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 ene
rgy 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 evaluated the static and dynamic polarizabilities of the 5s^2 ^1S_0 and 5s5p ^3P_0^o states of Sr using the high-precision relativistic configuration interaction + all-order method. Our calculation explains the discrepancy between the recent exper
imental 5s^2 ^1S_0 - 5s5p ^3P_0^o dc Stark shift measurement Delta alpha = 247.374(7) a.u. [Middelmann et. al, arXiv:1208.2848 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502R (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1 % uncertainty; -0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7 %) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.
Motivated by the prospect of an optical frequency standard based on 43Ca+, we calculate the blackbody radiation (BBR) shift of the 4s_1/2-3d_5/2 clock transition, which is a major component of the uncertainty budget. The calculations are based on the
relativistic all-order single-double method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. Additional calculations are conducted for the dominant contributions in order to evaluate some omitted high-order corrections and estimate the uncertainties of the final results. The BBR shift obtained for this transition is 0.38(1) Hz. The tensor polarizability of the 3d_5/2 level is also calculated and its uncertainty is evaluated as well. Our results are compared with other calculations.
