$^{88}$Sr$^{+}$ optical clock with $7.9\times 10^{-19}$ systematic uncertainty and measurement of its absolute frequency with $9.8\times 10^{-17}$ uncertainty

TL;DR

This work demonstrates a ${}^{88}$Sr$^{+}$ single-ion optical clock achieving a systematic uncertainty of $7.9\times 10^{-19}$, enabled by careful control of blackbody radiation effects, precise differential polarizability knowledge, and low rf heating. The clock employs a six-component Zeeman interrogation scheme with real-time averaging to suppress EQS and tensor Stark shifts, achieving outstanding stability (down to $2.0\times 10^{-15}\tau^{-1/2}$) limited primarily by the clock laser. Absolute-frequency measurements against a remote Cs fountain (CSF2) and against TAI establish values of $444779044095485.5(1.5)\ \text{Hz}$ and $444779044095485.373(44)\ \text{Hz}$, respectively, with the TAI-based result ($9.8\times 10^{-17}$) representing the most accurate optical-frequency measurement to date and implying a CIPM value overestimation by about $1.6\sigma$. The results validate the potential of ${}^{88}$Sr$^{+}$ clocks for metrology and geodesy, and for future integration into optical-clock calibrations of TAI and SI-timekeeping networks.

Abstract

We report on a $^{88}$Sr$^{+}$ single-ion optical clock with an estimated fractional systematic uncertainty of $7.9\times 10^{-19}$. The low uncertainty is enabled by small rf losses, a thorough evaluation of the blackbody-radiation temperature, and our recent measurement of the differential polarizability. A detailed uncertainty evaluation is presented. We also report on two absolute frequency measurements: one against a remote cesium fountain clock and one against International Atomic Time (TAI). The former lasted 12 days and resulted in a frequency value of 444779044095485.49(15) Hz. The latter spanned ten months with monthly optical-clock uptimes between 68% and 99% and yielded a frequency value of 444779044095485.373(44) Hz. With a fractional uncertainty of $9.8\times 10^{-17}$, it is, to our knowledge, the most accurate optical frequency measurement reported to date. Both frequency values are in agreement with other recent measurements, providing further evidence that the 2021 CIPM recommended frequency value is too high by 1.6 times its uncertainty.

Figures (9)

• Figure 1: (a) Partial energy level scheme of ${}^{88}\mathrm{Sr}^+$. Solid arrows indicate lasers, dashed arrows ASE sources. (b) Clock-laser setup and frequency chain to the ${}^{88}\mathrm{Sr}^+$ ion, frequency comb, hydrogen maser (HM), and geodetic GNSS receivers MI04--MI06 for time transfer. HROG---high resolution offset generator. Solid (dotted) lines indicate optical (rf) signals, while dashed lines indicate feedback loops for PDH locking (left), drift compensation of the cavity ($f_\text{drift}$, middle), and tracking the Zeeman components of the clock transition ($f_\text{Zeeman}$, right). AOMs for fiber noise cancellation are not shown.
• Figure 2: (a) Interrogation pulse sequence measured using a fast photodetector. Light pulses and the PMT detection windows are plotted as colored areas (with arbitrary amplitude), while the solid lines indicate the transmission of the mechanical shutter and MEMS switch. (b) Measured Zeeman spectra at a magnetic field of 4.8 with state preparation into either $S_{1/2}$ sublevel $m_J = \pm 1/2$, as labeled below the spectra. The corresponding $D_{5/2}$ sublevels $m_J'$ are labeled above. (c) Servo-cycle sequence for probing the red (R) and blue (B) sides of the Zeeman transitions $|S_{1/2}, m_J\rangle\rightarrow|D_{5/2}, m_{J}'\rangle$. Each of the 24 R or B interrogations consists of the pulse sequence in (a).
• Figure 3: (a) Measured clock self-comparison ADEV (symbols) and $\tau^{-1/2}$ slopes (lines). (b) Measured (520 probe pulses per point) and fitted line shape with 165-ms probe time. The $\pm\Delta f/2$ probing points (B/R) are also shown.
• Figure 4: (a) FEM model of the trap and vacuum chamber showing the simulated temperature distribution for an ambient temperature of $21\;^\circ$C and an rf voltage of 350 V. Materials are labeled in the figure (SS---stainless steel). The Cu rf feedthrough rod (1) and the Shapal heat sink are longer in reality, but are in the FEM model truncated at the point where their temperature was measured to provide well-defined boundary conditions. (b) Measured temperature rise (circles) of selected parts indicated by 1--5 in (a) as a function of the squared rf voltage. Error bars are shown for thermal camera data; for sensor data the uncertainties are smaller than the symbols. The simulated BBR temperature seen by the ion is plotted as crosses. The fit curves are of the form $\Delta T_i(V_\mathrm{rf}) = k_{2,i} V_\mathrm{rf}^2 + k_{4,i} V_\mathrm{rf}^4$. The vertical dash-dotted line indicates the nominal rf voltage.
• Figure 5: (a) Static magnetic field directions used for the Autler-Townes (AT) measurements. Direction 4 is along $Y$, the others displaced by $22^\circ$ in different directions. See Fig. \ref{['fig:BBR']}(a) for coordinate system. (b) Measured AT splittings of the least magnetically sensitive Zeeman pair for direction 1. By measuring a pair, there are four branches to fit, but only three free parameters: line center, Zeeman splitting, and rf Rabi frequency $\Omega_\mathrm{rf}$. The large Zeeman shifts cause optical pumping into $|{}^2\!S_{1/2}, m_J=-1/2\rangle$ by the cooling laser, which explains the difference in excitation probability (state preparation did not work with these field directions). (c) With direction 4, a splitting could barely be resolved at rf resonance with a probe time of 45 ms.