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

We describe an optical atomic clock based on quantum-logic spectroscopy of the ${}^1{S}_0\leftrightarrow {{}^{3}P}_0$ transition in ${}^{27}{\mathrm{Al}}^{+}$ with a systematic uncertainty of $9.4\times {10}^{-19}$ and a frequency stability of $1.2\times {10}^{-15}/\sqrt{\tau }$. A ${}^{25}{\mathrm{Mg}}^{+}$ ion is simultaneously trapped with the ${}^{27}{\mathrm{Al}}^{+}$ ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ${}^{27}{\mathrm{Al}}^{+}$ 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 ${}^{27}{\mathrm{Al}}^{+}$ 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.

Figure 1

Simplified schematic of the quantum-logic clock experimental setup. A frequency-quadrupled Yb-doped fiber laser is locked to the ${{}^{1}S}_0\leftrightarrow {{}^{3}P}_0$ transition ($\lambda \simeq 267\mathrm{nm}$) by alternating the probe direction between two counterpropagating laser beams (shown in violet). An enlarged view of the trapping region is shown on the right. Three nominally orthogonal beams used for micromotion measurements are shown in red. Acousto-optic modulator (AOM), beam splitter (BS), retro-reflector (RR), frequency doubling stage (x2).

Figure 2

Excess micromotion shift evaluation. (a) The sum of the EMM frequency shifts (black points) measured along three nearly orthogonal probe directions from August 2017 to June 2018, with the average and standard deviation (blue line and band). (b) Sample of EMM measurements on three consecutive days. Red points are data taken immediately after initial EMM compensation and blue points are data taken after $\approx 12$ hours of clock operation with interleaved micromotion compensation servos. (c) Histogram of possible total EMM shifts consistent with the measurements generated by a Monte Carlo analysis accounting for the nonorthogonality of the probe directions and assuming the worst-case scenario of either 0 or $\pi$ phase between ion motion along these directions. The total EMM shift of $\mathrm{\Delta }\nu /\nu =-(45.8\pm 5.9)\times {10}^{-19}$ is given by the mean and standard deviation of the calculated distribution and shown in (a) (green line and band). For reference, the red line shown in (c) is a normal (Gaussian) distribution with the same mean and standard deviation.

Figure 3

First-order Doppler shift characterization. (a) Clock transition line shapes for the two opposing probe directions (red and blue points) measured during clock operation without a first-order Doppler servo. Solid lines show fits to a Rabi line shape. The enlarged view shows that the transition probabilities at the probe frequencies used for the frequency lock are not balanced for each direction individually, indicating a non-zero first-order Doppler shift. (b) Similar data taken while running the first-order Doppler servo, with balanced transition probabilities at the lock points. (c) Distribution of possible ion speeds based on the measured first-order Doppler shift with and without an additional velocity constraint from EMM measurements.

Figure 4

Allan deviation of the frequency ratio ${\nu }_{{\mathrm{Al}}^{+}}/{\nu }_{\mathrm{Yb}}$ measured over $\approx 23000\mathrm{s}$. The asymptote is fit to extract a frequency stability of $\sigma (\tau )=1.2\times {10}^{-15}/\sqrt{\tau }$, where $\tau$ is the averaging time in seconds. Anticipated stabilities for a correlation spectroscopy comparison of two single-ion ${}^{27}{\mathrm{Al}}^{+}$ clocks [37] (orange), a single ${}^{27}{\mathrm{Al}}^{+}$ mixed-species correlation comparison [38] (green), and a single ${}^{27}{\mathrm{Al}}^{+}$ ion clock operated using Rabi spectroscopy at the interrogation time of 20.6 s, equal to the excited state lifetime (red) are also shown.