Absolute Frequency Measurements of the D Lines in ^{9}Be^{+} Using a Single Trapped Ion

Optical frequencies of the D line transitions in ^{9}Be^{+} were measured with a relative uncertainty of Δν/ν=5×10^{-11}. The results represent the highest accuracy achieved on a broad electric dipole-allowed (E1) transition in a trapped ion experiment to date, enabled in part by detailed consideration of photon recoil and quantum interference. Measurements were made on a single laser-cooled ion stored in a radio frequency Paul trap, using a spectroscopy laser stabilized to an optical frequency comb and referenced to UTC (NIST). The uncertainties in the D_{1} and D_{2} lines have been reduced by a factor of 10 and 30, respectively, compared to previous work. We have extracted the ^{2}P fine structure splitting, Δν_{fs}=197 064.54(7)  MHz, and the ^{2}P_{1/2} hyperfine constant, A_{P_{1/2}}=-117.92(4)  MHz.

Erratum: ^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18} [Phys. Rev. Lett. 123, 033201 (2019)]

This corrects the article DOI: 10.1103/PhysRevLett.123.033201.

Radium Ion Optical Clock

We report the first operation of a Ra^{+} optical clock, a promising high-performance clock candidate. The clock uses a single trapped ^{226}Ra^{+} ion and operates on the 7s ^{2}S_{1/2}→6d ^{2}D_{5/2} electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1×10^{-13}/sqrt[τ], where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν=9×10^{-16}. Using the clock, we realize the first measurement of the ratio of the D_{5/2} state to the S_{1/2} state Landé g-factors: g_{D}/g_{S}=0.598 805 3(11). A Ra^{+} optical clock could improve limits on the time variation of the fine structure constant, α[over ˙]/α, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ²⁷Al⁺ clock to enable a total fractional systematic uncertainty below 10^-18. For this clock, with 38(19) nPa of room-temperature H₂ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10^-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10^-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the ²⁷Al⁺ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.