We describe an optical atomic clock based on quantum-logic spectroscopy of the 1 S0 ↔ 3 P0 transition in 27 Al + with a systematic uncertainty of 9.4 × 10 −19 and a frequency stability of 1.2 × 10 −15 / √ 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.

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. Trapped and laser-cooled ions are useful for many applications in quantum information processing and quantum metrology because of their isolation from the ambient environment and mutual Coulomb interaction [1][2][3][4][5][6]. The Coulomb interaction establishes normal modes of motion, called secular modes, which enable information exchange and entanglement between ions. For many operations in quantum information processing and metrology, these secular modes should ideally be prepared in their ground state. For example, in state-of-the-art trapped-ion optical clocks [7], uncertainty in the Doppler shift due to the residual excitation of these modes is a dominant contribution to the total clock uncertainty [8][9][10].All trapped-ion optical clocks to date have been operated with the ions' motion near the Doppler cooling limit [7][8][9][10]. For clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al + [11], the smallest uncertainty has been achieved by performing continuous sympathetic Doppler cooling on the logic ion ( 25 Mg + ) during the clock interrogation [8]. Due to the difficulty of performing accurate temperature measurements of trapped ions near the Doppler cooling limit, the uncertainty of the secular motion temperature was limited to 30 % [8].To reduce the secular motion time-dilation shift and its uncertainty, sub-Doppler cooling techniques can be employed [12][13][14][15][16][17]. These schemes have not previously been implemented in ion-based clock experiments due to high ambient motional heating rates, the need for extra cooling laser beams, and the difficulty of characterizing the resulting motional state distribution, which can be nonthermal [8,10,18]. For example, in sideband cooling, a non-thermal distribution can result from zero-crossings in the cooling transition Rabi rate as a function of the Fock state [19,20] and from cooling durations insufficient to reach equilibrium. Although sideband cooling can reach extremely low energies, a small non-thermal component of the distribution may contribute more than 90 % of the total energy [21], rendering the temperature measurement technique using motional sideband ratios unsuitable for determining the energy [12,13].Here we demonstrate sympathetic cooling of a 25 Mg + -27 ...

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Optical frequencies of the D lines of (6,7)Li were measured with a relative accuracy of 5 × 10⁻¹¹ using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1 MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for ⁶Li and ⁷Li are 10052.837(22) MHz and 10053.435(21) MHz. The splitting isotope shift is 0.599(30) MHz, in reasonable agreement with recent theoretical calculations.