Thorium-229 with its 8.4 eV isomer is a unique system at the interface between nuclear physics and atomic physics, with a nuclear excitation energy in the range of transition energies of valence electrons. The magnetic dipole transition at 148 nm that connects the isomer with the ground state is accessible with the methods of precision laser spectroscopy. Among several possible applications, the development of a nuclear clock seems particularly attractive. This clock would offer high accuracy, high stability, and also high sensitivity in clock-based fundamental tests that involve the strong interaction in addition to electromagnetism. Laser excitation has been demonstrated with Th-229 dopant ions in crystals of calcium fluoride that are transparent in the vacuum-ultraviolet. These experiments can be seen as laser M & ouml;ssbauer spectroscopy where interactions between the nucleus and the crystal lattice can be studied. We are presently searching for the nuclear excitation in atomic Th-229 ions in ion traps where interactions with the environment are well controlled and very high accuracy can be expected, opening the way towards a future primary clock. Thorium-229 mit seinem 8,4-eV-Isomer, dessen Kernanregungsenergie im Bereich der & Uuml;bergangsenergien von Valenzelektronen liegt, ist ein einzigartiges System an der Schnittstelle zwischen Kernphysik und Atomphysik. Der magnetische Dipol & uuml;bergang bei 148 nm, der das Isomer mit dem Grundzustand verbindet, ist f & uuml;r die Methoden der Pr & auml;zisions-Laserspektroskopie zug & auml;nglich. Unter mehreren m & ouml;glichen Anwendungen erscheint die Entwicklung einer Kernuhr besonders attraktiv. Diese Uhr w & uuml;rde eine hohe Genauigkeit, hohe Stabilit & auml;t und auch eine hohe Empfindlichkeit bei Uhren-basierten Tests von Grundlagen der Physik bieten, die neben dem Elektromagnetismus auch die starke Wechselwirkung einbeziehen. Die Laseranregung wurde durchgef & uuml;hrt mit Th-229-Ionen als Dotierung in Kalziumfluorid-Kristallen, die im Vakuum-Ultraviolettbereich transparent sind. Diese Experimente sind eine Art von Laser-M & ouml;ssbauer-Spektroskopie, bei der Wechselwirkungen zwischen dem Kern und dem Kristallgitter untersucht werden k & ouml;nnen. Aktuell versuchen wir die Kernanregung auch mit gespeicherten Th-229-Ionen in Ionenfallen zu beobachten. Hier sind Wechselwirkungen mit der Umgebung gut kontrolliert und es kann eine sehr hohe Genauigkeit erwartet werden. Dies w & uuml;rde den Weg hin zu einer m & ouml;glichen neuen prim & auml;ren Uhr & ouml;ffnen.

Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below 1×10^-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 5.3×10^-19 and up to 10 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 single-ion clock yields an unperturbed frequency ratio of 0.6926711632159660405(20), with a statistical uncertainty of 0.9×10^-18 and a combined uncertainty of 2.9× 10^-18. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.

The recent breakthroughs in the distribution of quantum information and high-precision time and frequency (T F) signals over long-haul optical fibre networks have transformative potential for physically secure communications, resilience of timing infrastructure (such as that supporting Global Navigation Satellite Systems (GNSS)) and fundamental physics. To date, these capabilities remain confined to isolated testbeds, with quantum and T F signals accessible, for example in Germany, to only a few institutions. In this white paper we propose the QTF Backbone: a dedicated national fibre-optic infrastructure in Germany for the networked distribution of Quantum and T F signals using dark fibres and specialised hardware. The QTF Backbone is planned as a four-phase deployment over ten years to ensure scalable, sustainable access for research institutions and industry. The concept builds on successful demonstrations of time and frequency distribution at high Technology Readiness Levels (TRLs) across Europe, including PTB–MPQ links in Germany, REFIMEVE in France, and the Italian LIFT network. The QTF Backbone will enable transformative Research and Development (R D), support a nationwide QTF ecosystem, and ensure the transition from innovation to deployment. As a national and European hub, it will position Germany and Europe at the forefront of quantum networking, as well as T F transfer.

We present a scalable mixed-species Coulomb crystal clock based on the 1S0 <-> 3P0 transition in 115In+. 172Yb+ ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In+-3Yb+ crystal, achieving a relative systematic uncertainty of 2.5 x 10-18 and a relative frequency instability of 1.6 x 10-15/ absolute frequency measurements with an uncertainty of 1.3 x 10-16 and optical frequency comparisons with clocks based on 171Yb+ (E3) and 87Sr. With a fractional uncertainty of 4.4 x 10-18, the former is-to our knowledge-the most accurate frequency ratio value reported to date. For the 115In+/87Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate p ffiffiffiffiffiffiffiffiffiffi operation with four 115In+ clock ions, which reduces the instability to 9.2 x 10-16/ tau/1 s . pffiffiffiffiffiffiffiffiffiffi tau/1 s . We report on

The 10-minute radiative lifetime of the first excited ^229Th^4+ nuclear state in ionic crystals provides narrow spectroscopic linewidths, enabling the realization of a solid-state nuclear clock. Due to the 4+ noble gas configuration, electronic readout or state initialization schemes known from atomic clocks are inaccessible. This elongates the interrogation cycle, which will deteriorate the clock performance. To address this limitation we demonstrate laser-induced quenching (LIQ) as a method of depumping the ^229Th isomer population in CaF_2. We provide experimental evidence for LIQ at different wavelengths (148 - 420 nm) and temperatures (100 - 350 K), achieving a threefold reduction in the isomer lifetime with 20 mW of laser power.

We present a scalable mixed-species Coulomb crystal clock based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{115}In^{+}. ^{172}Yb^{+} ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In^{+}-3Yb^{+} crystal, achieving a relative systematic uncertainty of 2.5×10^{-18} and a relative frequency instability of 1.6×10^{-15}/sqrt[τ/1  s]. We report on absolute frequency measurements with an uncertainty of 1.3×10^{-16} and optical frequency comparisons with clocks based on ^{171}Yb^{+} (E3) and ^{87}Sr. With a fractional uncertainty of 4.4×10^{-18}, the former is-to our knowledge-the most accurate frequency ratio value reported to date. For the ^{115}In^{+}/^{87}Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four ^{115}In^{+} clock ions, which reduces the instability to 9.2×10^{-16}/sqrt[τ/1  s].

The recent laser excitation of the low-lying Th229 isomer transition has started a revolution in ultralight dark matter searches. The enhanced sensitivity of this transition to the large class of dark matter models dominantly coupling to quarks and gluons will ultimately allow us to probe coupling strengths 8 orders of magnitude smaller than the current bounds from optical atomic clocks, which are mainly sensitive to dark matter couplings to electrons and photons. We argue that, with increasing precision, observations of the Th229 excitation spectrum will soon give the world-leading constraints. Using data from the pioneering laser excitation of Th229 by Tiedau [], we present a first dark matter search in the excitation spectrum. While the exclusion limits of our detailed study of the lineshape are still below the sensitivity of currently operating clock experiments, we project the measurement of Zhang [] to surpass it.

A continuous-wave laser source at 148.4 nm based on second-harmonic generation in randomly quasi-phase-matched strontium tetraborate, SrB 4 O 7 , is demonstrated. It provides 1.3 −0.6 +0.7 nW of VUV power in a single pass for an incident UV laser power of 325 mW. The laser system is developed for the resonant laser excitation of the 229 Th nucleus to its low-energy isomeric state. For a frequency-stabilized laser system, we expect to reach similar VUV power spectral densities as in previous pulsed laser excitation experiments of the nuclear transition in 229 Th-doped crystals.

Multi-ion optical clocks offer the possibility of overcoming the low signal-to-noise ratio of single-ion clocks, while still providing low systematic uncertainties. We present simultaneous spectroscopy of up to four In-115(+) clock ions in a linear Coulomb crystal, sympathetically cooled with Yb-172(+) ions. In first clock comparisons, we see agreement below 1 x 10(-17) with results obtained using a single In+ ion, for which we have evaluated the systematic uncertainty to be 2.5 x 10(-18). Operation with four clock ions reduces the instability from 1.6 x 10(-15)/root t/(1s) to 9.2 x 10(-16)/root t/(1s). We derive a model for decay-related dead time during state preparation, which matches the observed scaling of instability with clock ion number N, and indicates that 1/root N scaling can be achieved with the addition of a repump laser.

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.

This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements and the open challenges related to the status of the optical frequency standards, their contribution to time scales and UTC, the possibility of their comparison and the knowledge of the Earth's gravitational potential at the necessary level of uncertainty are discussed. In addition, the mandatory criteria to be achieved before redefinition and their current fulfilment level, together with the redefinition options based on a single or on a set of transitions are described.

Sympathetic cooling of Th$^{3+}$ ions is demonstrated in an experiment where $^{229}$Th and $^{230}$Th are extracted from uranium recoil ion sources and are confined in a linear Paul trap together with laser-cooled $^{88}$Sr$^+$ ions. Because of their similar charge-to-mass ratios the ions are closely coupled and arrange themselves in two-species Coulomb crystals, containing up to a few tens of Th$^{3+}$ ions. To show the suitability of the sympathetically cooled Th$^{3+}$ ions for high-resolution laser spectroscopy, the absolute frequencies and isotope shifts of 5F$_{5/2}$\,$\rightarrow$\,6D$_{5/2}$ and 5F$_{7/2}$\,$\rightarrow$\,6D$_{5/2}$ transitions of $^{230}$Th$^{3+}$ have been measured. The system is developed for hyperfine spectroscopy of electronic transitions of nuclear ground and isomeric states in $^{229}$Th$^{3+}$.

The twisted light modes used in modern atomic physics experiments can be contaminated by small admixtures of plane wave radiation. Although these admixtures hardly reveal themselves in the beam intensity profile, they may seriously affect the outcome of high precision spectroscopy measurements. In the present study we propose a method for diagnosing such a plane wave contamination, which is based on the analysis of the magnetic sublevel population of atoms or ions interacting with the "twisted + plane wave" radiation. In order to theoretically investigate the sublevel populations, we solve the Liouville-von Neumann equation for the time evolution of atomic density matrix. The proposed method is illustrated for the electric dipole $5s \, {}^{2}\mathrm{S}_{1/2} \, - \, 5p \, {}^{2}\mathrm{P}_{3/2}$ transition in Rb induced by (linearly, radially, or azimuthally polarized) vortex light with just a small contamination. We find that even tiny admixtures of plane wave radiation can lead to remarkable variations in the populations of the ground-state magnetic sublevels. This opens up new opportunities for diagnostics of twisted light in atomic spectroscopy experiments.

We present a theoretical study of nondipole excitation of a single trapped atom by twisted light. Special emphasis is placed on effects that arise from the interplay between internal (electronic) and vibrational (centerof-mass) degrees of freedom of an atom. In order to provide a fully quantum mechanical understanding of the excitation, we used the density-matrix approach based on the Liouville-von Neumann equation. The developed theory has been applied to the particular case of the 4s 2S1/2 -> 3d 2D5/2 electric quadrupole (E2) transition in a 40Ca+ ion induced by Laguerre-Gaussian modes. It was found that the Rabi oscillations can show unconventional anharmonic behavior that is attributed to the strong coupling between vibrational levels of the trap. This effect is accompanied by the transfer of angular momentum to the center-of-mass motion and becomes most pronounced when the Rabi frequency is comparable to the trapping frequency.

We report on an evaluation of an optical clock that uses the ^{2}S_{1/2}→^{2}D_{5/2} transition of a single ^{88}Sr^{+} ion as the reference. In contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well-characterized sensitivity to thermal radiation. We measure the clock output frequency against an independent ^{171}Yb^{+} ion clock, based on the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition, and determine the frequency ratio with a total fractional uncertainty of 2.3×10^{-17}. Relying on a previous measurement of the ^{171}Yb^{+} (E3) clock frequency, we find the absolute frequency of the ^{88}Sr^{+} clock transition to be 444 779 044 095 485.277(59) Hz. Our result reduces the uncertainty by a factor of 3 compared with the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. We also show that for three simultaneously interrogated ^{88}Sr^{+} ions, the increased number causes the expected improvement of the short-term frequency instability of the optical clock without degrading its systematic uncertainty.

SummaryThis paper describes the design and operation of an additional, autonomous implementation of UTC(PTB). The realization of this time scale is set-up geographically separated from the primary UTC(PTB) realization. It is based on a passive hydrogen maser, steered via a custom algorithm by either the PTB’s caesium fountains or the BIPM product UTCr. Using a multi-site approach increases the resilience of UTC(PTB) in case of a major accident and allows for additional testing possibilities.

We present improved constraints on the coupling of ultralight bosonic dark matter to photons based on long-term measurements of two optical frequency ratios. In these optical clock comparisons, we relate the frequency of the ^{2}S_{1/2}(F=0)↔^{2}F_{7/2}(F=3) electric-octupole (E3) transition in ^{171}Yb^{+} to that of the ^{2}S_{1/2}(F=0)↔^{2}D_{3/2}(F=2) electric-quadrupole (E2) transition of the same ion, and to that of the ^{1}S_{0}↔^{3}P_{0} transition in ^{87}Sr. Measurements of the first frequency ratio ν_{E3}/ν_{E2} are performed via interleaved interrogation of both transitions in a single ion. The comparison of the single-ion clock based on the E3 transition with a strontium optical lattice clock yields the second frequency ratio ν_{E3}/ν_{Sr}. By constraining oscillations of the fine-structure constant α with these measurement results, we improve existing bounds on the scalar coupling d_{e} of ultralight dark matter to photons for dark matter masses in the range of about (10^{-24}-10^{-17})  eV/c^{2}. These results constitute an improvement by more than an order of magnitude over previous investigations for most of this range. We also use the repeated measurements of ν_{E3}/ν_{E2} to improve existing limits on a linear temporal drift of α and its coupling to gravity.

A tunable vacuum-ultraviolet (VUV) laser source based on four-wave frequency mixing in xenon is presented. Using seed radiation from two continuous-wave lasers, the system allows for precise control of the VUV frequency and is developed for the resonant laser excitation of the Th-229 nucleus to its low-energy isomeric state. The system is prepared to operate in a wide scanning range from 148 nm to 155 nm. The source produces pulses of 6-10 ns duration with up to 40 mu J energy and is coupled via a vacuum beamline to a linear radiofrequency ion trap. In a first implementation of VUV laser spectroscopy of trapped Th+ ions we excite three previously unknown resonance lines near 149 nm wavelength to electronic levels that are close to the Th-229 isomer energy. The resonances are detected and analyzed via fluorescence of the excited Th+ ions. An analysis of the lineshape is used to estimate the linewidth of the VUV radiation to be in the range of <= 6 GHz, dominated by phase noise that is enhanced in harmonic generation and in the four-wave mixing process. The prospects for the use of the system in nuclear laser spectroscopy of Th-229 are discussed.

Progress on optical clocks with laser cooled trapped ions is presented with a focus on two systems that both possess small systematic uncertainties and a high sensitivity in fundamental tests: The 171 Yb + ion with an E3 transition and the 229 Th 3+ ion with a low-energy nuclear transition.