arXiv subjects

K. Beloy

Publications and source records attributed to K. Beloy.

At least 19 recordsLinked to original sources

arXiv2026

Classical-limit formula for matrix elements between bound states of distinct one-dimensional potentials

A classical-limit formula is derived for matrix elements between bound states of distinct one-dimensional potentials. We leave open the physical interpretation of the potentials, but generally envision them to be Born-Oppenheimer-type potentials with the position variable $x$ identifying with a slowly evolving degree of freedom of the system. For instance, $x$ could represent the internuclear separation in a diatomic molecule, with the potentials being potential energy curves for different electronic states. In this scenario, the matrix elements could be, e.g., conventional Franck-Condon factors. To test the derived formula, we assume functional forms for the potentials and operator that afford analytical solutions for the matrix elements. As the classical limit is approached, the computed matrix elements exhibit a clear tendency towards the classical-limit formula, providing strong validation for the formula. In future work, we anticipate using the formula to model inhomogeneous excitation spectra of atoms in one-dimensional optical lattices, with an eye towards improved optical lattice clock performance.

quant-ph↗

arXiv2025

Blackbody radiation Zeeman shift in Rydberg atoms

We consider the Zeeman shift in Rydberg atoms induced by room-temperature blackbody radiation (BBR). BBR shifts to the Rydberg levels are dominated by the familiar BBR Stark shift. However, the BBR Stark shift and the BBR Zeeman shift exhibit different behaviors with respect to the principal quantum number of the Rydberg electron. Namely, the BBR Stark shift asymptotically approaches a constant value given by a universal expression, whereas the BBR Zeeman shift grows steeply with principal quantum number due to the diamagnetic contribution. We show that for transitions between Rydberg states, where only the differential shift between levels is of concern, the BBR Zeeman shift can surpass the BBR Stark shift. We exemplify this in the context of a proposed experiment targeting a precise determination of the Rydberg constant.

physics.atom-ph↗

arXiv2023

Trap-induced ac Zeeman shift of the thorium-229 nuclear clock frequency

We examine the effect of a parasitic rf magnetic field, attributed to ion trapping, on the highly anticipated nuclear clock based on $^{229}$Th$^{3+}$ [C. J. Campbell et al., Phys. Rev. Lett. 108, 120802 (2012)]. The rf magnetic field induces an ac Zeeman shift to the clock frequency. As we demonstrate, this shift threatens to be the dominant systematic frequency shift for the clock, exceeding other systematic frequency shifts and the projected systematic uncertainty of the clock by orders of magnitude. We propose practical means to suppress or eliminate this shift.

physics.atom-ph↗

arXiv2022

High-accuracy optical clocks based on group 16-like highly charged ions

We identify laser-accessible transitions in group 16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground $^{3}P_{J}$ fine structure manifold exhibits irregular (nonmonotonic in $J$) energy ordering for large enough ionization degree. We consider the $|^3P_2\rangle \longleftrightarrow |^3P_0\rangle$ (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are suitable for production in small-scale ion sources and lend themselves to sympathetic cooling and quantum-logic readout with singly charged ions.

physics.atom-ph↗

arXiv2022

Sub-recoil clock-transition laser cooling enabling shallow optical lattice clocks

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.

physics.atom-ph↗

arXiv2021

Prospects of a Pb$^{2+}$ ion clock

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have $I=J=F=0$, where $I$, $J$, and $F$ are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon $E1$+$M1$ process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

physics.atom-ph↗

arXiv2020

Modeling motional energy spectra and lattice light shifts in optical lattice 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.

physics.atom-ph↗

arXiv2019

Measurements of $^{27}$Al$^{+}$ and $^{25}$Mg$^{+}$ magnetic constants for improved ion clock accuracy

We have measured the quadratic Zeeman coefficient for the ${^{1}S_{0} \leftrightarrow {^{3}P_{0}}}$ optical 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, $ΔW / h = 1~788~762~752.85(13)$~Hz, with improved uncertainties. Both constants are relevant to the evaluation of the $^{27}$Al$^{+}$ quantum-logic clock systematic uncertainty. The measurement of $C_{2}$ is in agreement with a previous measurement and a new calculation at the $1~σ$ 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 $g_{I}/g_{J} = 9.299 ~308 ~313(60) \times 10^{-5}$ and the nuclear g-factor for the $^{25}$Mg nucleus $g_{I} = 1.861 ~957 ~82(28) \times 10^{-4}$. Using the values of $C_{2}$ and $ΔW$ presented here, we derive a quadratic Zeeman shift of the $^{27}$Al$^{+}$ quantum-logic clock of $Δν/ ν= -(9241.8 \pm 3.7) \times 10^{-19}$, for a bias magnetic field of $B \approx 0.12$~mT.

physics.atom-ph↗

arXiv2018

Towards Adoption of an Optical Second: Verifying Optical Clocks at the SI Limit

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, $μ=m_e/m_p$. Incorporating our measurements with the entire record of Yb and Sr absolute frequency measurements, we infer a coupling coefficient to gravitational potential of $k_\mathrmμ=(-1.9\pm 9.4)\times10^{-7}$ and a drift with respect to time of $\frac{\dotμ}μ=(5.3 \pm 6.5)\times10^{-17}/$yr.

physics.atom-ph↗

arXiv2018

Two-photon optical frequency reference with active ac Stark shift cancellation

An optical reference based on a two-photon optical transition with ac Stark shift cancellation is proposed. The reference uses two interrogating laser fields at different frequencies. Compared to conventional optical two-photon references, the new approach offers the possibility for improved short-term stability resulting from a higher signal-to-noise and improved long-term stability due to active ac Stark shift cancellation. We demonstrate the ac Stark shift cancellation method on the $5s\,{^2S}_{1/2} \rightarrow 5d\,{^2D}_{5/2}$ two-photon transition in $^{87}$Rb.

physics.atom-ph↗

arXiv2018

Atomic clock performance beyond the geodetic limit

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.

physics.atom-ph↗

arXiv2018

First observation with global network of optical atomic clocks aimed for a dark matter detection

We report on the first earth-scale quantum sensor network based on optical atomic clocks aimed at dark matter (DM) detection. Exploiting differences in the susceptibilities to the fine-structure constant of essential parts of an optical atomic clock, i.e. the cold atoms and the optical reference cavity, we can perform sensitive searches for dark matter signatures without the need of real-time comparisons of the clocks. We report a two orders of magnitude improvement in constraints on transient variations of the fine-structure constant, which considerably improves the detection limit for the standard model (SM) - DM coupling. We use Yb and Sr optical atomic clocks at four laboratories on three continents to search for both topological defect (TD) and massive scalar field candidates. No signal consistent with a dark-matter coupling is identified, leading to significantly improved constraints on the DM-SM couplings.

physics.atom-ph↗

arXiv2018

Hyper-Ramsey spectroscopy with probe laser intensity fluctuations

We examine the influence of probe laser intensity fluctuations on hyper-Ramsey spectroscopy. We assume, as is appropriate for relevant cases of interest, that the probe laser intensity $I$ determines both the Rabi frequency $(\propto\sqrt{I})$ and the frequency shift to the atomic transition $(\propto I)$ during probe laser interactions with the atom. The spectroscopic signal depends on these two quantities that co-vary with fluctuations in the probe laser intensity. Introducing a simple model for the fluctuations, we find that the signature robustness of the hyper-Ramsey method can be compromised. Taking the Yb$^+$ electric octupole clock transition as an example, we quantify the clock error under different levels of probe laser intensity fluctuations.

physics.atom-ph↗

arXiv2018

Faraday-shielded, DC Stark-free optical lattice clock

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.

physics.atom-ph↗

arXiv2017

Hyperpolarizability and operational magic wavelength in an optical lattice clock

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.

physics.atom-ph↗

arXiv2017

Hyperfine-mediated electric quadrupole shifts in Al$^+$ and In$^+$ ion clocks

We evaluate the electric quadrupole moments of the ${^1}\!S_0$ and ${^3}\!P_0$ clock states of $^{27}$Al$^+$ and $^{115}$In$^+$. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For $^{27}$Al$^+$, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are critical to other optical ion clocks.

physics.atom-ph↗

arXiv2016

Ultra-stable optical clock with two cold-atom ensembles

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 $6 \times 10^{-17} / \sqrtτ$ for an averaging time $τ$ 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 $Q> 4 \times 10^{15}$.

physics.atom-ph↗

arXiv2014

An atomic clock with $1\times 10^{-18}$ room-temperature blackbody Stark uncertainty

The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of $5.5 \times 10^{-19}$. Combined with uncertainty in the atomic response, the total uncertainty of the BBR Stark shift is now $1\times10^{-18}$. Further operation of the shield at elevated temperatures enables a direct measure of the BBR shift temperature dependence and demonstrates consistency between our evaluated BBR environment and the expected atomic response.

physics.atom-ph↗