Artificial spin ices (ASIs) are interacting arrays of lithographically defined nanomagnets in which novel, frustrated magnetic phases can be intentionally designed. A key emergent description of fundamental excitations in ASIs is that of magnetic monopoles—mobile quasiparticles that carry an effective magnetic charge. Here, we demonstrate that the archetypal square ASI lattice can host, in specific regions of its magnetic phase diagram, plasmalike regimes containing a high density of mobile magnetic monopoles. These regimes result from the magnetic field-tunable tension on the Dirac strings connecting mobile monopoles. By passively “listening” to spontaneous monopole noise under conditions of strict thermal equilibrium, we reveal their intrinsic dynamics and show that monopole kinetics are most diffusive (that is, minimally correlated) in the plasma regime. These results open the door to on-demand monopole regimes having continuously field-tunable densities and dynamic properties, thereby providing a new paradigm for probing the physics of effective magnetic charges in synthetic matter.

Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero-energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$-wave superconductors. We show that inversion symmetry breaking and charge transfer due to the missing atoms lead to the occupation of incipient impurity bands and mixed-parity spin-singlet and -triplet Cooper pairing of neighboring electrons traversing the line defect. Nontrivial topological invariants arise and occupy a large part of the parameter space, including the time-reversal symmetry-breaking Zeeman coupling due to applied magnetic field or defect-induced magnetism, creating TSCs in different topological classes with robust Majorana zero modes at both ends of the line defect. Beyond providing a novel mechanism for the recent discovery of zero-energy bound states at both ends of an atomic line defect in monolayer Fe(Te,Se) superconductors, the findings pave the way for new material realizations of the simplest and most robust 1D TSCs using embedded quantum structures in unconventional superconductors with large pairing energy gaps and high transition temperatures.

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension ($I_d$)—behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based $I_d$ estimators to compute the $I_d$ of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the $I_d$ uniquely characterizes the transition regime. The finite-size analysis of the $I_d$ allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent $\nu$ in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.

Topological magnets are a new family of quantum materials providing great potential to realize emergent phenomena, such as the quantum anomalous Hall effect and the axion-insulator state. Here, we present our discovery that the stoichiometric ferromagnet ${\mathrm{MnBi}}_8{\mathrm{Te}}_{13}$ with natural heterostructure ${\mathrm{MnBi}}_2{\mathrm{Te}}_4/({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_3$ is an unprecedented “half-magnetic topological insulator,” with the magnetization existing at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface but not at the opposite surface terminated by triple ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ layers. Our angle-resolved photoemission spectroscopy measurements unveil a massive Dirac gap at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface and a gapless Dirac cone on the other side. Remarkably, the Dirac gap (about 28 meV) at the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ surface decreases monotonically with increasing temperature and closes right at the Curie temperature, thereby representing the first smoking-gun spectroscopic evidence of a magnetization-induced topological surface gap among all known magnetic topological materials. We further demonstrate theoretically that the half-magnetic topological insulator is desirable to realize the surface anomalous Hall effect, which serves as direct proof of the general concept of axion electrodynamics in condensed matter systems.

Agile cryptography allows for a resource-efficient swap of a cryptographic core in case the security of an underlying classical cryptographic algorithm becomes compromised. Conversely, versatile cryptography allows the user to switch the cryptographic task without requiring any knowledge of its inner workings. In this paper, we suggest how these related principles can be applied to the field of quantum cryptography by explicitly demonstrating two quantum cryptographic protocols, quantum digital signatures (QDS) and quantum secret sharing (QSS), on the same hardware sender and receiver platform. Crucially, the protocols differ only in their classical postprocessing. The system is also suitable for quantum key distribution (QKD) and is highly compatible with deployed telecommunication infrastructures, since it uses standard quadrature phase-shift keying encoding and heterodyne detection. For the first time, QDS protocols are modified to allow for postselection at the receiver, enhancing protocol performance. The cryptographic primitives QDS and QSS are inherently multipartite, and we prove that they are secure not only when a player internal to the task is dishonest, but also when (external) eavesdropping on the quantum channel is allowed. In our first proof-of-principle demonstration of an agile and versatile quantum communication system, the quantum states are distributed at GHz rates. A 1-bit message may be securely signed using our QDS protocols in less than 0.05 ms over a 2-km fiber link and in less than 0.2 s over a 20-km fiber link. To our knowledge, this also marks the first demonstration of a continuous-variable direct QSS protocol.

Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here, we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter—a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This measurement allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations, and image the dominant fluctuation patterns. We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation. Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which are theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons.

The advent of the quantum gas microscope allowed for the in situ probing of ultracold gaseous matter on an unprecedented level of spatial resolution. However, the study of phenomena on ever smaller length scales, as well as the probing of three-dimensional systems, is fundamentally limited by the wavelength of the imaging light for all techniques based on linear optics. Here, we report on a high-resolution ion microscope as a versatile and powerful experimental tool to investigate quantum gases. The instrument clearly resolves atoms in an optical lattice with a spacing of 532 nm over a field of view of 50 sites and offers an extremely large depth of field on the order of at least $70\mu \mathrm{m}$. With a simple model, we extract an upper limit for the achievable resolution of approximately 200 nm from our data. We demonstrate a pulsed operation mode enabling 3D imaging and allowing for the study of ionic impurities and Rydberg physics.

Transforming an initial quantum state into a target state through the fastest possible route—a quantum brachistochrone—is a fundamental challenge for many technologies based on quantum mechanics. In two-level systems, the quantum brachistochrone solutions are long known. These solutions, however, are not applicable to larger systems, especially when the target state cannot be reached through a local transformation. Here, we demonstrate fast coherent transport of an atomic wave packet over a distance of 15 times its size—a paradigmatic case of quantum processes going beyond the two-level system. Our measurements of the transport fidelity reveal the existence of a minimum duration—a quantum speed limit—for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light on a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.

The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the $5d$-electron compound ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$.

Tissue, cell, and nucleus morphology change during tumor progression. In 2D confluent cell cultures, different tissue states, such as fluid (unjammed) and solid (jammed), are correlated with cell shapes. These results do not have to apply a priori to three dimensions. Cancer cell motility requires and corresponds to a fluidization of the tumor tissue on the bulk level. Here, we investigate bulk tissue fluidity in 3D and determine how it correlates with cell and nucleus shape. In patient samples of mamma and cervix carcinoma, we find areas where cells can move or are immobile. We compare 3D cell spheroids composed of cells from a cancerous and a noncancerous cell line. Through bulk mechanical spheroid-fusion experiments and single live-cell tracking, we show that the cancerous sample is fluidized by active cells moving through the tissue. The healthy, epithelial sample with immobile cells behaves more solidlike. 3D segmentations of the samples show that the degree of tissue fluidity correlates with elongated cell and nucleus shapes. This correlation links cell shapes to cell motility and bulk mechanical behavior. We find two active states of matter in solid tumors: an amorphous glasslike state with characteristics of 3D cell jamming and a disordered fluid state. Individual cell and nucleus shape may serve as a marker for metastatic potential to foster personalized cancer treatment.

We present a circuit design composed of two Josephson junctions coupled by a nonreciprocal element, the gyrator, whose ground space is doubly degenerate. The ground states are approximate code words of the Gottesman-Kitaev-Preskill code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron in a crystal, confined to a two-dimensional plane, and subjected to a strong, homogeneous magnetic field. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction. We also propose realistic design parameters for an experimental realization, and we describe possible protocols to perform logical one- and two-qubit gates, state preparation, and readout.

The cluster-multipole (CMP) expansion for magnetic structures provides a scheme to systematically generate candidate magnetic structures specifically including noncollinear magnetic configurations adapted to the crystal symmetry of a given material. A comparison with the experimental data collected on MAGNDATA shows that the most stable magnetic configurations in nature are linear combinations of only few CMPs. Furthermore, a high-throughput calculation for all candidate magnetic structures is performed in the framework of spin-density functional theory (SDFT). We benchmark the predictive power of $\mathrm{CMP}+\mathrm{SDFT}$ with 2935 calculations, which show that (i) the CMP expansion administers an exhaustive list of candidate magnetic structures, (ii) $\mathrm{CMP}+\mathrm{SDFT}$ can narrow down the possible magnetic configurations to a handful of computed configurations, and (iii) SDFT reproduces the experimental magnetic configurations with an accuracy of $\pm 0.5{\mu }_B$. For a subset the impact of on-site Coulomb repulsion $U$ is investigated by means of 1545 $\mathrm{CMP}+\mathrm{SDFT}+U$ calculations revealing no further improvement on the predictive power.

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This finding motivates us to introduce measurement-only models, in which the “scrambling” and “unscrambling” effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. These models represent a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is frustration, or mutual incompatibility, of the measurements. Surprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local ($\gtrsim 3$-body) operators. We identify a class of exceptions to this behavior (“bipartite ensembles”) which cannot sustain an entangling phase but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light cone, despite the nonlocality inherent to quantum measurements.

The chaotic nature of x-ray free-electron-laser pulses is a major bottleneck that has limited the joint temporal and spectral resolution of spectroscopic measurements. We show how to use the stochastic x-ray field statistics to overcome this difficulty through correlation signals averaged over independent pulse realizations. No control is required over the spectral phase of the pulse, enabling immediate application of existing, noisy x-ray free-electron-laser pulses. The proposed stimulated Raman technique provides the combined broad observation bandwidth and high time-frequency resolution needed for the observation of elementary molecular events. A model is used to simulate chaotic free-electron-laser pulses and calculate their correlation properties. The resulting joint temporal and spectral resolution is exemplified for a molecular model system with time-dependent frequencies and for the RNA base uracil passing through a conical intersection. Ultrafast coherences, which constitute a direct signature of the nonadiabatic dynamics, are resolved. The detail and depth of physical information accessed by the proposed stochastic signal are virtually identical to those obtained by phase-controlled pulses.

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many practical implementations. The Holevo Cramér-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multiparameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimization over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing and characterize the performance of state tomography on the code space of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial code states can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress toward the estimation of multiple incompatible observables.

We describe an approach to the high-fidelity measurement of a superconducting qubit using an on-chip microwave photon counter. The protocol relies on the transient response of a dispersively coupled measurement resonator to map the state of the qubit to “bright” and “dark” cavity pointer states that are characterized by a large differential photon occupation. Following this mapping, we photodetect the resonator using the Josephson photomultiplier, which transitions between classically distinguishable flux states when cavity photon occupation exceeds a certain threshold. Our technique provides access to the binary outcome of projective quantum measurement at the millikelvin stage without the need for quantum-limited preamplification and thresholding at room temperature. We achieve raw single-shot measurement fidelity in excess of 98% across multiple samples using this approach in total measurement times under 500 ns. In addition, we show that the backaction and crosstalk associated with our measurement protocol can be mitigated by exploiting the intrinsic damping of the Josephson photomultiplier itself.

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density but rather reaches a limiting value of $n\approx 1.7$. This limit arises purely from electrodynamics, as it occurs at densities far below those where chemical processes become important. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that, regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of the refractive index from a bottom-up, atomic physics perspective, and it also introduces the renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

We present sphere-on-ice friction experiments as a function of temperature, contact pressure, and speed. At temperatures well below the melting point, friction is strongly temperature dependent and follows an Arrhenius behavior, which we interpret as resulting from the thermally activated diffusive motion of surface ice molecules. We find that this motion is hindered when the contact pressure is increased; in this case, the friction increases exponentially, and the slipperiness of the ice disappears. Close to the melting point, the ice surface is plastically deformed due to the pressure exerted by the slider, a process depending on the slider geometry and penetration hardness of the ice. The ice penetration hardness is shown to increase approximately linearly with decreasing temperature and sublinearly with indentation speed. We show that the latter results in a nonmonotonic dependence of the ploughing force on sliding speed. Our results thus clarify the complex dependence of ice friction on temperature, contact pressure, and speed.

Layered van der Waals 2D magnetic materials are of great interest in fundamental condensed-matter physics research, as well as for potential applications in spintronics and device physics. We present neutron powder diffraction data using new ultrahigh-pressure techniques to measure the magnetic structure of Mott-insulating 2D honeycomb antiferromagnet ${\mathrm{FePS}}_3$ at pressures up to 183 kbar and temperatures down to 80 K. These data are complemented by high-pressure magnetometry and reverse Monte Carlo modeling of the spin configurations. As pressure is applied, the previously measured ambient-pressure magnetic order switches from an antiferromagnetic to a ferromagnetic interplanar interaction and from 2D-like to 3D-like character. The overall antiferromagnetic structure within the $ab$ planes, ferromagnetic chains antiferromagnetically coupled, is preserved, but the magnetic propagation vector is altered from $\mathbf{k}=(0,1,\frac{1}{2})$ to $\mathbf{k}=(0,1,0)$, a halving of the magnetic unit cell size. At higher pressures, coincident with the second structural transition and the insulator-metal transition in this compound, we observe a suppression of this long-range order and emergence of a form of magnetic short-range order which survives above room temperature. Reverse Monte Carlo fitting suggests this phase to be a short-ranged version of the original ambient-pressure structure—with the Fe moment size remaining of similar magnitude and with a return to antiferromagnetic interplanar correlations. The persistence of magnetism well into the HP-II metallic state is an observation in contradiction with previous x-ray spectroscopy results which suggest a spin-crossover transition.

Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in the realm of experimental capabilities. These techniques will likely lead to the first proof of principle of fault tolerance in the next 5 yr. In the long run, however, these approaches require a very large number of physical qubits to construct a fault-tolerant quantum circuit that can run interesting algorithms. As an alternative, it is proposed that quantum low-density parity-check (LDPC) codes could serve as an architecture that circumvents this problem. The best candidate class of quantum LDPC codes were discovered by Tillich and Zémor and are called hypergraph product codes. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold. With these features, they asymptotically offer a smaller overhead compared to topological codes. Here, we demonstrate how to perform Clifford gates on this class of codes using code deformation. To this end, we introduce wormhole defects on hypergraph product codes. Together with state injection, we can perform a universal set of gates within a single block of the class of hypergraph product codes.