Optical atomic clocks promise timekeeping at the highest precision and accuracy, owing to their high operating frequencies. Rigorous evaluations of these clocks require direct comparisons between them. We have realized a high-performance remote comparison of optical clocks over kilometer-scale urban distances, a key step for development, dissemination, and application of these optical standards. Through this remote comparison and a proper design of lattice-confined neutral atoms for clock operation, we evaluate the uncertainty of a strontium (Sr) optical lattice clock at the 1 x 10(-16) fractional level, surpassing the current best evaluations of cesium (Cs) primary standards. We also report on the observation of density-dependent effects in the spin-polarized fermionic sample and discuss the current limiting effect of blackbody radiation-induced frequency shifts.

/pdf/sr-lattice-clock-at-1-x-10-16-fractional-uncertainty-by-ezoqtzzig6.pdf

Sr lattice clock at 1 x 10(-16) fractional uncertainty by remote optical evaluation with a Ca clock.

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wavefunctions, interferometry with atom beams and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

https://iopscience.iop.org/article/10.1088/0953-4075/43/20/202001/pdf

Theory and applications of atomic and ionic polarizabilities

Ultracold neutral plasmas

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition and the differential $g$ factor between the two clock states for alkaline-earth-metal(-like) atoms, using $^{87}\mathrm{Sr}$ as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential $g$ factor in $^{87}\mathrm{Sr}$ is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below ${10}^{\ensuremath{-}17}$ in lattice clocks.

Nuclear spin effects in optical lattice clocks

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Wave-Packet and Coherent Control Dynamics

We report the use of photoassociative spectroscopy to determine the ground-state $s$-wave scattering lengths for the main bosonic isotopes of strontium, $^{86}\mathrm{Sr}$ and $^{88}\mathrm{Sr}$. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{1}P_{1}$ atomic resonance at 461 nm. A minimum in the transition amplitude for $^{86}\mathrm{Sr}$ at $\ensuremath{-}494\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{GHz}$ allows us to determine the scattering lengths $610{a}_{0}l{a}_{86}l2300{a}_{0}$ for $^{86}\mathrm{Sr}$ and a much smaller value of $\ensuremath{-}1{a}_{0}l{a}_{88}l13{a}_{0}$ for $^{88}\mathrm{Sr}$.

/pdf/spectroscopic-determination-of-the-s-wave-scattering-lengths-598a8xo8df.pdf

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr.

Absorption imaging and spectroscopy can probe the dynamics of an ultracold neutral plasma during the first few microseconds after its creation. Quantitative analysis of the data, however, is complicated by the inhomogeneous density distribution, expansion of the plasma and possible lack of global thermal equilibrium for the ions. In this paper, we describe methods for addressing these issues. Using simple assumptions about the underlying temperature distribution and ion motion, the Doppler-broadened absorption spectrum obtained from plasma images can be related to the average temperature in the plasma.

/pdf/absorption-imaging-and-spectroscopy-of-ultracold-neutral-1h0a2wbfux.pdf

Absorption imaging and spectroscopy of ultracold neutral plasmas

We report photoassociative spectroscopy of ${^{88}\mathrm{S}\mathrm{r}}_{2}$ in a magneto-optical trap operating on the $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{1}$ intercombination line at 689 nm. Photoassociative transitions are driven with a laser red detuned by 600--2400 MHz from the $^{1}S_{0}\ensuremath{\rightarrow}^{1}P_{1}$ atomic resonance at 461 nm. Photoassociation takes place at extremely large internuclear separation, and the photoassociative spectrum is strongly affected by relativistic retardation. A fit of the transition frequencies determines the $^{1}P_{1}$ atomic lifetime ($\ensuremath{\tau}=5.22\ifmmode\pm\else\textpm\fi{}0.03\text{ }\text{ }\mathrm{n}\mathrm{s}$) and resolves a discrepancy between experiment and recent theoretical calculations.

/pdf/photoassociative-spectroscopy-at-long-range-in-ultracold-40vu09ele6.pdf

Photoassociative spectroscopy at long range in ultracold strontium.

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Papers

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr.

Absorption imaging and spectroscopy of ultracold neutral plasmas

Photoassociative spectroscopy at long range in ultracold strontium.