A multi-ion optical clock with $\mathbf{5 \times 10^{-19}}$ uncertainty

Abstract

Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below $1\times10^{-18}$. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of $5.3\times10^{-19}$ and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the $10^{-20}$-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of $0.6926711632159660405(20)$, with a statistical uncertainty of $0.9\times10^{-18}$ and a combined uncertainty of $2.9\times 10^{-18}$. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.

Figures (4)

• Figure 1: Overview over experiment. a) Relevant level scheme of 88Sr+ and b) overview over measurement geometry: A chain of ions is trapped in a linear radiofrequency trap. The ions are addressed collectively: laser beams with elliptical cross-section are used for Doppler cooling and state detection (422 nm), state preparation and sideband cooling (674 nm), and repumping (1033 nm and 1092 nm). For clock operation, the ions are interrogated on the ${}^2S_{1/2}\leftrightarrow {}^2D_{5/2}$ clock transition with a 674 nm laser beam propagating along the trap axis. The magnetic field defining the quantization axis is set with an angle of 54.7° w.r.t. the trap axis to suppress the effect of varying electric field gradients along the ion chain (see text for details). c) Key components of the multi-ion optical clock: A narrow-linewidth clock laser is used to repeatedly interrogate the trapped ions on the clock transition. Successful excitation is detected in an ion-resolved fashion using an electron-multiplying charge-coupled device (EMCCD) camera. The experimental control sequence steers the global frequency offset $\Delta f$, which is applied using an acousto-optic modulator (AOM), via direct digital synthesis (DDS). A frequency comb, together with the time-resolved recording of $\Delta f$, enables frequency comparisons with other optical clocks.
• Figure 2: Quadrupole shift variation along the ion chain. a) Ion-resolved quadrupole shift variation for a chain of nine ions. Red data points are results from a measurement with a misalignment of the angle $\theta$ between the magnetic field and the trap axis of about 0.2° from the optimal value of 54.7°. Blue data points are results from a typical measurement run with close to optimal magnetic field alignment. Error bars correspond to statistical uncertainties. Red and blue crosses show the result of a discrete fit of \ref{['eq:qs_var']} to the data, yielding $\Delta\nu_{QS}=4.2(3)\,$mHz and $\Delta\nu_{QS}= 0.3(4)\,$mHz. Solid lines are quadratic fits to guide the eye. b) Simulated frequency shift due to line pulling as a function of the amount of quadrupole shift variation $\Delta\nu_{QS}$ across the ion chain. Each point corresponds to a Monte-Carlo simulation of the clock servo and the same interrogation times and weights as in the experiment. Error bars correspond to statistical uncertainties due to the finite number of simulated clock cycles. The solid lines are fits of the form $ax^2+bx^4$. The green and red dashed vertical lines and shaded areas correspond to the experimental examples in a). The latter corresponds to a clock shift of $0.038(5)\times 10^{-19}$.
• Figure 3: a) Measurements of the ratio between the frequencies $\nu_{\text{Sr}^+}$ of the $^2S_{1/2}\leftrightarrow{}^2D_{5/2}$ transition in 88Sr+ and $\nu_{\text{Yb}^+}$ of the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ transition in 171Yb+. Data points shown in blue were obtained with a single 88Sr+ ion, while data points shown in red correspond to measurements with eight to ten 88Sr+ ions. Error bars correspond to the statistical uncertainties of the individual measurements, assuming white frequency noise for each entire measurement interval. We find $\chi^2_\text{red}\approx1.1$ and an overall statistical uncertainty of $0.9\times10^{-18}$. The dashed line corresponds to the average of all measurements, weighted by their statistical uncertainties, and the grey shaded area depicts the combined overall uncertainty of $2.9\times 10^{-18}$. c) Measurement instability as characterized by the Allan deviation for operation of the 88Sr+ clock with a single ion (shown in blue) and eight to ten ions (shown in red). The error bars are the statistical uncertainties. The solid lines depict fits according to the $1/\sqrt{\tau}$ scaling for white frequency noise. We evaluated about $4.55\times10^6$ s of single-ion data and $1.22\times10^6$ s of multi-ion data, reaching statistical uncertainties of $1.2\times10^{-18}$ and $1.4\times10^{-18}$ respectively.
• Figure 4: Key components in the measurement of $\nu_{\text{Sr}^+}/\nu_{\textrm{E3}}$. Yb1 refers to the 171Yb+ single-ion clock, while YbSr2 refers to the apparatus realizing the new 88Sr+ multi-ion clock. Optical paths are depicted by red and blue lines; electric signals by dashed green lines. The E3 and Sr+ clock lasers are stabilized to optical cavities, and the E3 laser light is frequency doubled before being sent to the ion trap. The short-term stability of an ultrastable silicon cavity (Si) Matei2017 is transferred via a frequency comb to the E3 clock laser Benkler2019. The Sr+ laser frequency is controlled to provide a constant frequency ratio relative to the E3 laser at a frequency comb via the frequency offset $\Delta f_{\text{Sr}^+}$ and the cavity length, thereby inheriting the Si short term stability from the E3 laser. For simplicity, only one frequency comb is depicted, although two coherently linked frequency combs are employed. Spectroscopy of the E3 clock transition steers the corresponding laser frequency via direct digital synthesis (DDS) providing the frequency offset $\Delta f_\text{E3}$, while the frequency of the Sr+ laser is corrected by an additional offset to $\Delta f_2$ directly before the ion trap.