Atomic structure, spectra, collisions, and data. Confined atoms and ions.
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In the present study we determine from the available experimental data the cross section of muon transfer to molecular oxygen at low energies with account of the oxygen molecule structure. Building on an earlier work, the results highlight the role of the molecular structure effects and signifcantly improve the agreement with theoretical calculations of the muon transfer rate. An effcient computational model of the kinetics of processes involving muonic hydrogen atoms in gaseous mixture of H2 and O2 is developed and analyzed. The model is applied in the description of the FAMU experiment for the measurement of the hyperfine splitting in muonic hydrogen and the Zemach radius of the proton.
We report several technical approaches that significantly improve the performance of a vapor-cell atomic electrometer operating in the quasi-DC frequency domain ($\ll$ 1 kHz). With a very small active volume of approximately 11 mm$^3$ inside the vapor cell, we demonstrated a noise floor for electric field (E-field) sensitivity ranging from 0.2 to 7.7 mV/m$\sqrt{\rm Hz}$ for a frequency band of 1--100 Hz. Our work utilizes only a bare vapor cell for electrometry, without any metal parts or electrodes, to ensure minimal distortion of the measured E-field and to minimize the effective sensing volume for high spatial resolution. The E-field-sensitive atomic state (Rydberg state) is excited and read out optically, maximizing the simplicity of the system design and enabling the miniaturization of quasi-DC E-field sensors for potential applications, such as diagnostics of electronics without physical contact, communications in and below the super-low frequency (SLF) band, proximity detection, remote activity surveillance, tracing charge signatures, and research in bioscience and geoscience.
Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below $1\times10^{-18}$. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of $5.3\times10^{-19}$ and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the $10^{-20}$-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of $0.6926711632159660405(20)$, with a statistical uncertainty of $0.9\times10^{-18}$ and a combined uncertainty of $2.9\times 10^{-18}$. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.
The influence of pressure on finite-nuclear-size corrections to atomic energy levels and electron-capture decay rate is investigated in confined hydrogenlike ions. The ions are modeled inside an impenetrable spherical cavity, with a Gaussian distribution used to represent the nuclear charge distribution. For each confinement radius used to simulate external pressure, the energies and wave functions of the lowest-lying bound states are determined by numerically solving the Dirac equation via the kinetically balanced generalized pseudospectral method. In contrast to unconfined ions, both the FNS corrections and electron-capture decay rates increase markedly under pressure and exhibit parallel trends with increasing confinement. Pressure also removes level degeneracies and alters the relative magnitudes of FNS corrections across different bound states. Moreover, the nuclear charge radius is found to significantly affect the pressure-enhanced electron-capture decay rate.
We present a standalone frequency-offset locking system for controlling narrow-linewidth lasers using off-the-shelf electronic components. We lock two frequency-doubled 1560 nm lasers to a stable primary laser operating at 780 nm via their optical beat note. This radio-frequency beat note is fed through a broadband variable divider, a frequency-to-voltage converter, and a proportional-integrator controller to lock each follower laser to a tunable offset frequency relative to the primary. This architecture provides a large capture range ($> 1$ GHz), fast response times ($< 1$ ms), and high linearity. We achieve a frequency resolution of 1.9 kHz and a short-term fractional frequency instability $10^{-11}/\sqrt{τ\rm (s)}$ at 780 nm without the need for a dedicated, precise clock reference. We perform high-resolution spectroscopy of cold $^{87}$Rb atoms to demonstrate the tunability and precision of our locking system. We designed the system to be modular and extensible, making it applicable to a wide variety of atomic physics experiments, including laser cooling, spectroscopy, and quantum sensing with atoms, ions, and molecules.
We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the $Zα$-expansion and the all-order formalism (Furry picture) optimized for the medium-mass range $(3 \leq Z \lesssim 30)$ and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear charge radii, with unprecedented precision.
We demonstrate precision laser spectroscopy of a trapped $^{173}$Yb$^+$ ion that is not directly laser cooled by coupling it to ultracold atoms. The atomic bath continuously cools the internal degrees of freedom of the ion to its hyperfine ground state via spin-exchange collisions. Successful laser excitation is detected via state-selective charge transfer and subsequent ion loss. We probe the $6^2S_{1/2}\rightarrow 6^2P_{3/2}$ transition at 329 nm and measure the magnetic and electric hyperfine interaction constants for the $6^2P_{3/2}$ state to be $A=-241(1)$ MHz and $B=1460(8)$ MHz, respectively. Our results are in agreement with a previous measurement obtained in a hollow-cathode discharge experiment but are a factor of 6-9 more precise. The techniques demonstrated in this work may be extended to perform precision spectroscopy on other ions with complex level structures.
This paper presents the first experimental observation and investigation of a lineshape-asymmetry-caused shift (LACS) in a short-baseline atomic interferometer-gravimeter. It is shown that this shift scales inversely with the cube of the free evolution time, $\propto T^{-3}$, and can lead to a noticeable systematic error in the measured value of the gravitational acceleration g at the level of 0.1-1 mGal ($T\approx$ milliseconds). The obtained results are in good agreement with our previous theoretical studies and highlight the importance of accounting for LACS in high-precision absolute measurements of g in compact atomic gravimeters.
Trapped atomic ion qubits exhibit long coherence times and high fidelity qubit state preparation, manipulation and detection, making them well-suited for scalable quantum computing applications. Among several atomic species used in quantum computing and other application, singly-charged ions of barium stand out due to their long wavelength transitions and the presence of very long-lived metastable internal states. However, elemental barium is a highly reactive metal making it experimentally difficult to work with when making atomic beam sources. In this paper, we demonstrate a method of using resistively heated ovens loaded with a barium magnesium alloy (BaMg) as a source of barium for ion traps. This alloy is not very chemically reactive and does not oxidize in air. We found that a sample of BaMg in a resistively heated oven produced barium vapor pressures on the same order as a metallic barium sample prepared the same way. Two separate ovens, one with a sample of BaMg and one with metallic barium, were used as source for an ion trap. We observed reliable trapping of 138Ba+ ions both with the elemental barium source, and the BaMg source.
Electron emission from hydrogen atoms induced by antiproton impact at intermediate energies is investigated using the one-centre Basis Generator Method within a semi-classical impact-parameter framework. The formulation employs a single-centre expansion of the time-dependent Schrödinger equation with a pseudostate basis consisting of hydrogenic orbitals acted upon by powers of a Yukawa-regularized potential, providing a compact and effective representation of the electronic continuum. Ionization probabilities are obtained by projecting the time-evolved wavefunction onto Coulomb continuum states, from which energy-differential cross sections (EDCS) are extracted. Exponential piecewise functions are constructed to interpolate between the pseudostate eigenenergies, yielding smooth EDCS profiles for each partial wave. The total EDCS, reconstructed by summing over all partial-wave contributions, exhibits good agreement with results from other pseudostate-based approaches.
The rotational excitation of the three asymmetric-top molecular ion isotopologues H$_2$O$^+$, HDO$^+$, and D$_2$O$^+$ is studied theoretically using a combined framework of electron-molecule R-matrix scattering theory, multichannel quantum-defect theory, frame transformation theory, and the Coulomb-Born approximation. The latter two have been adapted here for asymmetric-top rotors. State-resolved cross sections and kinetic rate coefficients for transitions from the rotational ground state of the ions are presented. State-resolved rate coefficients for all calculated transitions $N=0\ldotstwo4$ are included as supplementary material and will be made available through the EMAA database.
Robust laser delivery and stabilization are key components in atom-based quantum technologies, such as quantum computing. Moving these technologies towards product-like deployment requires scalable, compact, cost-effective, and upgradable modules. Here we describe laser systems consisting of application-flexible modules, and demonstrate their performance by characterizing key metrics and by integration with ion trap systems. The laser system is confined to a single server rack and a compact locking station. Both are Class 1 laser products with fiber in-out and electronic control of the laser light. This is achieved through precision manufacture of optical boards that are designed to reduce the degrees of freedom, ease alignment, and increase the robustness to environmental factors. We present a range of 13 wavelengths from 375 nm to 1092 nm: efficiencies from laser source to ion trap range from 21 - 28%, with laser stabilization line widths below 1 MHz.
To time-resolve attosecond electronic dynamics in general photoionization processes, the technique that retrieves the phase of emitted electronic wave packets without intercepting the interactions is essential. Here, we theoretically demonstrate a scheme that uses isolated attosecond pulses (IAPs) to achieve this goal. Our approach utilizes the coherent interference between the electronic wave packets of interest and the one produced by a subsequent IAP. It is shown that the photoelectron spectral phase that has eluded direct detection so far can be fully recovered from observable photoelectron spectra without perturbing the electron-release process under investigation. By further performing a time-frequency-like analysis on the photoelectron energy spectra with the spectral phase, we reveal the birth processes of photoelectrons in time and the association between electronic energy and birth time in strong-field ionization driven by circularly polarized laser pulses. The present work explores a promising application of IAPs for ultrafast measurement and opens a viable venue for investigating electronic dynamics with quantum phase information.
We demonstrate a new magneto-optical trap (MOT) configuration using a simple pair of crossed wires rotated at 45 deg and an appropriate bias field to generate a MOT of >10^8 atoms. The same pair of wires, with slightly adjusted control parameters, is then used to magnetically trap the atoms and cool them via forced evaporative cooling into a Bose-Einstein condensate (BEC) with >10^4 atoms. We present the theoretical framework for generating a quadrupole field using a pair of crossed wires with arbitrary rotation angle, along with the atom chip design and fabrication. Finally, we describe the experimental protocols required for BEC production using only a single crossed-wire atom chip.
We develop an unsupervised physics-informed neural network to solve saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood testbed in which the saddle-point structure is known for tailored driving fields, enabling systematic validation of the proposed solver. The network is trained by minimizing the residual of the SPEs and requires only the definition of the driving-field shape and its parameters, such as intensity, carrier-envelope phase, ellipticity, and relative phase. We introduce a window parametrization strategy that maps network outputs to prescribed regions of the complex-time plane, guiding the optimization toward physically relevant solutions and improving convergence stability. We benchmark the PINN against a conventional solver for a range of fields, demonstrating robust recovery of the dominant complex ionization times over wide parameter ranges. The network tracks changes in ionization event dominance as laser parameters are varied, enabling exploration of regimes where conventional solvers require repeated manual initialization. Using the PINN-derived solutions, we compute coherent ATI photoelectron momentum distributions and show the symmetries of the driving fields are reflected in both the saddle-point structure and the resulting spectra. These results establish PINNs as a promising framework for semiclassical strong-field calculations and provide a foundation for extending machine-learning solvers to Coulomb-corrected models or to more complex processes, such as rescattered ATI for which the SPEs are highly nonlinear and the presence of multiple closely-spaced solutions makes conventional Newton-type root-finding highly sensitive to initial guesses, which hinders systematic investigations across laser-parameter spaces, particularly for tailored fields.
Molecules containing short-lived isotopes, namely radioactive molecules, are among the most promising candidates for probing new physics beyond the Standard Model, although their production and spectroscopic measurements remain technically challenging. Here, we demonstrate an integrated methodology that combines formation of molecular ion beams in a radiofrequency quadrupole cooler-buncher with collinear laser spectroscopy. As a proof-of-principle experiment, we successfully produce molecular ions such as $\rm BaF^+$ and $\rm YbF^+$ via in-trap ion-molecule reactions and perform high-resolution laser spectroscopy of the target molecule $\rm ^{138}BaF$. Vibrational and rotational structures of $\rm ^{138}BaF$ across different electronic states are obtained using resonance-enhanced multiphoton ionization schemes, confirming the feasibility of the proposed methodology. This work establishes a practical route for future formation and spectroscopic studies of short-lived radioactive molecules, such as those containing $\rm ^{225}Ra$, at radioactive ion beam facilities.
We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two channels are composed of coupled trilobite and butterfly electronic states, formed as a result of $S$-wave and $P$-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the $P$-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number $n$, and for certain $n$ there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect we also observe interesting multi-well tunneling effects, during low-energy oscillations for certain $n$-values. Our work serves to highlight that the unique $R$-dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.
The Wigner delay is defined as the energy derivative of the scattering phase of a particle in a given potential, unveiling the time taken (or gained) due to the interaction. The characterisation of this delay plays a central role in attosecond science, where the time resolution allows to gain information on the time interval required for a photoelectron to be emitted into the continuum after the absorption of a single photon. Attosecond interferometric techniques, based on two-colour (extreme ultraviolet and near-infrared) photoionisation schemes, cannot provide a direct measurement of the Wigner delay, because the low-frequency photon contributes with an additional delay, which is imprinted on the outgoing photoelectron. The isolation of the Wigner delay is usually achieved by appealing to the asymptotic approximation, which assumes that the two-photon delay is separable into a Wigner and a near-infrared-induced phase and provides a universal analytical expression for the latter. In this study, we introduce a self-referencing approach based on the implementation of non-consecutive extreme ultraviolet harmonics, in order to test the validity of the asymptotic approximation. We demonstrate its breakdown by observing a deviation of a few tens of milliradians (corresponding to a few attoseconds) between its predictions and the experimentally measured phases of the sideband oscillations generated in our scheme, in agreement with full-dimensional simulations.
Atom interferometric inertial sensors offer exceptional sensitivity but are fundamentally constrained by the periodic phase response of matter-wave interference, which imposes an intrinsic half-fringe dynamic-range limit and prevents continuous inertial tracking. In multi-axis configurations, additional cross coupling between acceleration and rotation further complicates closed-loop operation. Here we demonstrate the first dual-channel closed-loop operation of an atomic beam interferometer, realizing decoupled feedback control of acceleration- and rotation-induced phases and overcoming the half-fringe limitation. Using continuous, transversely cooled $^{87}$Rb atomic beams, the interferometric phases associated with rotation and acceleration are independently extracted, tracked across multiple fringes, and actively compensated through Raman frequency modulation. This closed-loop scheme enables unambiguous measurements up to $\pm1\,\mathrm{^{\circ}/s}$ in rotation and $\pm0.17\,\mathrm{g}$ in acceleration while maintaining high fringe contrast, corresponding to nearly two orders-of-magnitude extension beyond the conventional half-fringe limit. The sensor achieves a long-term stability of $4\times10^{-4}\,\mathrm{^{\circ}/h}$ for rotation and $4\,\mathrm{μg}$ for acceleration at an averaging time of $1000\,\mathrm{s}$. By converting the intrinsically periodic interferometric response into stabilized phase-encoded inertial channels, this work establishes a new operating regime for atomic beam interferometry and advances matter-wave sensors toward practical quantum inertial navigation under dynamic conditions.
Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.