Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional 'flag' qubit serves to detect errors occurring throughout the parity measurement, which would otherwise proliferate into uncorrectable weight-2 errors on the qubit register. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and phase-flip errors, we show that the fault-tolerant protocol is capable of reliably intercepting such faults. For holistic benchmarking of the parity measurement scheme, we use entanglement witnessing to show that the implemented circuit generates genuine six-qubit multi-partite entanglement. The fault-tolerant parity measurement scheme is an essential building block in a broad class of stabilizer quantum error correction protocols, including topological color codes. Our hardware platform is based on atomic ions stored in a segmented microchip ion trap. The qubit register is dynamically reconfigured via shuttling operations, enabling effective full connectivity without operational cross-talk, which provides key capabilities for scalable fault-tolerant quantum computing.

Muons produced in atmospheric cosmic ray showers account for the by far dominant part of the event yield in large-volume underground particle detectors. The IceCube detector, with an instrumented volume of about a cubic kilometer, has the potential to conduct unique investigations on atmospheric muons by exploiting the large collection area and the possibility to track particles over a long distance. Through detailed reconstruction of energy deposition along the tracks, the characteristics of muon bundles can be quantified, and individual particles of exceptionally high energy identified. The data can then be used to constrain the cosmic ray primary flux and the contribution to atmospheric lepton fluxes from prompt decays of short-lived hadrons. In this paper, techniques for the extraction of physical measurements from atmospheric muon events are described and first results are presented. The multiplicity spectrum of TeV muons in cosmic ray air showers for primaries in the energy range from the knee to the ankle is derived and found to be consistent with recent results from surface detectors. The single muon energy spectrum is determined up to PeV energies and shows a clear indication for the emergence of a distinct spectral component from prompt decays of short-lived hadrons. The magnitude of the prompt flux, which should include a substantial contribution from light vector meson di-muon decays, is consistent with current theoretical predictions.

A sample of $1.69\times 10^7$ fully reconstructed $\pi^0\to\gamma e^+e^-$ decay candidates collected by the NA48/2 experiment at CERN in 2003--2004 is analysed to search for the dark photon ($A'$) production in the $\pi^0\to\gamma A'$decay followed by the prompt$A'\to e^+e^-$ decay. No signal is observed, and an exclusion region in the plane of the dark photon mass $m_{A'}$ and mixing parameter $\varepsilon^2$ is established. The obtained upper limits on $\varepsilon^2$ are more stringent than the previous limits in the mass range $9~{\rm MeV}/c^2

We study the quantum gravitational effects in spherically symmetric black hole spacetimes. The effective quantum spacetime felt by a point-like test mass is constructed by ``renormalization group improving'' the Schwarzschild metric. The key ingredient is the running Newton constant which is obtained from the exact evolution equation for the effective average action. The conformal structure of the quantum spacetime depends on its ADM-mass M and it is similar to that of the classical Reissner-Nordstrom black hole. For M larger than, equal to, and smaller than a certain critical mass $M_{\rm cr}$ the spacetime has two, one and no horizon(s), respectively. Its Hawking temperature, specific heat capacity and entropy are computed as a function of M. It is argued that the black hole evaporation stops when M approaches $M_{\rm cr}$ which is of the order of the Planck mass. In this manner a ``cold'' soliton-like remnant with the near-horizon geometry of $AdS_2\times S^2$ is formed. As a consequence of the quantum effects, the classical singularity at r=0 is either removed completely or it is at least much milder than classically; in the first case the quantum spacetime has a smooth de Sitter core which would be in accord with the cosmic censorship hypothesis even if $M

Nth-root gates allow for a paced application of two-qubit operations. We apply them in quantum thermodynamic protocols for operating a quantum heat engine. A set of circuits for two and three qubits are compared by considering maximum work production and related efficiency. Our results show that for all circuits considered and most regions of initial parameter space, quantum coherence of one of the qubits strongly increases the maximum work production and improves the system's performance as a quantum heat engine. In such circuits, coherence is initially imprinted into one of the qubits, improving the overall maximum extractable work. Work gets generated with 84% to 100% efficiency. Further, we uncover a strong linear correlation between work production and many-body correlations in the working medium generated by these gates.

We have combined new high-resolution spectra obtained with the Hubble Space Telescope (HST) and ground-based facilities to make a comprehensive new abundance analysis of the metal-poor, halo star BD +17^\circ 3248. We have detected the third r-process peak elements osmium, platinum, and (for the first time in a metal-poor star) gold, elements whose abundances can only be reliably determined using HST. Our observations illustrate a pattern seen in other similar halo stars with the abundances of the heavier neutron-capture elements, including the third r-process peak elements, consistent with a scaled solar system r-process distribution. The abundances of the lighter neutron-capture elements, including germanium and silver, fall below that same scaled solar r-process curve, a result similar to that seen in the ultra-metal-poor star CS 22892--052. A single site with two regimes or sets of conditions, or perhaps two different sites for the lighter and heavier neutron-capture elements, might explain the abundance pattern seen in this star. In addition we have derived a reliable abundance for the radioactive element thorium. We tentatively identify U II at 3859 A in the spectrum of BD +17^\circ 3248, which makes this the second detection of uranium in a very metal-poor halo star. Our combined observations cover the widest range in proton number (from germanium to uranium) thus far of neutron-capture elements in metal-poor Galactic halo stars. Employing the thorium and uranium abundances in comparison with each other and with several stable elements, we determine an average cosmochronological age for BD +17^\circ 3248 of 13.8 +/- 4 Gyr, consistent with that found for other similar metal-poor halo stars.

A search for heavy neutral lepton ($N$) production in $K^+\to e^+N$ decays using the data sample collected by the NA62 experiment at CERN in 2017--2018 is reported. Upper limits of the extended neutrino mixing matrix element $|U_{e4}|^2$ are established at the level of $10^{-9}$ over most of the accessible heavy neutral lepton mass range 144--462 MeV/$c^2$, with the assumption that the lifetime exceeds 50 ns. These limits improve significantly upon those of previous production and decay searches. The $|U_{e4}|^2$ range favoured by Big Bang Nucleosynthesis is excluded up to a mass of about 340 MeV/$c^2$.

The NA62 experiment reports an investigation of the $K^+\rightarrow\pi^+\nu\bar{\nu}$ mode from a sample of $K^+$ decays collected in 2017 at the CERN SPS. The experiment has achieved a single event sensitivity of $(0.389\pm 0.024)\times10^{-10}$, corresponding to 2.2 events assuming the Standard Model branching ratio of $(8.4\pm1.0)\times10^{-11}$. Two signal candidates are observed with an expected background of 1.5 events. Combined with the result of a similar analysis conducted by NA62 on a smaller data set recorded in 2016, the collaboration now reports an upper limit of $1.78\times10^{-10}$ for the $K^+\rightarrow\pi^+\nu\bar{\nu}$ branching ratio at 90\%\,CL. This, together with the corresponding 68\%\,CL measurement of $(0.48^{+0.72 }_{-0.48})\times10^{-10}$, are currently the most precise results worldwide, and are able to constrain some New Physics models that predict large enhancements still allowed by previous measurements.

Large-scale underground water-Cherenkov neutrino observatories rely on single photon sensors whose sensitive area for Cherenkov photons one wants to maximise. Low dark noise rates and dense module spacing will thereby allow to substantially decrease the energy threshold in future projects. We describe a feasibility study of a novel type of single photon sensor that employs organic wavelength-shifting material (WLS) to capture Cherenkov photons and guide them to a PMT readout. Different WLS materials have been tested in lab measurements as candidates for use in such a sensor and photon capture efficiencies as high as 50 % have been achieved. Based on these findings we estimate that the effective photosensitive area of a prototype built with existing technology can easily exceed that of modules currently used e. g. in IceCube. Additionally, the dark noise rate of such a module can be exceptionally low in the order of 10 Hz. This is of special importance when targeting low-energy neutrinos that yield only few photons that need to be distinguished from noise hits.

FASER is a new experiment designed to search for new light weakly-interacting long-lived particles (LLPs) and study high-energy neutrino interactions in the very forward region of the LHC collisions at CERN. The experimental apparatus is situated 480 m downstream of the ATLAS interaction-point aligned with the beam collision axis. The FASER detector includes four identical tracker stations constructed from silicon microstrip detectors. Three of the tracker stations form a tracking spectrometer, and enable FASER to detect the decay products of LLPs decaying inside the apparatus, whereas the fourth station is used for the neutrino analysis. The spectrometer has been installed in the LHC complex since March 2021, while the fourth station is not yet installed. FASER will start physics data taking when the LHC resumes operation in early 2022. This paper describes the design, construction and testing of the tracking spectrometer, including the associated components such as the mechanics, readout electronics, power supplies and cooling system.

Using data from the IceCube Neutrino Observatory, we searched for high-energy neutrino emission from the gravitational-wave events detected by advanced LIGO and Virgo detectors during their third observing run. We did a low-latency follow-up on the public candidate events released during the detectors' third observing run and an archival search on the 80 confident events reported in GWTC-2.1 and GWTC-3 catalogs. An extended search was also conducted for neutrino emission on longer timescales from neutron star containing mergers. Follow-up searches on the candidate optical counterpart of GW190521 were also conducted. We used two methods; an unbinned maximum likelihood analysis and a Bayesian analysis using astrophysical priors, both of which were previously used to search for high-energy neutrino emission from gravitational-wave events. No significant neutrino emission was observed by any analysis and upper limits were placed on the time-integrated neutrino flux as well as the total isotropic equivalent energy emitted in high-energy neutrinos.

A sample of 3120 $K^\pm\to\pi^\pm\mu^+\mu^-$ decay candidates with $(3.3\pm0.7)$ background contamination has been collected by the NA48/2 experiment at the CERN SPS, allowing a detailed study of the decay properties. The branching ratio was measured to be ${\rm BR}=(9.62\pm0.25)\times 10^{-8}$. The form factor $W(z)$, where $z=(M_{\mu\mu}/M_K)^2$, was parameterized according to several models. In particular, the slope of the linear form factor $W(z)=W_0(1+\delta z)$ was measured to be $\delta=3.11\pm0.57$. Upper limits of $2.9\times 10^{-2}$ and $2.3\times 10^{-2}$ on possible charge asymmetry and forward-backward asymmetry were established at 90% CL. An upper limit {\rm BR}(K^\pm\to\pi^\mp\mu^\pm\mu^\pm)<1.1\times 10^{-9} was established at 90% CL for the rate of the lepton number violating decay.

We experimentally demonstrate a method to determine the temperature of trapped ions which is suitable for monitoring fast thermalization processes. We show that observing and analyzing the lineshape of dark resonances in the fluorescence spectrum provides a temperature measurement which accurate over a large dynamic range, applied to single ions and small ion crystals. Laser induced fluorescence is detected over a time of only $20\,\mu$s allowing for rapid determination of the ion temperature. In the measurement range of $10^{-1}-10^{+2}\,$mK we reach better than $15\,\%$ accuracy. Tuning the cooling laser to selected resonance features allows for controlling the ion temperatures between $0.7\,$mK and more than $10\,$mK. Experimental work is supported by a solution of the 8-level optical Bloch equations when including the ions classical motion. This technique paves the way for many experiments comprising heat transport in ion strings, heat engines, non-equilibrium thermodynamics or thermometry of large ion crystals.

The advent of multi-messenger astronomy has allowed for new types of source searches by neutrino detectors. We present the results of the search for 0.5-100 GeV astrophysical neutrinos detected with IceCube and emitted from compact binary mergers detected by the LIGO, Virgo, and KAGRA interferometers from their first run of observation (O1) to the end of the first part of the fourth (O4a). An innovative approach is used to lower the energy threshold to 0.5 GeV and to search for an excess of GeV neutrinos in time coincidence with astrophysical transient events. Furthermore, we use a statistical combination of all observations, a binomial test, to search for a subpopulation of neutrino emitters. No significant excess was found from the studied mergers, with a best post-trial $p$-value of $40\%$, and there is currently no hint of a population of GeV neutrino emitters found in the IceCube data (post-trial $p$-value = $81\%$).

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As \textit{sensor states}, we use Bell states of the type $\left|\uparrow\downarrow\right>+\text{e}^{\text{i}\varphi}\left|\downarrow\uparrow\right>$ encoded in two $^{40}$Ca$^+$ ions stored at different locations. Due to the linear Zeeman effect, the relative phase $\varphi$ serves to measure the magnetic field difference between the constituent locations, while common-mode fluctuations are rejected. Consecutive measurements on sensor states encoded in the $\text{S}_{1/2}$ ground state and in the $\text{D}_{5/2}$ metastable state are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We measure magnetic field differences over distances of up to $6.2~\text{mm}$, with accuracies of around 300~fT, sensitivities down to $12~\text{pT} / \sqrt{\text{Hz}}$, and spatial resolutions down to $10~\text{nm}$. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.

IceTop, the surface component of the IceCube Neutrino Observatory at the South Pole, is an air shower array with an area of 1 km2. The detector allows a detailed exploration of the mass composition of primary cosmic rays in the energy range from about 100 TeV to 1 EeV by exploiting the correlation between the shower energy measured in IceTop and the energy deposited by muons in the deep ice. In this paper we report on the technical design, construction and installation, the trigger and data acquisition systems as well as the software framework for calibration, reconstruction and simulation. Finally the first experience from commissioning and operating the detector and the performance as an air shower detector will be discussed.

The NA48/2 experiment at CERN collected a large sample of charged kaon decays to final states with multiple charged particles in 2003--2004. A new upper limit on the rate of the lepton number violating decay $K^{\pm}\to\pi^{\mp}\mu^{\pm}\mu^{\pm}$ is reported: \mathcal{B}(K^{\pm}\to\pi^{\mp}\mu^{\pm}\mu^{\pm})<8.6 \times 10^{-11} at 90% CL. Searches for two-body resonances $X$ in $K^{\pm}\to\pi\mu\mu$ decays (such as heavy neutral leptons $N_4$ and inflatons $\chi$) are also presented. In the absence of signals, upper limits are set on the products of branching fractions $\mathcal{B}(K^{\pm}\to\mu^{\pm}N_4)\mathcal{B}(N_4\to\pi\mu)$ and $\mathcal{B}(K^{\pm}\to\pi^{\pm}X)\mathcal{B}(X\to\mu^+\mu^-)$ for ranges of assumed resonance masses and lifetimes. The limits are in the $(10^{-11},10^{-9})$ range for resonance lifetimes below 100 ps.

The first FASER search for a light, long-lived particle decaying into a pair of photons is reported. The search uses LHC proton-proton collision data at $\sqrt{s}=13.6~\text{TeV}$ collected in 2022 and 2023, corresponding to an integrated luminosity of $57.7\text{fb}^{-1}$. A model with axion-like particles (ALPs) dominantly coupled to weak gauge bosons is the primary target. Signal events are characterised by high-energy deposits in the electromagnetic calorimeter and no signal in the veto scintillators. One event is observed, compared to a background expectation of $0.44 \pm 0.39$ events, which is entirely dominated by neutrino interactions. World-leading constraints on ALPs are obtained for masses up to $300~\text{MeV}$ and couplings to the Standard Model W gauge boson, $g_{aWW}$, around $10^{-4}$ GeV$^{-1}$, testing a previously unexplored region of parameter space. Other new particle models that lead to the same experimental signature, including ALPs coupled to gluons or photons, U(1)$_B$ gauge bosons, up-philic scalars, and a Type-I two-Higgs doublet model, are also considered for interpretation, and new constraints on previously viable parameter space are presented in this paper.

Fragmentation functions for eta mesons are extracted at next-to-leading order accuracy of QCD in a global analysis of data taken in electron-positron annihilation and proton-proton scattering experiments. The obtained parametrization is in good agreement with all data sets analyzed and can be utilized, for instance, in future studies of double-spin asymmetries for single-inclusive eta production. The Lagrange multiplier technique is used to estimate the uncertainties of the fragmentation functions and to assess the role of the different data sets in constraining them.

We show that, within a meson-exchange dynamical model describing most of the existing pion electromagnetic production data up to the second resonance region, one is also able to obtain a good agreement with the pi0 photo- and electroproduction data near threshold. The potentials used in the model are derived from an effective chiral Lagrangian. The only sizable discrepancy between our results and the data is in the P-wave amplitude P3 = 2M1+ + M1-, where our prediction underestimate the data by about 20%. In the case of pi0 production, the effects of final state interaction in the threshold region are nearly saturated by single charge exchange rescattering. This indicates that in ChPT it might be sufficient to carry out the calculation just up to one-loop diagrams for threshold neutral pion production.