For the BCS theory of superconductivity, the electron-phonon interaction is transformed to an attractive electron-electron interaction in the vicinity of the Fermi energy only. At the same time, its formal derivation using a unitary transformation reveals that the electrons attract one another whenever their energies do not differ by more than the phonon energy ${\omega }_{\mathrm{D}}$, independent of closeness to the Fermi energy. Consequently, the order parameter becomes finite even away from the Fermi level. Yet, for small interactions, its magnitude is usually small and can be safely ignored, justifying the BCS approximation. Intriguingly, we find that an accumulation of density of states at an energy ${\varepsilon }_{\mathrm{peak}}$ in proximity to the Fermi energy induces a significant order parameter magnitude around ${\varepsilon }_{\mathrm{peak}}$, which exceeds the one at $E_{\mathrm{F}}$ for moderate coupling strengths. This strong enhancement is heralded by the softening of an additional collective mode, which resembles a second phase transition. We predict measurable signatures in the thermodynamic and spectroscopic responses to this unexpected phenomenon, guiding future experimental searches for it. Finally, we demonstrate that these signatures remain robust upon including a phenomenological Coulomb repulsion, indicating that the enhancement is not an artifact of the idealized model.

Resolving the ultrafast decay of metastable electronic states into channels associated with spin-orbit-split ionization thresholds is a long-standing goal of attosecond photoelectron spectroscopy. Here, we use a variant of the rainbow reconstruction of attosecond beating by interference of two-photon transitions technique to study, experimentally and theoretically, the ultrafast dynamics, resolved in photoelectron energy and emission angle, of the autoionizing states comprised in the narrow 177 meV energy gap between the $3p^{-1} {}^{2}P_{3/2}^o$ and ${}^{2}P_{1/2}^o$ thresholds in argon. The scheme employs three pulses: an XUV attosecond pulse train (pump), generated as odd harmonics of a fundamental IR frequency $\omega$; a weak replica of the IR field (driver) that copropagates phase-locked with the pump; and a second IR pulse (probe) with controllable delay $\tau$ with respect to the pump. Two harmonics excite bound states below the ${}^{2}P_{3/2}^o$ threshold and the continuum above the ${}^{2}P_{1/2}^o$ threshold, and their overlapping sideband populates even-parity resonant states between the two thresholds, giving rise to resonant signals beating at both $\omega$ and $2\omega$. From the photoemission cross section and the ${\beta }_2$ and ${\beta }_4$ asymmetry parameters, we resolve both the $nf$ and the $np$ resonant series. In both theory and experiment, the relative weight of the $\omega$ and $2\omega$ beatings changes significantly across the interthreshold gap, an evolution that we trace back to higher-order probe-photon processes. The resonant photoelectron emission is found to be strongly localized in small spots within the $({\beta }_2,{\beta }_4)$ region admissible for two-photon transitions.

We propose a method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate from few micrometers to few hundred nanometers of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate toward the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder force coefficient in the retarded regime ($c_4$). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters, and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of $c_4$ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here, we establish a link between mixed unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions 3 and 4, and show how the method can detect non-mixed-unitary behavior based on incomplete channel tomography.

Data assimilation (DA) optimally fuses observational data with mathematical models, serving as a core computational framework for forecasting complex dynamical systems like the weather. Because manipulating large-scale high-rank error covariances is classically intractable, conventional DA is forced into severe structural compromises such as artificial localization or static parametrizations that destroy genuine cross-variable correlations. Future fault-tolerant quantum computing (FTQC) could offer transformative advantages to overcome these classical computational limits. While quantum linear system solvers theoretically provide exponential speedups for matrix inversion, the practical mapping of large-scale, uncompromised DA onto quantum architectures remains largely unexplored. Our framework builds upon two emerging technologies: FTQC hardware and efficient block-encoded oracles of the error covariance and observation operators, which we envision being supplied by future artificial intelligence surrogate models. Under this premise, we identify a potential bottleneck in the quantum implementation. We show that a direct mapping of the DA equations leads to a quadratic increase in the subnormalization factor ($\alpha$) associated with block encoding when typical nonlocal observations are utilized. To mitigate this algorithmic overhead, we propose a quantum-ready, combined state-observation space formulation. By reconfiguring the DA problem into an expanded saddle-point block-matrix system, our approach avoids the explicit multiplication of nonlocal observation operators. This maintains a linear scaling of $\alpha$ and confines the conditioning of the quantum solver to that of the observation error covariance, decoupled from the severely ill-conditioned prior. Numerical verification using the chaotic Lorenz-96 model demonstrates that our formulation achieves perfect fidelity with the uncompromised DA solution. Although reading out the full analysis state reduces the exponential speedup to a polynomial one, the framework retains a substantial advantage over the classical matrix inversion. This work bridges computational geosciences and quantum information science, providing the essential algorithmic foundation for large-scale DA to become a compelling application for FTQC.

Levitated nanoparticles are being investigated as ultrasensitive quantum sensors of forces and accelerations, with applications ranging from fundamental physics phenomena such as dark matter or quantum gravity to real-world applications. Attention is now turning to multiparticle regimes, and an important question is whether collective effects offer advantages for sensing. We investigate here the spectral characteristics of collective motion of $N$ trapped nanoparticles interacting via the optical mode of a cavity. We find that the collective motion typically exhibits two generic spectral features: a broad spectral feature, the collective bright mode (CBM), which has been previously studied, and a structure of sharp peaks, the mechanical mode comb (MMC). We can describe all the detailed spectral features of the system, with a simple closed-form expression, by reducing the motion to a one-dimensional generic collective mode, which is non-Hermitian. We show that the MMC is more advantageous than the usual CBM for increased sensitivity in force sensing. We find that the mechanical comb can autonomously repair loss of “teeth” due to particle loss, a feature that may offer robustness in sensing.

Molecules containing short-lived isotopes, namely, radioactive molecules, are among the most promising candidates for probing new physics beyond the standard model, although their production and spectroscopic measurements remain technically challenging. Here, we demonstrate an integrated methodology that combines the formation of molecular ion beams in a radio-frequency quadrupole cooler-buncher with collinear laser spectroscopy. As a proof-of-principle experiment, we successfully produce molecular ions ${\mathrm{BaF}}^{+}$ and ${\mathrm{YbF}}^{+}$ via in-trap ion-molecule reactions and perform high-resolution laser spectroscopy of the target molecule ${}^{138}\mathrm{BaF}$. Vibrational and rotational structures of ${}^{138}\mathrm{BaF}$ molecules across different electronic states are obtained using resonance-enhanced multiphoton ionization schemes, confirming the feasibility of the proposed methodology. This work establishes a practical route for future formation and spectroscopic studies of short-lived radioactive molecules, such as those containing ${}^{225}\mathrm{Ra}$, at radioactive ion beam facilities.

We characterize spectroscopic and coherence properties of the 1451.37 nm excited-state zero-phonon line (ZPL) between the ${}^3\mathrm{F}_4$ and the ${}^3\mathrm{H}_4$ manifolds of a thulium-doped yttrium aluminum perovskite (${\mathrm{Tm}}^{3+}:{\mathrm{YAlO}}_3$) crystal at temperatures around 1.5 K. We measure the absorption spectrum between ${}^3\mathrm{H}_6\text{−}{}^3\mathrm{F}_4$ and ${}^3\mathrm{F}_4\text{−}{}^3\mathrm{H}_4$ manifolds, the inhomogeneous broadening of the ${}^3\mathrm{F}_4\text{−}{}^3\mathrm{H}_4$ (excited-state) ZPL, and the lifetimes of the higher-lying and lower-lying excited states. We also investigate level shifts caused by the quadratic Zeeman interaction as well as spectral hole-burning spectra with varying magnetic fields, providing insights into hyperfine interactions. Using spectral holes again but also optical free induction decays, we assess optical coherence times, finding a maximum of $4.75\pm 0.07 \mu \mathrm{s}$ at $B$ = 2 T and low ion concentration in the ${}^3\mathrm{F}_4$ level. Our results—the first to demonstrate coherence of an excited-state transition in a rare-earth crystal—suggest the possibility of exploiting such transitions for quantum technology.

We experimentally demonstrate a nonlinear dependence of the spin-noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin-noise spectroscopy (SNS) near the ${\mathit{D}}_2$ transition of rubidium, a quadratic spin-noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in noninteracting ensembles. This nonlinear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross correlations due to resonant dipole-dipole interaction (ddi) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin-noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.

Block encoding of sparse matrices underpins quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear system solvers, yet its efficient gate-level realization remains challenging, with index-mapping oracles constituting one important source of overhead. We introduce a block-encoding framework that focuses on the index-mapping component, where coherent permutation is used as the central mechanism to optimize shift, delete, and insert operations. This provides a unified treatment of index mapping and reduces local multicontrolled X control complexity through structured compression. We further connect coherent amplitude permutation to combinatorial optimization, enabling systematic assignment of control states under hardware connectivity constraints. The resulting construction supports entrywise block encoding for general sparse matrices, with efficiency gains in structured cases. We demonstrate the approach on representative examples and provide resource analysis using IBM superconducting backends, showing significant reductions in circuit depth.

Nanoscale engineered spin systems, ranging from spins on surfaces to nanographenes, provide flexible platforms to realize entangled quantum magnets from a bottom-up approach. However, assessing the quantum many-body Hamiltonian realized in a specific experiment remains an exceptional open challenge, due to the difficulty of disentangling competing terms accounting for the many-body excitations. Here, we demonstrate a machine learning strategy to learn a quantum many-body spin Hamiltonian from scanning spectroscopy measurements of spin excitations. Our methodology leverages the spatially resolved reconstruction of the many-body excitations induced by depositing quantum impurities next to the quantum magnet. We demonstrate that our algorithm allows us to predict long-range Heisenberg exchange interactions, anisotropic exchange, and antisymmetric Dzyaloshinskii-Moriya interaction, including in the presence of sizable noise. Our methodology establishes defect-induced spatially resolved dynamical excitations in quantum magnets as a powerful strategy to understand the nature of quantum spin many-body models.

One of the surprising, and potentially very useful, capabilities of analog quantum computers, such as D-Wave quantum annealers, is sampling from the Boltzmann, or Gibbs, distribution defined by a classical Hamiltonian. In this study, we thoroughly examine the ability of D-Wave quantum annealers to sample from the Boltzmann distribution defined by a canonical type of competing magnetic frustration $J_1\text{−}{J}_2$ model, the one-dimensional ANNNI (axial next-nearest-neighbor Ising) model. Boltzmann sampling error rate is quantified for standard linear-ramp anneals ranging from 5 ns annealing times up to 2000 µs on two different D-Wave quantum annealing processors. Interestingly, we find some analog hardware parameters that result in a very high accuracy (down to a total variation distance of 0.0003) and low-temperature sampling (down to $\beta =32.2$) in a frustrated region of the ANNNI model magnetic phase diagram. This bolsters the viability of current analog quantum computers for thermodynamic sampling applications of highly frustrated magnetic spin systems.

Flocking is a prime example of how robust collective behavior can emerge from simple interaction rules. The flocking transition has been studied extensively since the inception of the original Vicsek model. Here, we introduce a self-propelled particle model with quenched disorder in the pairwise alignment interaction couplings akin to a spin-glass model. We find that increasing the variance of the coupling distribution can promote (rather than destroy) the emergence of global polar order. In particular, we show that our model can display a flocking phase even when the majority of the interaction couplings are antialigning. Activity is the key ingredient to reduce frustration in the system as it allows local particle clustering combined with self-organization of the particles to favor neighborhoods with strong cooperative interactions.

We elaborate a mechanism for the creation of stable three-dimensional (3D) solitons in spin-orbit-coupled (SOC) atomic-molecular Bose-Einstein condensates, modeled by the mean-field equations with the quadratic three-wave interaction, characterized by mismatch $\alpha$. The planar (effectively two-dimensional) SOC is applied to the soliton’s atomic component, structuring it as a mixed mode (MM) or semivortex (SV). The molecular component of the SV soliton is shaped as a 3D vortex, while the molecular component in the MM soliton is an MM too. The solitons exist up to a critical value of $\alpha$. The system demonstrates a relatively large norm share of the vortex components, exceeding $50\%$ of the total norm, which is an essential feature of SOC-supported solitons. This is a scheme for realizing stable vortex solitons in free space with the quadratic nonlinearity.

Functional connectivity (FC) is fundamentally nonstationary, undergoing continuous reconfigurations that track shifting behavioral and cognitive states. Despite the importance of these transitions, existing analytical frameworks struggle to reconcile the high-dimensional nature of these reconfigurations with the need for structured trajectories and mechanistic interpretability. Specifically, identifying the precise network components responsible for driving these dynamics remains a significant challenge. To bridge this gap, we introduce RONI (Riemannian filtering of network interactions), a geometry-aware, unsupervised framework that treats time-varying FC as a signal evolving on the manifold of symmetric positive semidefinite (SPSD) matrices. By defining intrinsic filtering operators along the SPSD geodesics, RONI produces a multiresolution decomposition of FC dynamics directly on the manifold. This representation allows for the isolation of “dynamic drivers”—specific network elements that dominate coherent connectivity modes across distinct temporal scales. We demonstrate the versatility of RONI by applying it to a diverse array of large-scale neural recordings, including hippocampal electrophysiology data, cortex-wide and dendritic calcium imaging, and human electroencephalography. Across these varied modalities and spatiotemporal scales, RONI identifies biologically meaningful subnetworks that shape the geometry of the connectivity trajectory, providing a unified, interpretable, and quantitative framework for studying the evolution of distributed neural interactions.

Biological cells and synthetic analogues use liquid-liquid phase separation to dynamically compartmentalize their environment for various applications. In many cases, multiple droplets need to coexist, and their size needs to be controlled, which is challenging because large droplets tend to grow at the expense of smaller ones. Chemical reactions can, in principle, control droplet sizes, but there are no clear guidelines on how to robustly achieve size control. To provide guidelines, we consider a binary fluid model driven out of equilibrium by chemical reactions. We reveal two different classes of size-controlled droplets, depending on the ratio of droplet radius to the reaction-diffusion length. Moreover, we determine parameter regimes in which droplets become small. Taken together, our theory allows us to separately predict the chemical reactions necessary for maintaining droplets of a given class or size.

Despite extensive experimental efforts over the past two decades, topological superconductivity and Majorana fermions have remained elusive. By shifting focus from superconductors—whose topological nature is often debated—to the well-established $p$-wave superfluid ${}^3\mathrm{He}$, we propose an experimental approach designed to identify quantum Hall nature of the chiral superfluid ${}^3\mathrm{He}-A$ phase. The method exploits the interaction between surface waves and the induced current transverse to varying density of the superfluid. It allows one to quantitatively measure this Hall current and thus to directly evaluate whether the Hall current is quantized or not. As the quantum Hall effect is a hallmark of topological condensed matter, such an experiment would offer direct evidence of nontrivial topology of superfluid ${}^3\mathrm{He}$. With the advent of microscopic superfluid resonators coupled to optical cavities, this proposal is both realistic and promising, potentially opening the door to future experiments ranging from topological acoustics to fault-tolerant quantum computing.

Quantum networks promise scalable distributed quantum information processing. Realizing this potential depends critically on the efficient use of nonclassical resources. Sequential sharing of quantum nonlocality provides a resource-efficient route for recycling entanglement across multiple observers. In network settings, however, such recycling is typically constrained by a trade-off between the number of active branches and the achievable sharing depth. Here, we investigate this problem in star networks using probabilistic projective measurements. We establish an explicit entanglement threshold above which nonlocality can be shared across all branches up to any target depth, and below which we determine the optimal trade-off between the number of active branches and the achievable number of sequential rounds. We further analyze the protocol’s robustness to noise and its experimental observability, clarifying its practical feasibility. These results establish quantitative design principles and entanglement requirements for scalable nonlocality recycling in quantum networks.