Energy of the 229Th nuclear clock transition

Compact tunable 80 MHz repetition rate vacuum ultraviolet light source up to 10 eV: intracavity high harmonic generation by nonlinear reflection on a AlN nanofilm in a mode locked Ti:sapphire oscillator

We report the realization of an intra-oscillator high harmonic source based on a Kerr lens mode locked Ti:sapphire laser running at 80 MHz repetition rate. A nonlinear medium consisting of an AlN nanofilm on a thin sapphire substrate is placed inside the oscillator cavity. The harmonics are generated, in reflection geometry, on the AlN nanofilm, directing the harmonic beam out of the cavity. Exploiting the benefits of this approach, a compact size, tunable, high repetition rate and coherent vacuum ultraviolet light source with a spectrum up to the 7th harmonic has been achieved. In particular, the powerful 5th harmonic covering the 145-163 nm range aims to be an attractive tunable light source for spectroscopical applications.

Laser Excitation of the Th-229 Nucleus

The 8.4 eV nuclear isomer state in Th-229 is resonantly excited in Th-doped CaF_{2} crystals using a tabletop tunable laser system. A resonance fluorescence signal is observed in two crystals with different Th-229 dopant concentrations, while it is absent in a control experiment using Th-232. The nuclear resonance for the Th^{4+} ions in Th:CaF_{2} is measured at the wavelength 148.3821(5) nm, frequency 2020.409(7) THz, and the fluorescence lifetime in the crystal is 630(15) s, corresponding to an isomer half-life of 1740(50) s for a nucleus isolated in vacuum. These results pave the way toward Th-229 nuclear laser spectroscopy and realizing optical nuclear clocks.

Laser spectroscopy of triply charged 229Th isomer for a nuclear clock

Thorium-229 (229Th) possesses an optical nuclear transition between the ground state (229gTh) and low-lying isomer (229mTh). A nuclear clock based on this nuclear-transition frequency is expected to surpass existing atomic clocks owing to its insusceptibility to surrounding fields1-5. In contrast to other charge states, triply charged 229Th (229Th3+) is the most suitable for highly accurate nuclear clocks because it has closed electronic transitions that enable laser cooling, laser-induced fluorescence detection and state preparation of ions1,6-8. Although laser spectroscopic studies of 229Th3+ in the nuclear ground state have been performed8, properties of 229mTh3+, including its nuclear decay lifetime that is essential to specify the intrinsic linewidth of the nuclear-clock transition, remain unknown. Here we report the trapping of 229mTh3+ continuously supplied by a 233U source and the determination of nuclear decay half-life of the isolated 229mTh3+ to be1,400 - 300 + 600 s through nuclear-state-selective laser spectroscopy. Furthermore, by determining the hyperfine constants of 229mTh3+, we reduced the uncertainty of the sensitivity of the 229Th nuclear clock to variations in the fine-structure constant by a factor of four. These results offer key parameters for the 229Th3+ nuclear clock and its applications in the search for new physics.

Structures and Properties of High-Concentration Doped Th:CaF2 Single Crystals for Solid-State Nuclear Clock Materials

Thorium-doped vacuum ultraviolet (VUV) transparent crystals is a promising candidate for establishing a solid-state nuclear clock. Here, we report the research results on high-concentration doping of 232Th:CaF2 single crystals. The structures, defects, and VUV transmittance performances of highly doped Th:CaF2 crystals are investigated by theoretical and experimental methods. The defect configurations formed by Th and the charge compensation mechanism (Ca vacancy or interstitial F atoms) located at its first nearest neighbor position are mainly considered and studied. The preferred defect configuration is identified according to the doping concentration dependence of structural changes caused by the defects and the formation energies of the defects at different Ca or F chemical potentials. The cultivated Th:CaF2 crystals maintain considerable high VUV transmittance levels while accommodating high doping concentrations, showcasing an exceptional comprehensive performance. The transmittances of 1-mm-thick samples with doping concentrations of 1.91 × 1020 and 2.76 × 1020 cm-3 can reach ∼62% and 53% at 150 nm, respectively. The VUV transmittance exhibits a weak negative doping concentration dependence. The system factors that may cause distortion and additional deterioration of the VUV transmittance are discussed. Balancing and controlling the impacts of various factors will be of great significance for fully exploiting the advantages of Th:CaF2 and other Th-doped crystals for a solid-state nuclear optical clock.

Nonbonding Electron Delocalization Stabilizes the Flexible N8 Molecular Assembly

Electron delocalization has an important impact on the physical properties of condensed materials. However, the L-electron delocalization in inorganic, especially nitrogen, compounds needs exploitation to improve the energy efficiency, safety, and environmental sustainability of high-energy-density materials (HEDMs). This Letter presents an intriguing N8 molecule, ingeniously utilizing nitrogen's L-electron delocalization. The molecule, exhibiting a unique lollipop-shaped conformation, can fold at various angles with very low energy barriers, self-assembling into environmentally stable, all-nitrogen crystals. These crystals demonstrate unparalleled stability, high energy density, low mechanical sensitivity, and optimal electronic thermal conductivity, outperforming existing HEDMs. The remarkable properties of these designed materials are attributed to two distinct delocalized systems within nitrogen's L-shell: π- and lone pair σ-electrons, which not only stabilize the molecular structure but also facilitate interconnected 3D networks of intermolecular nonbonding interactions. This work might pave the way to the experimental synthesis of environmentally stable all-nitrogen solids.

Effects of Electrons on Nuclear Clock Transition Frequency in ^{229}Th Ions

We perform calculations of the energy shift of the nuclear clock transition frequency ^{229}Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant, for example, removing one electron from the atom leads to relative shift of the nuclear frequency ∼10^{-7}, which is 12 orders of magnitude larger than the expected relative uncertainty of the nuclear clock transition frequency (∼10^{-19}). This leads to the difference of the nuclear clock frequencies in Th IV, Th III, Th II, and Th I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.

Resonant X-ray excitation of the nuclear clock isomer 45Sc

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices1. The search for more stable and convenient reference oscillators is continuing2-6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations7-9. One of the most promising cases is an ultra-narrow nuclear resonance transition in 45Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. 10). The scientific potential of 45Sc was realized long ago, but applications require 45Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources11 that have become available only recently. Here we report on resonant X-ray excitation of the 45Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as [Formula: see text] with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

High power optical frequency comb with 10-19 frequency instability

Optical frequency combs with more than 10 W have paved the way for extreme ultraviolet combs generation by interaction with inert gases, leading to extreme nonlinear spectroscopy and the ultraviolet nuclear clock. Recently, the demand for an ultra-long-distance time and frequency space transfer via optical dual-comb proposes a new challenge for high power frequency comb in respect of power scaling and optical frequency stability. Here we present a frequency comb based on fiber chirped pulse amplification (CPA), which can offer more than 20 W output power. We further characterize the amplifier branch noise contribution by comparing two methods of locking to an optical reference and measure the out-of-loop frequency instability by heterodyning two identical high-power combs. Thanks to the low noise CPA, reasonable locking method, and optical path-controlled amplifiers, the out-of-loop beat note between two combs demonstrates the unprecedented frequency stability of 4.35 × 10-17 at 1s and 6.54 × 10-19 at 1000 s.

Pulsed CW laser for long-term spectroscopic measurements at high power in deep-UV

We present a novel technique for in-vacuum cavity-enhanced UV spectroscopy that allows nearly continuous measurements over several days, minimizing mirror degradation caused by high-power UV radiation. Our method relies on pulsing of the cavity's internal power, which increases the UV intensity to maximum only for short periods when the studied atom is within the cavity mode volume while keeping the average power low to prevent mirror degradation. Additionally, this method significantly decreases laser-induced background on charged particle detectors. The described 244 nm laser system is designed for 1S-2S two-photon CW spectroscopy of muonium in the Mu-MASS project. It was tested to provide intracavity powers above 20 W, requiring maintenance only a few times a day. The pulsing technique demonstrates minimal impact on the radiation frequency, with no observed shifts exceeding 15 kHz. Our approach represents a promising new technique for high-precision spectroscopy of atoms in harsh UV environments and demonstrates the feasibility of CW spectroscopy of muonium.

Observation of the radiative decay of the 229Th nuclear clock isomer

The radionuclide thorium-229 features an isomer with an exceptionally low excitation energy that enables direct laser manipulation of nuclear states. It constitutes one of the leading candidates for use in next-generation optical clocks^1-3. This nuclear clock will be a unique tool for precise tests of fundamental physics^4-9. Whereas indirect experimental evidence for the existence of such an extraordinary nuclear state is substantially older¹⁰, the proof of existence has been delivered only recently by observing the isomer's electron conversion decay¹¹. The isomer's excitation energy, nuclear spin and electromagnetic moments, the electron conversion lifetime and a refined energy of the isomer have been measured^12-16. In spite of recent progress, the isomer's radiative decay, a key ingredient for the development of a nuclear clock, remained unobserved. Here, we report the detection of the radiative decay of this low-energy isomer in thorium-229 (^229mTh). By performing vacuum-ultraviolet spectroscopy of ^229mTh incorporated into large-bandgap CaF₂ and MgF₂ crystals at the ISOLDE facility at CERN, photons of 8.338(24) eV are measured, in agreement with recent measurements^14-16 and the uncertainty is decreased by a factor of seven. The half-life of ^229mTh embedded in MgF₂ is determined to be 670(102) s. The observation of the radiative decay in a large-bandgap crystal has important consequences for the design of a future nuclear clock and the improved uncertainty of the energy eases the search for direct laser excitation of the atomic nucleus.

Below-threshold harmonic generation in gas-jets for Th-229 nuclear spectroscopy

The generation of below-threshold harmonics in gas-jets constitutes a promising path towards optical frequency combs in the vacuum ultra-violet (VUV) spectral range. Of particular interest is the 150 nm range, which can be exploited to probe the nuclear isomeric transition of the Thorium-229 isotope. Using widely available high-power, high-repetition-rate Ytterbium-based laser sources, VUV frequency combs can be generated through the process of below-threshold harmonic generation, in particular 7^th harmonic generation of 1030 nm. Knowledge about the achievable efficiencies of the harmonic generation process is crucial for the development of suitable VUV sources. In this work, we measure the total output pulse energies and conversion efficiencies of below-threshold harmonics in gas-jets in a phase-mismatched generation scheme using Argon and Krypton as nonlinear media. Using a 220 fs, 1030 nm source, we reach a maximum conversion efficiency of 1.1 × 10^-5 for the 7^th harmonic (147 nm) and 0.78 × 10^-4 for the 5^th harmonic (206 nm). In addition, we characterize the 3^rd harmonic of a 178 fs, 515 nm source with a maximum efficiency of 0.3%.

Isomeric Excitation of ^{229}Th in Laser-Heated Clusters

We consider theoretically isomeric excitation of ^{229}Th in a laser-heated cluster. A ^{229}Th cluster is first radiated by an intense femtosecond laser pulse, causing ionization of the constituting atoms. The cluster will then survive for a time on the order of 1 ps, during which the electrons collide with the nuclei repeatedly and excite them to the isomeric state. Two mechanisms are responsible for the isomeric excitation: nuclear excitation by electron capture (NEEC) and nuclear excitation by inelastic electron scattering (NEIES). By changing the laser intensity, one can tune between NEEC and NEIES continuously. This laser-heated-cluster scheme not only provides a highly efficient means for isomeric excitation, but also provides an approach for the confirmation of the NEEC process, which has been predicted for over forty years without conclusive experimental verifications.

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)PRLTAO0031-900710.1103/PhysRevLett.108.120802]. 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.

Growth and characterization of thorium-doped calcium fluoride single crystals

We have grown [Formula: see text]Th:CaF[Formula: see text] and [Formula: see text]Th:CaF[Formula: see text] single crystals for investigations on the VUV laser-accessible first nuclear excited state of [Formula: see text]Th, with the aim of building a solid-state nuclear clock. To reach high doping concentrations despite the extreme scarcity (and radioactivity) of [Formula: see text]Th, we have scaled down the crystal volume by a factor 100 compared to established commercial or scientific growth processes. We use the vertical gradient freeze method on 3.2 mm diameter seed single crystals with a 2 mm drilled pocket, filled with a co-precipitated CaF[Formula: see text]:ThF[Formula: see text]:PbF[Formula: see text] powder in order to grow single crystals. Concentrations of [Formula: see text] cm[Formula: see text] have been realized with [Formula: see text]Th with good (> 10%) VUV transmission. However, the intrinsic radioactivity of [Formula: see text]Th drives radio-induced dissociation during growth and radiation damage after solidification. Both lead to a degradation of VUV transmission, currently limiting the [Formula: see text]Th concentration to [Formula: see text] cm[Formula: see text].

Photoelectron tomography with an intra-cavity velocity-map imaging spectrometer at 100 MHz repetition rate

We present a compact velocity-map imaging (VMI) spectrometer for photoelectron imaging at 100 MHz repetition rate. Ultrashort pulses from a near-infrared frequency comb laser are amplified in a polarization-insensitive passive femtosecond enhancement cavity. In the focus, multi-photon ionization (MPI) of gas-phase atoms is studied tomographically by rotating the laser polarization. We demonstrate the functioning of the VMI spectrometer by reconstructing photoelectron angular momentum distributions from xenon MPI. Our intra-cavity VMI setup collects electron energy spectra at high rates, with the advantage of transferring the coherence of the cavity-stabilized femtosecond pulses to the electrons. In addition, the setup will allow studies of strong-field effects in nanometric tips.

Tunable VUV frequency comb for 229mTh nuclear spectroscopy

Laser spectroscopy of the ^229mTh nuclear clock transition is necessary for the future construction of a nuclear-based optical clock. Precision laser sources with broad spectral coverage in the vacuum ultraviolet are needed for this task. Here, we present a tunable vacuum-ultraviolet frequency comb based on cavity-enhanced seventh-harmonic generation. Its tunable spectrum covers the current uncertainty range of the ^229mTh nuclear clock transition.

Fano-like Resonance due to Interference with Distant Transitions

Narrow optical resonances of atoms or molecules have immense significance in various precision measurements, such as testing fundamental physics and the generation of primary frequency standards. In these studies, accurate transition centers derived from fitting the measured spectra are demanded, which critically rely on the knowledge of spectral line profiles. Here, we propose a new mechanism of Fano-like resonance induced by distant discrete levels and experimentally verify it with Doppler-free spectroscopy of vibration-rotational transitions of CO_{2}. The observed spectrum has an asymmetric profile and its amplitude increases quadratically with the probe laser power. Our results facilitate a broad range of topics based on narrow transitions.

New Developments in the Production and Research of Actinide Elements

This article briefly reviews topics related to actinide research discussed at the virtual workshop Atomic Structure of Actinides & Related Topics organized by the University of Mainz, the Helmholtz Institute Mainz, and the GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany, and held on the 26–28 May 2021. It includes references to recent theoretical and experimental work on atomic structure and related topics, such as element production, access to nuclear properties, trace analysis, and medical applications.

Recent advances in the applications of thorium-based metal-organic frameworks and molecular clusters

This perspective highlights the recent advances in the structural and practical aspects of thorium-based metal-organic frameworks (Th-MOFs) and molecular clusters. Thorium, as an underexplored actinide, features surprisingly rich coordination geometries and accessibility of the 5f orbital. These features lead to a myriad of topologies and electronic structures, many of which are undocumented for other tetravalent metal-containing MOFs or clusters. Moreover, Th-MOFs inherit the modularity, structural tunability, porosity, and versatile functionality of the state-of-the-art MOFs. Recognizing the radioactive nature of these thorium-bearing materials that may limit their practical uses, Th-MOFs and Th-clusters still have great potential for various applications, including radionuclide sequestration, hydrocarbon storage/separation, radiation detection, photoswitch, CO₂ conversion, photocatalysis, and electrocatalysis. The objective of this updated perspective is to propose pathways for the renaissance of interest in thorium-based materials.

Extending Our Knowledge about the 229Th Nuclear Isomer

The first nuclear excited state in 229Th possesses the lowest excitation energy of all currently known nuclear levels. The energy difference between the ground- and first-excited (isomeric) state (denoted with 229mTh) amounts only to ≈8.2 eV (≈151.2 nm), which results in several interesting consequences: Since the excitation energy is in the same energy range as the binding energy of valence electrons, the lifetime of 229mTh is strongly influenced by the electronic structure of the Th atom or ion. Furthermore, it is possible to potentially excite the isomeric state in 229Th with laser radiation, which led to the proposal of a nuclear clock that could be used to search for new physics beyond the standard model. In this article, we will focus on recent technical developments in our group that will help to better understand the decay mechanisms of 229mTh, focusing primarily on measuring the radiative lifetime of the isomeric state.

Ground-State g Factor of Highly Charged ^{229}Th Ions: An Access to the M1 Transition Probability between the Isomeric and Ground Nuclear States

A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (∼8  eV) first isomeric state and the ground state of ^{229}Th from a measurement of the ground-state g factor of few-electron ^{229}Th ions. As a tool, the effect of nuclear hyperfine mixing in highly charged ^{229}Th ions such as ^{229}Th^{89+} or ^{229}Th^{87+} is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like ^{229}Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.

Radium Ion Optical Clock

We report the first operation of a Ra^{+} optical clock, a promising high-performance clock candidate. The clock uses a single trapped ^{226}Ra^{+} ion and operates on the 7s ^{2}S_{1/2}→6d ^{2}D_{5/2} electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1×10^{-13}/sqrt[τ], where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν=9×10^{-16}. Using the clock, we realize the first measurement of the ratio of the D_{5/2} state to the S_{1/2} state Landé g-factors: g_{D}/g_{S}=0.598 805 3(11). A Ra^{+} optical clock could improve limits on the time variation of the fine structure constant, α[over ˙]/α, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of ^{229}Th

Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2)  eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.

Exciting the Isomeric ^{229}Th Nuclear State via Laser-Driven Electron Recollision

We propose a new approach to excite the isomeric ^{229}Th nuclear state, which has attracted much attention recently as a potential "nuclear clock." Our approach is based on a laser-driven electron recollision process, the core process of strong-field atomic physics. Bringing together knowledge of recollision physics and of the related nuclear physics, we calculate the isomeric excitation probability. This new approach does not require precise knowledge of the energy of the isomeric state. The excitation is well timed which may be exploited to control the coherence of the isomeric state. Experimental realization is within reach using tabletop laser systems.

XUV frequency comb production with an astigmatism-compensated enhancement cavity

We have developed an extreme ultraviolet (XUV) frequency comb for performing ultra-high precision spectroscopy on the many XUV transitions found in highly charged ions (HCI). Femtosecond pulses from a 100 MHz phase-stabilized near-infrared frequency comb are amplified and then fed into a femtosecond enhancement cavity (fsEC) inside an ultra-high vacuum chamber. The low-dispersion fsEC coherently superposes several hundred incident pulses and, with a single cylindrical optical element, fully compensates astigmatism at the w₀ = 15 µm waist cavity focus. With a gas jet installed there, intensities reaching ∼ 10¹⁴ W/cm² generate coherent high harmonics with a comb spectrum at 100 MHz rate. We couple out of the fsEC harmonics from the 7th up to the 35th (42 eV; 30 nm) to be used in upcoming experiments on HCI frequency metrology.

Shape and electromagnetic properties of the 229mTh isomer

We examine the physical conditions, and specifically the role of the quadrupole-octupole deformation, for the emergence of the 8 eV “clock” isomer 229mTh. Our nuclear structure model suggests that such an extremely low-energy state can be the result of a very fine interplay between the shape and single-particle (s.p.) dynamics in the nucleus. We find that the isomer can only appear in a rather limited region of quadrupoleoctupole deformation space close to a line along which the ground-state and isomer s.p. orbitals 5/2[633] and 3/2[631], respectively, cross each other providing the isomer-formation quasi-degeneracy condition. The crucial role of the octupole deformation in the formation mechanism is pointed out. Our calculations within the outlined deformation region show a smooth behaviour of the 229Th electromagnetic properties, including the isomer decay rate, allowing for their more precise theoretical determination

Absolute X-ray energy measurement using a high-accuracy angle encoder

This paper presents an absolute X-ray photon energy measurement method that uses a Bond diffractometer. The proposed system enables the prompt and rapid in situ measurement of photon energies over a wide energy range. The diffractometer uses a reference silicon single-crystal plate and a highly accurate angle encoder called SelfA. The performance of the system is evaluated by repeatedly measuring the energy of the first excited state of the potassium-40 nuclide. The excitation energy is determined as 29829.39 (6) eV, and this is one order of magnitude more accurate than the previous measurement. The estimated uncertainty of the photon energy measurement was 0.7 p.p.m. as a standard deviation and the maximum observed deviation was 2 p.p.m.

Alpha spectrometric characterization of thin 233U sources for 229(m)Th production

Four different techniques were applied for the production of 233U alpha recoil ion sources, providing 229Th ions. They were compared with respect to a minimum energy spread of the 229Th recoil ions, using the emitted alpha particles as an indicator. The techniques of Molecular Plating, Drop-on-Demand inkjet printing, chelation from dilute nitric acid solution on chemically functionalized silicon surfaces, and self-adsorption on passivated titanium surfaces were used. All fabricated sources were characterized by using alpha spectrometry, radiographic imaging, and scanning electron microscopy. A direct validation for the estimated recoil ion rate was obtained by collecting 228Th recoil ions from 232U recoil ion sources prepared by self-adsorption and Molecular Plating. The chelation and the self-adsorption based approaches appear most promising for the preparation of recoil ion sources delivering monochromatic recoil ions.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Chemical bonding between thorium atoms and a carbon hexagon in carbon nanomaterials

We explore the unusual nature of chemical bonding of thorium atoms with a ring of six carbon atoms (hexagon) in novel carbon materials. Our ab initio calculations of Th-based metallofullerenes (Th@C60 and Th@C20) and Th bound to benzene or coronene at the Hartree-Fock level with the second order perturbation (MP2) correction accounting for the van der Waals interactions demonstrate that the optimal position of the thorium atom is where it faces the center of a hexagon and is located at a distance of 2.01-2.07 Å from the center. For Th encapsulated in C60 it is found at 2.01 Å, whereas the other local energy minima are shifted to larger energies (0.22 eV and higher). Inside C60 the highest local minimum at 1.17 eV is observed when Th faces the center of the five member carbon ring (pentagon). Based on our calculations for Th with benzene and coronene where the global minimum for Th corresponds to its position at 2.05 Å (benzene) or 2.02 Å (coronene) from the hexagon center, we conclude that a well pronounced minimum is likely to be present in graphene and in a single wall carbon nanotube. The ground state of Th is singlet, and other high spin states (triplet and quintet) lie higher in energy (>1.62 eV). We discuss a potential use of carbon nanomaterials with the 229Th isotope having its nuclear transition in the optical range, for metrological purposes.

Measurement of the ^{229}Th Isomer Energy with a Magnetic Microcalorimeter

We present a measurement of the low-energy (0-60 keV) γ-ray spectrum produced in the α decay of ^{233}U using a dedicated cryogenic magnetic microcalorimeter. The energy resolution of ∼10  eV, together with exceptional gain linearity, allows us to determine the energy of the low-lying isomeric state in ^{229}Th using four complementary evaluation schemes. The most precise scheme determines the ^{229}Th isomer energy to be 8.10(17) eV, corresponding to 153.1(32) nm, superseding in precision previous values based on γ spectroscopy, and agreeing with a recent measurement based on internal conversion electrons. We also measure branching ratios of the relevant excited states to be b_{29}=9.3(6)% and b_{42}<0.7%.

Interrogating the Temporal Coherence of EUV Frequency Combs with Highly Charged Ions

A scheme to infer the temporal coherence of EUV frequency combs generated from intracavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, which interact with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at timescales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to δω/ω∼10^{-17}.

Noncollinear Enhancement Cavity for Record-High Out-Coupling Efficiency of an Extreme-UV Frequency Comb

We demonstrate a femtosecond enhancement cavity with a crossed-beam geometry for efficient generation and extraction of extreme-ultraviolet (XUV) frequency combs at a 154 MHz repetition rate. We achieve a record-high out-coupled power of 600  μW, directly usable for spectroscopy, at a wavelength of 97 nm. This corresponds to a >60% out-coupling efficiency. The XUV power scaling and generation efficiency are similar to that achieved with a single Gaussian-mode fundamental beam inside a collinear enhancement cavity. The noncollinear geometry also opens the door for the generation of isolated attosecond pulses at >100  MHz repetition rate.

Nuclear Excitation of the ^{229}Th Isomer via Defect States in Doped Crystals

When Th nuclei are doped in CaF_{2} crystals, a set of electronic defect states appear in the crystal band gap which would otherwise provide complete transparency to vacuum-ultraviolet radiation. The coupling of these defect states to the 8 eV ^{229m}Th nuclear isomer in the CaF_{2} crystal is investigated theoretically. We show that although previously viewed as a nuisance, the defect states provide a starting point for nuclear excitation via electronic bridge mechanisms involving stimulated emission or absorption using an optical laser. The rates of these processes are at least 2 orders of magnitude larger than direct photoexcitation of the isomeric state using available light sources. The nuclear isomer population can also undergo quenching when triggered by the reverse mechanism, leading to a fast and controlled decay via the electronic shell. These findings are relevant for a possible solid-state nuclear clock based on the ^{229m}Th isomeric transition.

Laser Resonance Chromatography of Superheavy Elements

Optical spectroscopy constitutes the historical path to accumulate basic knowledge on the atom and its structure. Former work based on fluorescence and resonance ionization spectroscopy enabled identifying optical spectral lines up to element 102, nobelium. The new challenges faced in this research field are the refractory nature of the heavier elements and the decreasing production yields. A new concept of ion-mobility-assisted laser spectroscopy is proposed to overcome the sensitivity limits of atomic structure investigations persisting in the region of the superheavy elements. The concept offers capabilities of both broadband-level searches and high-resolution hyperfine spectroscopy of synthetic elements beyond nobelium.

Excitation of ^{229m}Th at Inelastic Scattering of Low Energy Electrons

Excitation of the anomalously low lying nuclear isomer ^{229m}Th(3/2^{+},8.28±0.17  eV) in the process of inelastic electron scattering is studied theoretically in the framework of the perturbation theory for the quantum electrodynamics. The calculated cross sections of ^{229m}Th by the extremely low energy electrons in the range 9-12 eV for the Th atom and Th^{1+,4+} ions lie in the range 10^{-25}-10^{-26}  cm^{2}. Being so large, the cross section opens up new possibilities for the effective nonresonant excitation of ^{229m}Th in experiments with an electron beam or electron (electric) current. This can be crucial, since the energy of the isomeric state is currently known with an accuracy insufficient for the resonant excitation by photons. In addition, the cross section of the time reversed process is also large, and as a consequence, the probability of the nonradiative ^{229m}Th decay via the conduction electrons in metal is ≈10^{6}  s^{-1}, that is, close to the internal conversion probability in the Th atom.

DFT calculation of 229thorium-doped magnesium fluoride for nuclear laser spectroscopy

The ²²⁹thorium nucleus has an extremely low-energy isomeric state that could be manipulated with light in the vacuum ultraviolet (VUV) range. Recent measurements based on internal conversion electrons place the isomer energy at 8.28(17) eV (Seiferle B et al 2019), within the transmission window of large-band-gap materials, such as fluoride single crystals. Doping ²²⁹Th into VUV-transparent materials realizes a spectroscopy target with a high nuclei density and might form the basis of a solid-state nuclear clock. This paper presents a theoretical study of the optical properties of a thorium-doped MgF₂ crystal. Using the Vienna Ab-initio Simulation Package, we perform density functional theory calculations of the electronic and optical properties of Th:MgF₂. We determine whether thorium will be accepted as a dopant and identify the charge compensation mechanism and geometry. The simulations indicate, that the band gap of Th-doped MgF₂ will be significantly reduced compared to undoped MgF₂, below the expected ²²⁹Th isomer energy. This result is in striking contrast to a similar study performed for Th-doped CaF₂ (Dessovic P et al 2014 J. Phys. Condens. Matter 26 105402).

Electronic Bridge Excitation in Highly Charged ^{229}Th Ions

The excitation of the 8 eV ^{229m}Th isomer through the electronic bridge mechanism in highly charged ions is investigated theoretically. By exploiting the rich level scheme of open 4f orbitals and the robustness of highly charged ions against photoionization, a pulsed high-intensity optical laser can be used to efficiently drive the nuclear transition by coupling it to the electronic shell. We show how to implement a promising electronic bridge scheme in an electron beam ion trap starting from a metastable electronic state. This setup would avoid the need for a tunable vacuum ultraviolet laser. Based on our theoretical predictions, determining the isomer energy with an uncertainty of 10^{-5}  eV could be achieved in one day of measurement time using realistic laser parameters.

Detection of metastable electronic states by Penning trap mass spectrometry

State-of-the-art optical clocks¹ achieve precisions of 10^-18 or better using ensembles of atoms in optical lattices^2,3 or individual ions in radio-frequency traps^4,5. Promising candidates for use in atomic clocks are highly charged ions⁶ (HCIs) and nuclear transitions⁷, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range⁸ that are accessible to frequency combs⁹. However, insufficiently accurate atomic structure calculations hinder the identification of suitable transitions in HCIs. Here we report the observation of a long-lived metastable electronic state in an HCI by measuring the mass difference between the ground and excited states in rhenium, providing a non-destructive, direct determination of an electronic excitation energy. The result is in agreement with advanced calculations. We use the high-precision Penning trap mass spectrometer PENTATRAP to measure the cyclotron frequency ratio of the ground state to the metastable state of the ion with a precision of 10^-11-an improvement by a factor of ten compared with previous measurements^10,11. With a lifetime of about 130 days, the potential soft-X-ray frequency reference at 4.96 × 10¹⁶ hertz (corresponding to a transition energy of 202 electronvolts) has a linewidth of only 5 × 10^-8 hertz and one of the highest electronic quality factors (10²⁴) measured experimentally so far. The low uncertainty of our method will enable searches for further soft-X-ray clock transitions^8,12 in HCIs, which are required for precision studies of fundamental physics⁶.

The Emergence of Chaos in Quantum Mechanics

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.

Energy of the ^{229}Th Nuclear Clock Isomer Determined by Absolute γ-ray Energy Difference

The low-lying isomeric state of ^{229}Th provides unique opportunities for high-resolution laser spectroscopy of the atomic nucleus. We determine the energy of this isomeric state by taking the absolute energy difference between the excitation energy required to populate the 29.2-keV state from the ground state and the energy emitted in its decay to the isomeric excited state. A transition-edge sensor microcalorimeter was used to measure the absolute energy of the 29.2-keV γ ray. Together with the cross-band transition energy (29.2  keV→ground) and the branching ratio of the 29.2-keV state measured in a recent study, the isomer energy was determined to be 8.30±0.92  eV. Our result is in agreement with the latest measurements based on different experimental techniques, which further confirms that the isomeric state of ^{229}Th is in the laser-accessible vacuum ultraviolet range.