We revisit the extraction of the $|V_{ud}|$ CKM matrix element from the superallowed transition decay rate of $^{26m}$Al$\rightarrow$$^{26}$Mg, focusing on finite nuclear size effects. We show that the dependence of the decay rate of $^{26m}$Al on its charge radius is 4 times greater than previously believed, so it must be determined with high precision. However, for a short-lived isotope of an odd $Z$ element such as $^{26m}$Al, radius extraction relies on challenging many-body atomic calculations. We performed the needed calculations, finding an excellent agreement with previous ones, which used a highly different methodology. This sets a new standard for the reliability of isotope shift factor calculations in many-electron systems. The $\mathcal{F}t$ value obtained from our analysis is lower by $2.2\,\sigma$ than the corresponding value in the previous critical survey, resulting in an increase in $|V_{ud}|^2$ by $0.9\,\sigma$. Adopting $|V_{ud}|$ from this decay alone reduces the CKM unitarity deficit by one standard deviation, irrespective of the choice of $|V_{us}|

Quantum fluctuations and noise are fundamental in quantum technologies, affecting computing, sensing, cryptography, and thermodynamics. These include fluctuations in the variation of energy, charge, and other observables driven by interactions with lasers, amplifiers, and baths. Despite the precise rules quantum mechanics provides for measuring observables at single points in time, no standard framework exists for characterizing the fluctuations of their variations over time. This gap not only makes physical conclusions dependent on the chosen measurement protocol but also leads to inconsistencies in fluctuation predictions, impacting quantum technologies. We propose four basic criteria that any consistent measurement of these variations must satisfy, grounded in conservation laws, the no-signaling principle, and expected constraints on physical realism. We demonstrate that only one protocol fulfills all these criteria: the two-times quantum observables. This result enables the extension of key quantum information concepts, such as entanglement, steering, and Bell's inequalities, to processes rather than instantaneous observables. Beyond resolving ambiguities in quantum fluctuation measurements, our framework offers a foundation for improved fluctuation control in quantum devices, with potential applications in quantum computing, metrology, and thermodynamics.

Although quasiparticles in flat bands have zero group velocity, they can display an anomalous velocity due to the quantum geometry. We address the thermal and thermoelectric transport in flat bands in the clean limit with a small amount of broadening due to inelastic scattering. We derive general Kubo formulas for flat bands in the DC limit up to linear order in the broadening and extract expressions for the thermal conductivity, the Seebeck and Nernst coefficients. We show that the Seebeck coefficient for flat Chern bands is topological up to second order corrections in the broadening. We identify thermal and thermoelectric transport signatures for two generic flat Chern bands and also for the generalized flattened Lieb model, which describes a family of three equally spaced flat Chern bands where the middle one is topologically trivial. Finally, we address the saturation of the quantum metric lower bound for a general family of Hamiltonians with an arbitrary number of flat Chern bands corresponding to SU(2) coherent states. We find that only the extremal bands in this class of Hamiltonians saturate the bound, provided that the momentum dependence of their Hamiltonians is described by a meromorphic function.

The generation and control of extreme ultraviolet (XUV) radiation by high harmonic generation (HHG) have advanced ultrafast science, providing direct insights into electron dynamics on their natural time scale. Attosecond science has established the capability to resolve ultrafast quantum phenomena in matter by characterizing and controlling the classical properties of the high harmonics. Recent theoretical proposals have introduced novel schemes for generating and manipulating XUV HHG with distinct quantum features, paving the way to attosecond quantum optics. In this work, we transfer fundamental concepts in quantum optics into attosecond science. By driving the HHG process with a combination of an infrared bright squeezed vacuum (BSV, a non-classical state of light), and a strong coherent field, we imprint the quantum correlations of the input BSV onto both the ultrafast electron wavefunction and the harmonics' field. Performing in-situ HHG interferometry provides an insight into the underlying sub-cycle dynamics, revealing squeezing in the statistical properties of one of the most fundamental strong-field phenomena -- field induced tunneling. Our measurement allows the reconstruction of the quantum state of the harmonics through homodyne-like tomography, resolving correlated fluctuations in the harmonic field that mirror those of the input BSV. By controlling the delay between the two driving fields, we manipulate the photon statistics of the emitted attosecond pulses with sub-cycle accuracy. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.

In this work we define a new classical constraint satisfaction problem that shares many of the properties of the quantum local Hamiltonian problem, distinguishing it from the usual classical k-SAT problem. The problem consists of minimizing the number of violated local constraints over a restricted set of distributions of assignments. We show that these distributions can be 1-to-1 mapped to a superset of the quantum states, which we call k-local quasi-quantum states. Nevertheless, we claim that our optimization problem is essentially classical, by proving that it is an NP-complete problem. Interestingly, the optimal distribution shares many of the properties of quantum states. In particular, it is not determined straightforwardly by its local marginals, and consequently, it can be used as a classical toy model to study several aspects of Hamiltonian complexity that are different from their classical counter parts. These include the complexity of 1D systems (which is in P for classical CSPs, but is QMA-hard for quantum systems), and the lack of an easy search-to-decision reduction. Finally, we believe that our model can be used to gain insights into the quantum PCP conjecture. Indeed, while we have shown that approximating the minimal number of unsatisfiable constraints to within an Θ(1) is NP-hard, it is not clear if the problem remains hard if we want to approximate the minimal fraction of unsatisfiable constraints to within an Θ(1); as in the quantum PCP conjecture, naive quantization of the classical proofs does not seem to work.

Exploiting the spin-valley degree of freedom of electrons in materials is a promising avenue for energy-efficient information storage and quantum computing. A key challenge in utilizing spin-valley polarization is the realization of spin-valley locking in bulk systems. Here we report a comprehensive study of the noncentrosymmetric bulk misfit compound ${(\mathrm{PbS})}_{1.13}({\mathrm{TaS}}_{2})$, showing a strong spin-valley locking. Our investigation reveals Ising superconductivity with a transition temperature of 3.14 K, closely matching that of a monolayer of ${\mathrm{TaS}}_{2}$. Notably, the absence of charge density wave signatures in transport measurements suggests that the PbS layers primarily act as spacers between the dichalcogenide monolayers. This is further supported by angle-resolved photoemission spectroscopy (ARPES), which shows negligible interlayer coupling, a lack of dispersion along the ${k}_{\ensuremath{\perp}}$ direction, and significant charge transfer from the PbS to the ${\mathrm{TaS}}_{2}$ layers. Spin-resolved ARPES shows strong spin-valley locking of the electronic bands. Muon spin rotation experiments conducted in the vortex phase reveal an isotropic superconducting gap. However, the temperature dependence of the upper critical field and low-temperature specific-heat measurements suggest the possibility of multigap superconductivity. These findings underscore the potential of misfit compounds as robust platforms for both realizing and utilizing spin-valley locking in bulk materials, as well as exploring proximity effects in two-dimensional structures.

We explore the potential of precision spectroscopy of heavy exotic atoms where electrons are substituted by negative hadrons to detect new force carriers with hadronic couplings. The selected transitions are unaffected by nuclear contact terms, thus enabling highly accurate calculations using bound-state QED, provided that the nuclear polarization is under control. Alternatively, we demonstrate that the dipole polarizability, a fundamental property of nuclei, can be extracted from the spectroscopy of exotic atoms in a novel way by combining two transitions while maintaining high sensitivity to new physics. Based on existing data, we extracted world-leading bounds on mediator masses ranging from $0.1\,$MeV to $10\,$MeV for two benchmark models and show that forthcoming experiments could enhance the sensitivity to new physics by two orders of magnitude.

We present a constructive method utilizing the Cartan decomposition to characterize topological properties and their connection to two-qubit quantum entanglement, in the framework of the tenfold classification and Wootters' concurrence. This relationship is comprehensively established for the 2-qubit system through the antiunitary time reversal (TR) operator. The TR operator is shown to identify concurrence and differentiate between entangling and non-entangling operators. This distinction is of a topological nature, as the inclusion or exclusion of certain operators alters topological characteristics. Proofs are presented which demonstrate that the 2-qubit system can be described in the framework of the tenfold classification, unveiling aspects of the connection between entanglement and a geometrical phase. Topological features are obtained systematically by a mapping to a quantum graph, allowing for a direct computation of topological integers and of the 2-qubit equivalent of topological zero-modes. An additional perspective is provided regarding the extension of this new approach to condensed matter systems, illustrated through examples involving indistinguishable fermions and arrays of quantum dots.

Weyl semimetals are a novel class of topological materials with unique electronic structures and distinct properties. HfRhGe stands out as a noncentrosymmetric Weyl semimetal with unconventional superconducting characteristics. Using muon-spin rotation and relaxation (µSR) spectroscopy and thermodynamic measurements, a fully gapped superconducting state is identified in HfRhGe that breaks time-reversal symmetry at the superconducting transition. This breaking can trigger a topological phase transition, as time-reversal symmetry protects the normal-state Weyl topology characterized by comprehensive first-principles calculations. Ginzburg-Landau analysis suggests an unconventional loop supercurrent superconducting state realized in HfRhGe. The presence of multiple Weyl points near the Fermi level and surface Fermi arcs dispersing across the Fermi level further support HfRhGe as a promising platform for topological superconductivity. Additionally, its noncentrosymmetric nature with time-reversal symmetry breaking superconducting state suggests that it can exhibit an intrinsic superconducting diode effect, offering novel optical and transport properties, with potential applications in dissipationless quantum electronics.

The emerging field of free-electron quantum optics enables electron-photon entanglement and holds the potential for generating nontrivial photon states for quantum information processing. Although recent experimental studies have entered the quantum regime, rapid theoretical developments predict that qualitatively unique phenomena only emerge beyond a certain interaction strength. It is thus pertinent to identify the maximal electron-photon interaction strength and the materials, geometries, and particle energies that enable one to approach it. We derive an upper limit to the quantum vacuum interaction strength between free electrons and single-mode photons, which illuminates the conditions for the strongest interaction. Crucially, we obtain an explicit energy selection recipe for electrons and photons to achieve maximal interaction at arbitrary separations and identify two optimal regimes favoring either fast or slow electrons over those with intermediate velocities. We validate the limit by analytical and numerical calculations on canonical geometries and provide near-optimal designs indicating the feasibility of strong quantum interactions. Our findings offer fundamental intuition for maximizing the quantum interaction between free electrons and photons and provide practical design rules for future experiments on electron-photon and electron-mediated photon-photon entanglement. They should also enable the evaluation of key metrics for applications such as the maximum power of free-electron radiation sources and the maximum acceleration gradient of dielectric laser accelerators.