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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., Comment: 19 pages; accepted to PRA

The pursuit of ever more precise measures of time and frequency is likely to lead to the eventual redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on a microwave transition between hyperfine levels in ground-state $^{133}$Cs, it is necessary to measure the absolute frequency of candidate standards, which is done by comparing against a primary cesium reference. A key verification of this process can be achieved by performing a loop closure$-$comparing frequency ratios derived from absolute frequency measurements against ratios determined from direct optical comparisons. We measure the $^1$S$_0\!\rightarrow^3$P$_0$ transition of $^{171}$Yb by comparing the clock frequency to an international frequency standard with the aid of a maser ensemble serving as a flywheel oscillator. Our measurements consist of 79 separate runs spanning eight months, and we determine the absolute frequency to be 518 295 836 590 863.71(11) Hz, the uncertainty of which is equivalent to a fractional frequency of $2.1\times10^{-16}$. 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 of $<$3$\times10^{-16}$, limited by the current realization of the SI second. We use these measurements to tighten the constraints on variation of the electron-to-proton mass ratio, $\mu=m_e/m_p$. Incorporating our measurements with the entire record of Yb and Sr absolute frequency measurements, we infer a coupling coefficient to gravitational potential of $k_\mathrm{\mu}=(-1.9\pm 9.4)\times10^{-7}$ and a drift with respect to time of $\frac{\dot\mu}{\mu}=(5.3 \pm 6.5)\times10^{-17}/$yr.

The passage of time is tracked by counting oscillations of a frequency reference, such as Earth's revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the $10^{-17}$ level. However, the theory of relativity prescribes that the passage of time is not absolute, but impacted by an observer's reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate optical clock measurements surpassing the present-day ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented levels in three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of $1.4 \times 10^{-18}$, measurement instability of $3.2 \times 10^{-19}$ and reproducibility characterised by ten blinded frequency comparisons, yielding a frequency difference of $[-7 \pm (5)_{stat} \pm (8)_{sys}] \times 10^{-19}$. While differential sensitivity to gravity could degrade the performance of these optical clocks as terrestrial standards of time, this same sensitivity can be used as an exquisite probe of geopotential. Near the surface of Earth, clock comparisons at the $1 \times 10^{-18}$ level provide 1 cm resolution along gravity, outperforming state-of-the-art geodetic techniques. These optical clocks can further be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter., Comment: 32 pages, 5 figures

We demonstrate the absence of a DC Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the DC Stark shift at the $10^{-20}$ level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel non-zero DC Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of DC Stark shifts in optical lattice clocks., Comment: 5 pages + supplemental material; accepted to PRL

Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an $^{171}$Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the $10^{-18}$ level and beyond., Comment: 5 + 2 pages, 3 figures, added supplemental

Atomic clocks based on optical transitions are the most stable, and therefore precise, timekeepers available. These clocks operate by alternating intervals of atomic interrogation with dead time required for quantum state preparation and readout. This non-continuous interrogation of the atom system results in the Dick effect, an aliasing of frequency noise of the laser interrogating the atomic transition. Despite recent advances in optical clock stability achieved by improving laser coherence, the Dick effect has continually limited optical clock performance. Here we implement a robust solution to overcome this limitation: a zero-dead-time optical clock based on the interleaved interrogation of two cold-atom ensembles. This clock exhibits vanishingly small Dick noise, thereby achieving an unprecedented fractional frequency instability of $6 \times 10^{-17} / \sqrt{\tau}$ for an averaging time $\tau$ in seconds. We also consider alternate dual-atom-ensemble schemes to extend laser coherence and reduce the standard quantum limit of clock stability, achieving a spectroscopy line quality factor $Q> 4 \times 10^{15}$.

We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms., Comment: 5+3 pages

Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms held in an optical dipole trap at a range of wavelengths near a calculated magic value.

We present two complementary designs of pneumatically actuated and kinematically positioned optics mounts: one designed for vertical mounting and translation, the other designed for horizontal mounting and translation. The design and measured stability make these mounts well-suited to experiments with laser-cooled atoms.

The competition of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study non-equilibrium magnetization dynamics in an extended 2D system by loading effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the underlying Hamiltonian parameters associated with superexchange and tunneling. Remarkably, with tunneling off-resonantly suppressed, we are able to observe superexchange dominated dynamics over two orders of magnitude in magnetic coupling strength, despite the presence of vacancies. In this regime, the measured timescales are in agreement with simple theoretical estimates, but the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques.

We present a wide array of quantum measures on numerical solutions of 1D Bose- and Fermi-Hubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated "wedding cake" structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von-Neumann entropy, generalized entanglement or Q-measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical vs. grand canonical ensembles and Gutzwiller vs. entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size., Comment: 13 pages, 10 figures