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Modern resonant spectroscopic experiments to measure transition frequencies in atoms have reached a level where a meticulous description of all aspects of the processes under study has become obligatory. The precision achieved in the…
Atomic frequency standards are used to generate accurate and precise time and frequency, enabling many communications, synchronization, and navigation systems in modern life. GPS and other satellite navigation systems, voice and data…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension…
We use advanced computational techniques to study the electronic structure of the Hf$^{12+}$ ion, with the goal of assessing its potential for use in highly accurate atomic optical clocks and search for new physics. Such clocks should…
This work is based on the letter Phys. Lett. B, 865, 139484 (2025), where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian order in General Relativity for a compact…
We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of…
We calculate the dependence of atomic transition frequencies on the fine structure constant, $\alpha = e^2/\hbar c$, for some ions of Ti, Mn, Na, C, and O. The results of these calculations will be used in the search for variation of alpha…
Divalent atoms and ions with a singlet $S$ ground state and triplet $P$ excited state form the basis of many high-precision optical atomic clocks. Along with the metastable $^{3}\mathrm{P}_{0}$ clock state, these atomic systems also have a…
Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly-charged ions (HCIs) made HCIs accessible for high resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
We have developed a broadly-applicable approach that drastically increases the ability to accurately predict properties of complex atoms. We applied it to the case of Ir$^{17+}$, which is of particular interest for the development of novel…
Narrow linewidth optical atomic transitions provide a valuable resource for frequency metrology, and form the basis of today's most precise and accurate clocks. Recent experiments have demonstrated that ensembles of atoms can be interfaced…
Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on…
This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the $^{133}$Cs and $^{87}$Rb atomic fountains are described. Thanks to the routine use of a cryogenic…
The proposal for the development of a nuclear optical clock has triggered a multitude of experimental and theoretical studies. In particular the prediction of an unprecedented systematic frequency uncertainty of about $10^{-19}$ has…
We demonstrate that the present superaccurate measurements of transition processes between atomic states in hydrogen atom reached the limit of accuracy when transition frequency cannot be defined anymore in a unique way. This was predicted…
While optical clock technology has advanced rapidly in recent years, incorporating the technology into operational timescales has progressed more slowly. The highest accuracy frequency standards for groundbreaking measurements do not easily…
Singly-ionized ytterbium, with ultra-narrow optical clock transitions at 467 nm and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the…
Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physical ``constants'' in the Universe. Detection of high-redshift absorption systems intersecting the sight lines towards distant…