly charged ions (HCIs). Normal E1 transitions in HCIs are in X-ray range, however level crossings allow for optical electromagnetic transitions that could form the reference transition for high accuracy atomic clocks. Optical E1 (due to configuration mixing), M1 and E2 transitions are available in HCIs near level crossings. We present scaling laws for energies and amplitudes that allow us to make simple estimates of systematic effects of relevance to atomic clocks. HCI clocks could have some advantages over existing optical clocks because certain systematic effects are reduced, for example they can have much smaller thermal shifts. Other effects such as fine-structure and hyperfine splitting are much larger in HCIs, which can allow for richer spectra. HCIs are excellent candidates for probing variations in the fine-structure constant, alpha, in atomic systems as there are transitions with the highest sensitivity to alpha-variation.
We study electronic transitions in highly-charged Cf ions that are within the frequency range of optical lasers and have very high sensitivity to potential variations in the fine-structure constant, alpha. The transitions are in the optical despite the large ionisation energies because they lie on the level-crossing of the 5f and 6p valence orbitals in the thallium isoelectronic sequence. Cf16+ is a particularly rich ion, having several narrow lines with properties that minimize certain systematic effects. Cf16+ has very large nuclear charge and large ionisation energy, resulting in the largest alpha-sensitivity seen in atomic systems. The lines include positive and negative shifters.
The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of Ba$^+$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $Omega$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $Omega$ without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in Ba$^+$ experiments.
