X. Zhang’s research while affiliated with National Institute of Standards and Technology and other places

We implement coherent delocalization as a tool for improving the two primary metrics of atomic clock performance: systematic uncertainty and instability. By decreasing atomic density with coherent delocalization, we suppress cold-collision shifts and two-body losses. Atom loss attributed to Landau-Zener tunneling in the ground lattice band would compromise coherent delocalization at low trap depths for our Yb171 atoms; hence, we implement for the first time delocalization in excited lattice bands. Doing so increases the spatial distribution of atoms trapped in the vertically oriented optical lattice by ∼7 times. At the same time, we observe a reduction of the cold-collision shift by 6.5(8) times, while also making inelastic two-body loss negligible. With these advantages, we measure the trap-light-induced quenching rate and natural lifetime of the P30 excited state as 5.7(7)×10−4 Er−1 s−1 and 19(2) s, respectively.

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the μK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow S10−P30 clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10−19 level.

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the uK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow 1S0-3P0 clock transition in ytterbium to realize sub-recoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10-19 level.

Using frequency comb mediated phase-coherent and synchronous clock comparisons we demonstrate close to a factor of 10 improvement in short-term measurement instability, σ y (τ) < 2 x 10 ⁻¹⁶ @ 1s averaging, between ¹⁷¹ Yb and ²⁷ Al ⁺ optical clocks.

We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our model respects the coupling between axial and radial degrees of freedom, as well as other anharmonicities inherent in the confining potential. We further demonstrate how our model can be used to characterize lattice light shifts in optical lattice clocks, including shifts due to higher-multipolar (magnetic dipole and electric quadrupole) and higher-order (hyperpolarizability) coupling to the lattice field. We compare results for our model with results from other lattice light shift models in the literature under similar conditions.

We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our model respects the coupling between axial and radial degrees of freedom, as well as other anharmonicities inherent in the confining potential. We further demonstrate how our model can be used to characterize lattice light shifts in optical lattice clocks, including shifts due to higher multipolar (magnetic dipole and electric quadrupole) and higher order (hyperpolarizability) coupling to the lattice field. We compare results for our model with results from other lattice light shift models in the literature under similar conditions.

We demonstrate optical frequency comparison of the ¹⁷¹ Yb, ²⁷ Al ⁺ and ⁸⁷ Sr atomic clocks with measurement uncertainties below 1 part in 10 ¹⁷ , and discuss how phase-coherent and synchronous clock comparisons can be used to improve measurement stability.

We have measured the quadratic Zeeman coefficient for the S01↔P03 optical clock transition in Al+27, C2=−71.944(24)MHz/T2, and the unperturbed hyperfine splitting of the Mg+25S1/22 ground electronic state, ΔW/h=1788762752.85(13)Hz, with improved uncertainties. Both constants are relevant to the evaluation of the Al+27 quantum-logic clock systematic uncertainty. The measurement of C2 is in agreement with a previous measurement and a recent calculation at the 1σ level. The measurement of ΔW is in good agreement with a recent measurement and differs from a previously published result by approximately 2σ. With the improved value for ΔW, we deduce an improved value for the nuclear-to-electronic g-factor ratio gI/gJ=9.299308313(60)×10−5 and the nuclear g-factor for the Mg25 nucleus gI=1.86195782(28)×10−4. Using the values of C2 and ΔW presented here, we derive a quadratic Zeeman shift of the Al+27 quantum-logic clock of Δν/ν=−(9241.8±3.7)×10−19, for a bias magnetic field of B≈0.12mT.

The pursuit of ever more precise measures of time and frequency motivates redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on the microwave hyperfine transition in , it is necessary to measure the absolute frequency of candidate optical standards relative to primary cesium references. Armed with independent measurements, a stringent test of optical clocks can be made by comparing ratios of absolute frequency measurements against optical frequency ratios measured via direct optical comparison. Here we measure the transition of using satellite time and frequency transfer to compare the clock frequency to an international collection of national primary and secondary frequency standards. Our measurements consist of 79 runs spanning eight months, yielding the absolute frequency to be 518 295 836 590 863.71(11) Hz and corresponding to a fractional uncertainty of . This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty , limited for the first time by the current realization of the second in the International System of Units (SI). Doing so represents a key step towards an optical definition of the SI second, as well as future optical time scales and applications. Furthermore, these high accuracy measurements distributed over eight months are analyzed to tighten the constraints on variation of the electron-to-proton mass ratio, . Taken together with past Yb and Sr absolute frequency measurements, we infer new bounds on the coupling coefficient to gravitational potential of and a drift with respect to time of .

We have measured the quadratic Zeeman coefficient for the $^{1}S_{0} \leftrightarrow ^{3}P_{0}$ clock transition in $^{27}$Al$^{+}$, $C_{2}=-71.944(24)$ MHz/T$^{2}$, and the unperturbed hyperfine splitting of the $^{25}$Mg$^{+}$ $^{2}S_{1/2}$ ground electronic state, $\Delta W / h = 1~788~762~752.85(13)$ Hz, with improved uncertainties. Both constants are relevant to the evaluation of the $^{27}$Al$^{+}$ quantum-logic clock accuracy. The measurement of $C_{2}$ is in agreement with a previous measurement and a new calculation at the $1\sigma$ level. The measurement of $\Delta W$ is in good agreement with a recent measurement and differs from a previously published result by approximately $2\sigma$. With the improved value for $\Delta W$, we deduce an improved value for the nuclear-to-electronic g-factor ratio $g_{I}/g_{J} = 9.299 ~308 ~313(60) \times 10^{-5}$ and the nuclear g-factor for the $^{25}$Mg$^{+}$ ion $g_{I} = 1.861 ~957 ~82(28) \times 10^{-4}$. Using the values of $C_{2}$ and $\Delta W$ presented here, we derive a quadratic Zeeman shift of the $^{27}$Al$^{+}$ quantum-logic clock of $\Delta \nu / \nu = -(9241.6 \pm 3.7) \times 10^{-19}$, for a bias magnetic field of $B \approx 0.12$ mT.