Sergey G. Porsev

Single ion optical clocks have shown systematic frequency uncertainties below $10^{-18}$, but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically-induced transparency (EIT) of an \Al clock ion via a co-trapped \Ca ion during clock interrogation suppresses the heating of the ions. \Al can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time dilation shift of $(-1.69\pm0.20)\times10^{-18}$. The \Ca cooling light introduces an additional light shift on the \Al clock transition of $(-9.27\pm 1.03)\times10^{-18}$. We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with $10^{-19}$ motional and cooling laser-induced uncertainties for \Al and can be employed in other ion clocks as well.

Optical transitions of highly charged ions can be very sensitive to hypothetical beyond-the-Standard-Model phenomena. Those near the $5s-4f$ level crossing, where the $5s$ and $4f$ are degenerate are especially promising. We present predictions from atomic theory and measurements of Os$^{15,16,17+}$ at an electron beam ion trap for identification of several transitions suitable for searches for a hypothetical fifth force and possible violations of local Lorentz invariance. The electric quadrupole (E2) transitions of Os$^{16+}$ that were found are especially suitable for frequency metrology due to their small linewidth of 44 $μ$Hz. Our calculations show the need for including enough inner-shell excitations to predict transition rates between configurations, which can otherwise be overestimated. Ultimately, the predicted interconfiguration transitions were too weak to be detected.

We measured the $g$-factor of the excited state $^3\text{P}_1$ in $\text{Ca}^{14+}$ ion to be $g = 1.499032(6)$ with a relative uncertainty of $4\times10^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a $\text{Be}^+$ ion, co-trapped in the same linear Paul trap as the highly charged $\text{Ca}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the $^3\text{P}_0$ - $^3\text{P}_1$ clock transition. For the $m_J=0\rightarrow m_{J'}=0$ transition, we obtain $C_2 = 0.39\pm0.04\text{HzmT}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement, and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states and QED effects on magnetic moments.

We propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn$^{2+}$ ions confined in a linear RF Paul trap. Sn$^{2+}$ has a unique combination of features that is not available in previously considered ions: a $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn$^{2+}$ Coulomb-crystal clocks.

Questioning the presumably most basic assumptions about the structure of space and time has revolutionized our understanding of Nature. State-of-the-art atomic clocks make it possible to precisely test fundamental symmetry properties of spacetime, and search for physics beyond the standard model at low energy scales of just a few electron volts. Here, we experimentally demonstrate for the first time agreement of two single-ion clocks at the $10^{-18}$ level and directly confirm the validity of their uncertainty budgets over a half-year long comparison period. The two clock ions are confined in separate ion traps with quantization axes aligned along nonparallel directions. Hypothetical Lorentz symmetry violations would lead to sidereal modulations of the frequency offset. From the absence of such modulations at the $10^{-19}$ level we deduce stringent limits on Lorentz symmetry violation parameters for electrons in the range of $10^{-21}$, improving previous limits by two orders of magnitude.

In many applications a source of the black-body radiation (BBR) can be highly anisotropic. This leads to the BBR shift that depends on tensor polarizability and on the projection of the total angular momentum of ions and atoms in a trap. We derived formula for the anisotropic BBR shift and performed numerical calculations of this effect for Ca$^+$ and Yb$^+$ transitions of experimental interest. These ions used for a design of high-precision atomic clocks, fundamental physics tests such as search for the Lorentz invariance violation and space-time variation of the fundamental constants, and quantum information. Anisotropic BBR shift may be one of the major systematic effect in these experiments.