Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, a practical continuous-variable bosonic code that can simultaneously correct both photon loss and dephasing errors, while achieving a high level of compliance with the Knill-Laflamme conditions within an experimentally friendly structure, remains elusive. Here, we propose a code based on the superposition of squeezed Fock states with an error-correcting capability that scales as $\propto \exp (-7r)$, where $r$ is the squeezing level. The codewords remain orthogonal at all squeezing levels. In particular, this code achieves high-precision error correction for both single-photon loss and dephasing, even at moderate squeezing levels. Building on this code, we develop quantum error correction schemes that exceed the breakeven point, supported by analytical derivations of all necessary quantum gates. Our code offers a competitive alternative to previous encodings for quantum computation using continuous bosonic qubits.

We report on high-resolution laser spectroscopy of ${}^{255}\mathrm{Fm}$ ($T_{1/2}=20\mathrm{h}$), one of the heaviest nuclides available from reactor breeding. The hyperfine structures in two different atomic ground-state transitions at 398.4 nm and 398.2 nm were probed by in-source laser spectroscopy at the RISIKO mass separator in Mainz, using the perpendicularly illuminated laser ion source and trap (PI-LIST) high-resolution ion source. Experimental results were combined with hyperfine fields from various atomic ab initio calculations, in particular using multiconfiguration Dirac-Hartree-Fock theory, as implemented in grasp18. In this manner, the nuclear magnetic dipole and electric quadrupole moments were derived to be $\mu =-0.75(5){\mu }_{\mathrm{N}}$ and $Q_{\mathrm{s}}=+5.84(13)\mathrm{eb}$, respectively. The magnetic moment indicates occupation of the $\nu 7/2[613]$ Nilsson orbital, while the large quadrupole moment confirms strong, stable prolate deformation consistent with systematics in the heavy actinides. Comparisons with available expectation values from nuclear theory show good agreement, providing a stringent benchmark for the used theoretical models. These results revise earlier data and establish ${}^{255}\mathrm{Fm}$ as a reference isotope for future high-resolution studies.

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-André potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasidegenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.

We study the behavior of catalytically active droplets in multicomponent conserved mixtures affected by noise. Working in the thin interface limit, we analytically determine the state diagram of the system, characterized by multiple dynamical regimes, and verify our findings using numerical simulations. In particular, we show the emergence of a nonreciprocal, chemically mediated interaction between the droplets, which leads to the formation of (meta)stable clusters of droplets of different species. We find that the clusters can display self-propulsion in a large part of the parameter space, including regions where the nonreciprocal interactions between the droplets are purely attractive. This surprising feature arises from the nonlocal nature of the chemical interactions, and points to locality violations as a general mechanism for energy dissipation and emergence of out-of-equilibrium steady states in active matter.

Entropy production distinguishes equilibrium from nonequilibrium. Calculating the entropy production rate (EPR) is challenging in systems where some degrees of freedom cannot be observed. Here we introduce a perturbative framework to calculate the time irreversibility of an active particle with hidden self-propulsion, termed the “partial EPR,” which provides a lower bound to the full, physical EPR. We find that the parity symmetry, $\mathcal{P}$, and time reversibility, $\mathcal{T}$, of the hidden variable determine the partial EPR. Nontrivial partial EPR appears at least at sixth order in the self-propulsion velocity. We apply our framework to two processes that break $\mathcal{P}$- and $\mathcal{T}$ symmetries, respectively: an asymmetric telegraph process and diffusion with stochastic resetting.

Biological membranes often exhibit heterogeneous protein patterns, which cells control. Strong patterns, like the polarity spot in budding yeast, can be described as surface condensates, formed by physical interactions between constituents. However, it is unclear how these interactions affect the material exchange with the bulk. To study this, we analyze a thermodynamically consistent model, which reveals that passive exchange generally accelerates the coarsening of surface condensates. Active exchange can further accelerate coarsening, although it can also fully arrest it and induce complex patterns involving various length scales. We reveal how these behaviors are related to nonlocal transport via diffusion through the bulk, rationalizing the various scaling laws that we observe and allowing us to interpret biologically relevant scenarios.

The elegant joint measurement (EJM) is a highly symmetric, partially entangled two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere and which has a low entanglement cost for local implementation. It plays a central role in quantum networks exhibiting nonclassical correlations and serves as a paradigmatic example of an entangled measurement with local structure. Despite its significance, generalizing the EJM beyond two qubits has remained unresolved. Here, we extend the EJM to the multipartite setting by identifying all tetrahedrally symmetric, efficiently localizable multiqubit bases. For two qubits, these criteria uniquely select the EJM. For three or more, they yield a discrete set of equivalence classes, reflecting the richer structure of multiparticle entanglement.

Gaussian states are central to continuous-variable quantum systems, as they are experimentally accessible and admit a compact mathematical description. Nevertheless, many proposed quantum technologies require non-Gaussian elements. In resource-theoretic terms, non-Gaussian states are resources, while Gaussian states and operations are free. The task of broadcasting, then, asks whether the resource content of a state can be meaningfully cloned. In this Letter, we prove that broadcasting of non-Gaussian states via Gaussian operations is not possible. We first show that the relative entropy of non-Gaussianity is not superadditive, ruling it out for such no-go analyses. Our proof instead uses fixed points of Gaussian operations and relates to control theory. The theorem also implies that if two initially uncorrelated systems interact by Gaussian dynamics, and one subsystem gains non-Gaussianity, the other must lose it irreversibly. Keeping the set of free operations fixed to Gaussian operations, we also comment on the broadcasting of Wigner negativity and genuine quantum non-Gaussianity.

We present a theoretical study of fast all-to-all entangling gates in trapped-ion quantum processors, based on impulsive excitation of spin-dependent motion with broadband laser pulses. Previous studies have shown that such fast gate schemes are highly scalable and naturally performant outside the Lamb-Dicke regime, however, are limited to nearest-neighbor operations. Here we demonstrate that impulsive spin-dependent excitation can be used to perform high-fidelity nonlocal entangling operations in quasiuniform chains of up to 40 ions. We identify a regime of phonon-mediated entanglement between arbitrary pairs of ions in the chain, where any two pairs of ions in the chain can be entangled in approximately 1.3–2 center-of-mass oscillation periods. We assess the experimental feasibility of the proposed gate schemes, which reveals pulse error requirements that are weakly dependent on the length of the ion chain and the distance between the target qubits. These results suggest entangling gates based on impulsive spin-dependent excitation present new possibilities for large-scale computation in near-term ion-trap devices.

We report a search for an invisible particle $X$ in the decay $K_L^0\to \gamma X$ ($X\to \text{invisible}$), where $X$ can be interpreted as a massless or massive dark photon. No evidence for $X$ was found, based on 13 candidate events consistent with a predicted background of $12.66\pm 4.42_{\mathrm{stat}}\pm 2.13_{\mathrm{syst}}$ events. Upper limits on the branching ratio of $K_L^0\to \gamma X$ were set for the $X$ mass range $0\le m_X\le 425\mathrm{MeV}/c^2$. For massless $X$, the upper limit was $3.4\times {10}^{-7}$ at the 90% confidence level, improving the previous indirect bound by over three orders of magnitude. This result yielded a new lower bound of $4.1\times {10}^6\mathrm{TeV}$ on the probed effective mass scale governing flavor-changing dark-photon couplings, representing approximately two orders of magnitude improvement on existing constraints. For massive $X$, the upper limits in the searched mass region ranged from $\mathcal{O}({10}^{-7})$ to $\mathcal{O}({10}^{-3})$.

We present a novel experimental approach to retrieve both the ionization and return times in high harmonic generation from the spectral phases of the radiation generated by a two-color femtosecond field. By performing a detailed characterization of the phases as both the ratio and delay between the two colors of the field are varied, we have unraveled specific conditions under which the electrons emerge in a nearly single-color field. This unique feature in the HHG process allows for retrieval of the return times directly from the phases, and subsequently, the born and tunneling times. In addition, it allows for the referencing of the delay scale, which in turn, permits the evaluation of those times under the condition of maximal contribution of the second color. Our findings pave the way toward accessing subcycle electron dynamics under the influence of multicolor laser fields.

Recent quench experiments on ultracold atoms in optical cavities provide a clean platform for studying how long-range interactions in atomic media structure their nonequilibrium dynamics. Motivated by these experiments, we provide a theoretical analysis of the quench instabilities that lead to the formation of superradiance as the hybrid system is driven across the self-organization transition. Working with both ultracold bosonic and fermionic gases, we compute the rate at which order forms and quantify the fluctuations of the prequench state that seed the instability. Our results quantitatively match existing experiments on free fermions and make predictions for quench experiments involving interacting Bose and Fermi gases. Our Letter suggests that the nonlocal nature of the photon-mediated interactions generates ordering dynamics that are qualitatively different than those observed in short-range interacting systems.

We report the first experimental observation of discrete time crystal phases and crystallites in an actively mode-locked semiconductor laser. By tuning either the bias current or the modulation frequency, the system undergoes a spontaneous symmetry-breaking transition from the harmonically mode-locked state toward robust, highly coherent time crystal states that persist indefinitely. Two equivalent time crystal configurations can coexist as domains separated by sharp, long-lived boundaries analogous to domain walls. The phenomenon is successfully reproduced by a time-delayed model. Our findings demonstrate that mode-locked semiconductor lasers offer a readily accessible platform to explore and control nonequilibrium phases of light, enabling practical implementations of time crystal physics in photonic systems.

Continuous time crystals (CTCs) are nonequilibrium phases that spontaneously break continuous time-translation symmetry to sustain persistent oscillations under time-invariant driving. Here we report the first realization of CTC in a photorefractive carrier-transport system, using iron-doped lithium niobate (${\mathrm{LiNbO}}_3$) crystals under continuous-wave optical excitation. In this platform, carrier-driven nonlinearities give rise to persistent, tunable oscillations of phase-conjugate waves, directly evidencing time-crystalline order at room temperature. By varying excitation conditions, the ordered CTC phase evolves into intermittent chaotic dynamics with quasicrystal-like temporal features, where spikelike fluctuations reveal critical behavior near nonequilibrium phase transitions. Our work demonstrates that photorefractive carrier transport provides a solid-state route to time-crystalline order, offering new opportunities to probe symmetry breaking and criticality in driven many-body systems.

Water drops sliding on hydrophobic surfaces spontaneously separate charges at their rear. It is unclear how this charge separation affects the contact angles of a sliding drop. We slide grounded and insulated drops on hydrophobic surfaces at low capillary numbers ($\le {10}^{-4}$). We find that the drop charge leads to spontaneous electrowetting that decreases the contact angles. The deposited charges lead to a surface charge effect and decrease the contact angle. Both phenomena compensate each other at the receding contact line, resulting in an insignificant change in the receding contact angle of a sliding drop.

We show that nonequilibrium spin injection into a superconductor can generate an anomalous supercurrent or induce a phase gradient, even for spin voltages below the superconducting gap. Our mechanism does not require breaking time-reversal symmetry in the effective superconducting Hamiltonian, but instead relies on nonequilibrium spin injection. We further demonstrate that superconductivity enhances spin injection due to the large quasiparticle density of states near the gap edge, an effect that persists well below the gap. This contrasts with earlier works predicting the absence of spin injection at zero temperature and small spin voltages. Our results provide a natural explanation for long-standing experimental observations of spin injection in superconductors and predict novel effects arising from spin-charge coupling, including the electrical control of anomalous phase gradients in superconducting systems with spin-orbit coupling. These effects are broadly testable in a variety of materials and hybrid superconducting structures.

We use variational exact diagonalization (VED) to calculate the two-electron removal spectral weight for the Hubbard-Holstein model, starting from the ground state with two electrons on a one-dimensional chain. We argue that this spectral weight provides a valuable proxy for the intensity of 2eARPES processes. Our results show that when contrasted to the presumably larger signal due to two electrons ejected from two different pairs, the presumably weaker signal due to two electrons ejected from the same pair (i) is segregated in energy, appearing at a lower binding energy, and (ii) has a very characteristic momentum dependence, with a different symmetry than that of the signal corresponding to two electrons emitted from two different pairs. We verify that these fingerprints appear for pairs with different symmetries, and prove that they arise as a direct consequence of momentum and energy conservation, therefore they are generic for any model with electron-boson coupling that can lead to formation of electron pairs. Experimental observation of these fingerprints will confirm the existence of pairs. Moreover, the momentum dependence map allows one to distinguish whether the pairs are coherent (superconducting) or not. Finally, we argue that these considerations generalize to finite but low electron concentrations, finite temperatures, and higher dimensions.

Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained with data generated by artificial neural networks themselves. We study this process for models that belong to exponential families, deriving equations of motion that govern the dynamics of the parameters. We show that maximum likelihood estimation of the parameters endows sufficient statistics with the martingale property and that as a result the process converges to absorbing states that amplify initial biases present in the data. However, we show that, for exponential families, this outcome may be prevented if, at each closed-loop retraining iteration, the data contains at least one data point generated from a ground truth model, by relying on maximum a posteriori estimation or by introducing regularization.