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Abstract The performance of a caesium fountain frequency reference for use in precision measurements of trapped antihydrogen in the ALPHA experiment at CERN is evaluated. A description of the fountain is provided together with a characterisation of systematic effects. The impact of the magnetic environment in the Antimatter Factory, where the fountain is installed, on the performance of the fountain is considered and shown to be insignificant. The systematic fractional frequency uncertainty of the fountain is 3.0 × 10^-16. The short-term frequency stability of the measured frequency from the ALPHA-HM1 maser is 1.5 × 10^-13τ^-1/2, whereas the fountain itself shows a stability limit of 4.7 × 10^-14τ^-1/2. We find a fractional frequency difference of (1.0 ± 2.2 (stat.) ± 6.5 (syst.)) × 10^-16 in a comparison with Terrestrial Time via a GNSS Common View satellite link between January 2023 and June 2024. The fountain will enables a significant increase in frequency precision in antihydrogen spectroscopic measurements, and paves the way for improved limits on matter-antimatter comparisons. 

Abstract We have made improvements in the stability, accuracy, and performance of the NRC-FCs2 fountain clock. The dominant systematic effects have been re-evaluated. Optically-stabilized microwaves are used to improve the short-term stability, now reaching $$\sigma_y = 3\;\times10^{-14}\;\tau^{-\frac{1}{2}}$$. We evaluate the distributed cavity phase shift using absorption imaging. This technique dramatically reduces the evaluation time and final uncertainty. We have re-evaluated biases due to microwave leakage and synchronous phase transients with higher accuracy. The total systematic uncertainty of NRC-FCs2 is now $$1.1 \times 10^{-16}$$ in fractional frequency, a factor of $$2$$ improvement over its most recent evaluation. 

Abstract This work describes the apparatus for NIST-F4, an updated cesium atomic fountain at the National Institute of Standards and Technology (NIST), and presents an accuracy evaluation of the fountain as a primary frequency standard. The fountain uses optical molasses to laser cool a cloud of cesium atoms and launch it vertically in a fountain geometry. In high-density mode, the fractional frequency stability of NIST-F4 is ${\sigma }_y\left(\tau \right)=1.5\times {10}^{-13}/\sqrt{\tau }$, whereτis the measurement time in seconds. The short-term stability is limited by quantum projection noise and by phase noise from the local oscillator, an oven-controlled crystal oscillator operating at 5 MHz. Systematic frequency shifts and their uncertainties have been evaluated, resulting in a systematic (type B) fractional frequency uncertainty ${\sigma }_{\mathrm{B}}=2.2\times {10}^{-16}$. 

Abstract Cadmium is laser-cooled and trapped with excitations to triplet states with UVA light, first using only the 67 kHz wide 326 nm intercombination line and subsequently, for large loading rates, the 25 MHz wide 361 nm³P₂→³D₃transition. Eschewing the hard UV 229 nm¹S₀→¹P₁transition, only small magnetic fields gradients, less than 6 G cm⁻¹, are required enabling a 100% transfer of atoms from the 361 nm trap to the 326 nm narrow-line trap. All 8 stable cadmium isotopes are straightforwardly trapped, including two nuclear-spin- $\frac{1}{2}$fermions that require no additional repumping. We observe evidence of³P₂collisions limiting the number of trapped metastable atoms, report isotope shifts for¹¹¹Cd and¹¹³Cd of the 326 nm¹S₀→³P₁, 480nm³P₁→³S₁, and 361 nm³P₂→³D₃transitions, and measure the¹¹⁴Cd 5s5p³P₂→ 5s5d³D₃transition frequency to be 830 096 573(15) MHz. 

Abstract We demonstrate programmable control over the spatial distribution of ultra-cold atoms confined in an optical lattice. The control is facilitated through a combination of spatial manipulation of the magneto-optical trap and atomic population shelving to a metastable state. We first employ the technique to load an extended (5 mm) atomic sample with uniform density in an optical lattice clock (OLC), reducing atomic interactions and realizing remarkable frequency homogeneity across the atomic cloud. We also prepare multiple spatially separated atomic ensembles, and realize multi-ensemble clock operation within the standard one-dimensional (1D) OLC architecture. Leveraging this technique, we prepare two oppositely spin-polarized ensembles that are independently addressable, offering a platform for implementing spectroscopic protocols for enhanced tracking of local oscillator phase. Finally, we demonstrate a relative fractional frequency instability at one second of $2.4\left(1\right)\times {10}^{-17}$between two ensembles, useful for characterization of intra-lattice differential systematics. 

Abstract Isotope shifts (ISs) of atomic energy levels are sensitive probes of nuclear structure and new physics beyond the standard model. We present an analysis of the ISs of the cadmium atom (Cd I) and singly charged cadmium ion (Cd II). ISs of the 229 nm, 326 nm, 361 nm and 480 nm lines of Cd I are measured with a variety of techniques; buffer–gas-cooled beam spectroscopy, capturing atoms in a magneto-optic-trap, and optical pumping. IS constants for the D₁and D₂lines of Cd II are calculated with high accuracy by employing analytical response relativistic coupled-cluster theory in the singles, doubles and triples approximations. Combining the calculations for Cd II with experiments, we infer IS constants for all low-lying transitions in Cd I. We benchmark existing calculations via different many-body methods against these constants. Our calculations for Cd II enable nuclear charge radii of Cd isotopes to be extracted with unprecedented accuracy. The combination of our precise calculations and measurements shows that King plots for Cd I can improve the state-of-the-art sensitivity to a new heavy boson by up to two orders of magnitude. 

We describe a many-channel experiment control system based on a field-programmable gate array (FPGA). The system has 16 bit resolution on 10 analog 100 megasamples-per-second (MS/s) input channels, 14 analog 100 MS/s output channels, 16 slow analog input and output channels, dozens of digital inputs and outputs, and a touchscreen display for experiment control and monitoring. The system can support ten servo loops with 155 ns latency and MHz bandwidths, in addition to as many as 30 lower bandwidth servos. We demonstrate infinite-impulse-response (IIR) proportional–integral–differential filters with 30 ns latency by using only bit-shifts and additions. These IIR filters allow timing margin at 100 MS/s and use fewer FPGA resources than straightforward multiplier-based filters, facilitating many servos on a single FPGA. We present several specific applications: Hänsch–Couillaud laser locks with automatic lock acquisition and a slow dither correction of lock offsets, variable duty cycle temperature servos, and the generation of multiple synchronized arbitrary waveforms.