Recently reported with nontrivial topological properties and magnetic orders, ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is an intrinsic, magnetic topological insulator which holds promise for exploring exotic quantum phenomena such as the quantum anomalous Hall effect. However, the layer-dependent magnetism of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which is fundamental and crucial for further exploration of related quantum phenomena in this system, remains elusive. Here, by using polar reflective magnetic circular dichroism spectroscopy, we show that few-layered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ exhibits an evident odd-even layer-number effect, i.e., the oscillations of the coercivity of the hysteresis loop (at ${\mu }_0{H}_c$) and the spin-flop transition (at ${\mu }_0{H}_1$), concerning the Zeeman energy and magnetic anisotropy energy. Noticeably, an anomalous magnetic hysteresis loop is observed in the even-number septuple-layered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which might be attributed to the thickness-independent surface-related magnetization. A linear-chain model is applied to elucidate this odd-even layer-number effect of the spin-flop field and to determine the evolution of the magnetic states when subjected to an external magnetic field. A mean-field method further allows us to fully map the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ flake’s magnetic phase diagrams in the parameter space of the magnetic field, layer number, and, especially, temperature. By harnessing the unusual layer-dependent magnetic properties, our work paves the way for further study of quantum phenomena of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

Herein we show that nonresonant inelastic x-ray scattering involving an $s$ core level is a powerful spectroscopic method to characterize the excited states of transition metal compounds. The spherical charge distribution of the $s$ core hole allows the orientational dependence of the intensities of the various spectral features to produce a spatial charge image of the associated multiplet states in a straightforward manner, thereby facilitating the identification of their orbital character. In addition, the $s$ core hole does not add an extra orbital angular momentum component to the multiplet structure so that the well-established Sugano-Tanabe-Kamimura diagrams can be used for the analysis of the spectra. For $\alpha$-MnS we observe the spherical charge density corresponding to its high-spin $3d^5$ (${}^6{A}_1$) ground state configuration and we were able to selectively image its excited states and identify them as $t_{2g}$ (${}^5{T}_2$) and $e_g$ (${}^{5}E$) with an energy splitting $10Dq$ of 0.78 eV.

Rectified electric current induced by irradiating light, a so-called photocurrent, is an established phenomenon in optoelectronic physics. In this paper, we present a comprehensive classification of the photocurrent response arising from the parity violation in bulk systems. We clarify the contrasting role of $\mathcal{T}$ and $\mathcal{P}\mathcal{T}$ symmetries and consequently find new types of photocurrent phenomena characteristic of parity-violating magnets—the intrinsic Fermi surface effect and the gyration current. In particular, the gyration current is induced by circularly polarized light, and it is the counterpart of the shift current caused by linearly polarized light. This photocurrent adds a new functionality of materials studied in various fields of condensed matter physics such as multiferroics and spintronics. A list of materials is provided. Furthermore, we show that the gyration current is strongly enhanced by topologically nontrivial band dispersion. On the basis of the microscopic analysis of Dirac models, we demonstrate the divergent photocurrent response and elucidate the importance of the tilting of Dirac cones.

We present experimental results of vacuum laser acceleration (VLA) of electrons using radially polarized laser pulses interacting with a plasma mirror. Tightly focused, radially polarized laser pulses have been proposed for electron acceleration because of their strong longitudinal electric field, making them ideal for VLA. However, experimental results have been limited until now because injecting electrons into the laser field has remained a considerable challenge. Here, we demonstrate experimentally that using a plasma mirror as an injector solves this problem and permits us to inject electrons at the ideal phase of the laser, resulting in the acceleration of electrons along the laser propagation direction while reducing the electron beam divergence compared to the linear polarization case. We obtain electron bunches with few-MeV energies and a 200-pC charge, thus demonstrating, for the first time, electron acceleration to relativistic energies using a radially polarized laser. High-harmonic generation from the plasma surface is also measured, and it provides additional insight into the injection of electrons into the laser field upon its reflection on the plasma mirror. Detailed comparisons between experimental results and full 3D simulations unravel the complex physics of electron injection and acceleration in this new regime: We find that electrons are injected into the radially polarized pulse in the form of two spatially separated bunches emitted from the p-polarized regions of the focus. Finally, we leverage on the insight brought by this study to propose and validate a more optimal experimental configuration that can lead to extremely peaked electron angular distributions and higher energy beams.

The quantum anomalous Hall (QAH) effect in a magnetic topological insulator (TI) represents a new state of matter originating from the interplay between topology and magnetism. The defining characteristics of the QAH ground state are the quantized Hall resistivity (${\rho }_{\mathrm{yx}}$) and vanishing longitudinal resistivity (${\rho }_{\mathrm{xx}}$) in the absence of an external magnetic field. A fundamental question concerning the QAH effect is whether it is merely a zero-magnetic-field quantum Hall (QH) effect or if it can host unique quantum phases and phase transitions that are unavailable elsewhere. The most dramatic departure of the QAH systems from other QH systems lies in the magnetic disorders that induce spatially random magnetization. Because disorder and magnetism play pivotal roles in the phase diagram of two-dimensional electron systems, the high degree of magnetic disorders in QAH systems may create novel phases and quantum critical phenomena. In this work, we perform systematic transport studies of a series of magnetic TIs with varied strength of magnetic disorders. We find that the ground state can be categorized into two distinct classes: the QAH phase and the anomalous Hall (AH) insulator phase, as the zero-magnetic-field counterparts of the QH liquid and Hall insulator phases in the QH systems. In the low-disorder limit of the QAH phase, we observe a universal quantized longitudinal resistance ${\rho }_{\mathrm{xx}}=h/e^2$ at the coercive field. In the AH insulator regime, we find that a magnetic field can drive it to the QAH phase through a quantum critical point with scaling behaviors that are distinct from those in the QH phase transition. We propose that the transmission between chiral edge states at domain boundaries, tunable by magnetic disorder and magnetic fields, is the key for determining the QAH ground state.

We explore field and temperature scaling of magnetoresistance in underdoped ($x=0$, $x=0.19$) and optimally doped ($x=0.31$) samples of the high-temperature superconductor ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$. In all cases, the magnetoresistance is $H$ linear at high fields. We demonstrate that the data can be explained by an orbital model in the presence of strongly anisotropic quasiparticle spectra and scattering time due to antiferromagnetism. In optimally doped samples, the magnetoresistance is controlled by the properties of small regions of the Fermi surface called “hot spots,” where antiferromagnetic excitations induce a large quasiparticle scattering rate. The anisotropic scattering rate results in hyperbolic $H/T$ magnetoresistance scaling, which competes with the more conventional Kohler scaling. We argue that these results constitute a coherent picture of magnetotransport in ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$, which links the origin of $H$-linear resistivity to antiferromagnetic hot spots. Implications for the $T$-linear resistivity at zero field are discussed.

We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this 2-orders-of-magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) setup at ISOLDE at CERN. Using liquid samples as hosts, we obtain narrow, subkilohertz-linewidth, resonances, while a simultaneous in situ ${}^1\mathrm{H}$ NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus ${}^{26}\mathrm{Na}$, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path toward a wide range of applications of the ultrasensitive $\beta$-NMR in physics, chemistry, and biology.

We present a theoretical study of the temporal and spatial coherence properties of a topological laser device built by including saturable gain on the edge sites of a Harper-Hofstadter lattice for photons. For small enough lattices, the Bogoliubov analysis applies, and the coherence time is almost determined by the total number of photons in the device in agreement with the standard Schawlow-Townes phase diffusion. In larger lattices, looking at the lasing edge mode in the comoving frame of its chiral motion, the spatiotemporal correlations of long-wavelength fluctuations display a Kardar-Parisi-Zhang (KPZ) scaling. Still, at very long times, when the finite size of the device starts to matter, the functional form of the temporal decay of coherence changes from the KPZ stretched exponential to a Schawlow-Townes-like exponential, while the nonlinear dynamics of KPZ fluctuations remains visible as a broadened linewidth as compared to the Bogoliubov-Schawlow-Townes prediction. While we establish the above behaviors also for nontopological 1D laser arrays, the crucial role of topology in protecting the coherence from static disorder is finally highlighted: Our numerical calculations suggest the dramatically reinforced coherence properties of topological lasers compared to corresponding nontopological devices. These results open exciting possibilities for both fundamental studies of nonequilibrium statistical mechanics and concrete applications to laser devices.

We investigate the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field-suppression effect on the longitudinal thermal conductivity ${\kappa }_{xx}$ sets in below approximately 25 K. This field-suppression effect at 15 T becomes as large as 80% at low temperatures, suggesting a large spin contribution ${\kappa }_{xx}^{\mathrm{sp}}$ in ${\kappa }_{xx}$. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity ${\kappa }_{xy}$ shows a significant dependence on the sample’s scattering time, as seen in the rise of the peak ${\kappa }_{xy}$ value in almost linear fashion with the magnitude of ${\kappa }_{xx}$. On the other hand, the temperature dependence of ${\kappa }_{xy}$ is similar in all Cd-K samples; ${\kappa }_{xy}$ shows a peak at almost the same temperature of the peak of the phonon thermal conductivity ${\kappa }_{xx}^{\mathrm{ph}}$ which is estimated by ${\kappa }_{xx}$ at 15 T. These results indicate the presence of a dominant phonon thermal Hall ${\kappa }_{xy}^{\mathrm{ph}}$ at 15 T. In addition to ${\kappa }_{xy}^{\mathrm{ph}}$, we find that the field dependence of ${\kappa }_{xy}$ at low fields turns out to be nonlinear at low temperatures, concomitantly with the appearance of the field suppression of ${\kappa }_{xx}$, indicating the presence of a spin thermal Hall ${\kappa }_{xy}^{\mathrm{sp}}$ at low fields. Remarkably, by assembling the ${\kappa }_{xx}$ dependence of ${\kappa }_{xy}^{\mathrm{sp}}$ data of other kagome antiferromagnets, we find that, whereas ${\kappa }_{xy}^{\mathrm{sp}}$ stays a constant in the low-${\kappa }_{xx}$ region, ${\kappa }_{xy}^{\mathrm{sp}}$ starts to increase as ${\kappa }_{xx}$ does in the high-${\kappa }_{xx}$ region. This ${\kappa }_{xx}$ dependence of ${\kappa }_{xy}^{\mathrm{sp}}$ indicates the presence of both intrinsic and extrinsic mechanisms in the spin thermal Hall effect in kagome antiferromagnets. Furthermore, both ${\kappa }_{xy}^{\mathrm{ph}}$ and ${\kappa }_{xy}^{\mathrm{sp}}$ disappear in the antiferromagnetic ordered phase at low fields, showing that phonons alone do not exhibit the thermal Hall effect. A high field above approximately 7 T induces ${\kappa }_{xy}^{\mathrm{ph}}$, concomitantly with a field-induced increase of ${\kappa }_{xx}$ and the specific heat, suggesting a coupling of the phonons to the field-induced spin excitations as the origin of ${\kappa }_{xy}^{\mathrm{ph}}$.

We study the quantum dynamics of massive impurities embedded in a strongly interacting, two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasihole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge, and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasiholes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted—in particular, in photonic systems.

We present a sign-problem-free quantum Monte Carlo study of a model that exhibits quantum phase transitions without symmetry breaking and associated changes in the size of the Fermi surface. The model is an Ising gauge theory on the square lattice coupled to an Ising matter field and spinful “orthogonal” fermions at half filling, both carrying Ising gauge charges. In contrast to previous studies, our model hosts an electronlike, gauge-neutral fermion excitation providing access to Fermi-liquid phases. One of the phases of the model is a previously studied orthogonal semimetal, which has ${\mathbb{Z}}_2$ topological order and Luttinger-volume-violating Fermi points with gapless orthogonal fermion excitations. We elucidate the global phase diagram of the model: Along with a conventional Fermi-liquid phase with a large Luttinger-volume Fermi surface, we also find a “deconfined” Fermi liquid in which the large Fermi surface coexists with fractionalized excitations. We present results for the electron spectral function, showing its evolution from the orthogonal semimetal with a spectral weight near momenta $\{\pm \pi /2,\pm \pi /2\}$ to a large Fermi surface.

The nature of transient electronic states created by photoabsorption critically determines the dynamics of the subsequently evolving system. Here, we investigate $K$-shell photoionized atomic neon by absorbing a second photon within the Auger-decay lifetime of 2.4 fs using the European XFEL, a unique high-repetition-rate, wavelength-tunable x-ray free-electron laser. By high-resolution electron spectroscopy, we map out the transient Rydberg resonances unraveling the details of the subsequent decay of the hollow atom. So far, ultra-short-lived electronic transients, which are often inaccessible by experiments, were mainly inferred from theory but are now addressed by nonlinear x-ray absorption. The successful characterization of these resonances with femtosecond lifetimes provides the basis for a novel class of site-specific, nonlinear, and time-resolved studies with strong impact for a wide range of topics in physics and chemistry.

On 31 December, 2019, an outbreak of a novel coronavirus, SARS-CoV-2, that causes the COVID-19 disease, was first reported in Hubei, mainland China. This epidemics’ health threat is probably one of the biggest challenges faced by our interconnected modern societies. According to the epidemiological reports, the large basic reproduction number $R_0\sim 3.0$, together with a huge fraction of asymptomatic infections, paved the way for a major crisis of the national health capacity systems. Here, we develop an age-stratified mobility-based metapopulation model that encapsulates the main particularities of the spreading of COVID-19 regarding (i) its transmission among individuals, (ii) the specificities of certain demographic groups with respect to the impact of COVID-19, and (iii) the human mobility patterns inside and among regions. The full dynamics of the epidemic is formalized in terms of a microscopic Markov chain approach that incorporates the former elements and the possibility of implementing containment measures based on social distancing and confinement. With this model, we study the evolution of the effective reproduction number $\mathcal{R}(t)$, the key epidemiological parameter to track the evolution of the transmissibility and the effects of containment measures, as it quantifies the number of secondary infections generated by an infected individual. The suppression of the epidemic is directly related to this value and is attained when $\mathcal{R}<1$. We find an analytical expression connecting $\mathcal{R}$ with nonpharmacological interventions, and its phase diagram is presented. We apply this model at the municipality level in Spain, successfully forecasting the observed incidence and the number of fatalities in the country at each of its regions. The expression for $\mathcal{R}$ should assist policymakers to evaluate the epidemics’ response to actions, such as enforcing or relaxing confinement and social distancing.

The ability to control and measure the temperature of propagating microwave modes down to very low temperatures is indispensable for quantum information processing and may open opportunities for studies of heat transport at the nanoscale, also in the quantum regime. Here, we propose and experimentally demonstrate primary thermometry of propagating microwaves using a transmon-type superconducting circuit. Our device operates continuously, with a sensitivity down to $4\times {10}^{-4}\mathrm{photons}/\sqrt{\mathrm{Hz}}$ and a bandwidth of 40 MHz. We measure the thermal occupation of the modes of a highly attenuated coaxial cable in a range of 0.001 to 0.4 thermal photons, corresponding to a temperature range from 35 mK to 210 mK at a frequency around 5 GHz. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. This thermometry scheme can find applications in benchmarking and characterization of cryogenic microwave setups, temperature measurements in hybrid quantum systems, and quantum thermodynamics.

Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics. One such example is a multicomponent Fermi gas with $\mathrm{SU}(N)$ symmetry that is expected to behave like spinless bosons in the large-$N$ limit, where the large number of internal states weakens constraints from the Pauli exclusion principle. However, bosonization in $\mathrm{SU}(N)$ fermions has never been established in high dimensions where exact solutions are absent. Here, we report direct evidence for bosonization in a $\mathrm{SU}(N)$ fermionic ytterbium gas with tunable $N$ in three dimensions (3D). We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a $1/N$ scaling in the low-fugacity regime consistent with our theoretical prediction. This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity. Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions. It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.

Quantum nondemolition (QND) measurement is a remarkable tool for the manipulation of quantum systems. It allows specific information to be extracted while still preserving fragile quantum observables of the system. Here we apply cavity-based QND measurement to an optical lattice clock—a type of atomic clock with unrivaled frequency precision—preserving the quantum coherence of the atoms after readout with 80% fidelity. We apply this technique to stabilize the phase of an ultrastable laser to a coherent atomic state via a series of repeated QND measurements. We exploit the improved phase coherence of the ultrastable laser to interrogate a separate optical lattice clock, using a Ramsey spectroscopy time extended from 300 ms to 2 s. With this technique we maintain 95% contrast and observe a sevenfold increase in the clock’s $Q$ factor to $1.7\times {10}^{15}$.

Resonant transverse driving of a two-level system as viewed in the rotating frame couples two degenerate states at the Rabi frequency, an equivalence that emerges in quantum mechanics. While successful at controlling natural and artificial quantum systems, certain limitations may arise (e.g., the achievable gate speed) due to nonidealities like the counterrotating term. We introduce a superconducting composite qubit (CQB), formed from two capacitively coupled transmon qubits, which features a small avoided crossing—smaller than the environmental temperature—between two energy levels. We control this low-frequency CQB using solely baseband pulses, nonadiabatic transitions, and coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit operations with Clifford fidelities exceeding 99.7%. We also perform coupled qubit operations between two low-frequency CQBs. This work demonstrates that universal nonadiabatic control of low-frequency qubits is feasible using solely baseband pulses.

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio $Q_i/Q_e$ as a function of the compressive-to-Alfvénic driving power ratio $P_{\text{compr}}/P_{\mathrm{AW}}$, of the ratio of ion thermal pressure to magnetic pressure ${\beta }_i$, and of the ratio of ion-to-electron background temperatures $T_i/T_e$. It is shown that $Q_i/Q_e$ is an increasing function of $P_{\text{compr}}/P_{\mathrm{AW}}$. When the compressive driving is sufficiently large, $Q_i/Q_e$ approaches $\simeq P_{\text{compr}}/P_{\mathrm{AW}}$. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfvén waves is absent for both low and high ${\beta }_i$, meaning that the compressive driving is directly connected to the ion-entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low ${\beta }_i$ and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.

More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here, we give an answer to this question for temporal processes that are probed sequentially by means of projective measurements of the same observable. Defining classical processes as those that can, in principle, be simulated by means of classical resources only, we fully characterize the set of such processes. Based on this characterization, we show that for non-Markovian processes (i.e., processes with memory), the absence of coherence does not guarantee the classicality of observed phenomena; furthermore, we derive an experimentally and computationally accessible measure for nonclassicality in the presence of memory. We then provide a direct connection between classicality and the vanishing of quantum discord between the evolving system and its environment. Finally, we demonstrate that—in contrast to the memoryless setting—in the non-Markovian case, there exist processes that are genuinely quantum; i.e., they display nonclassical statistics independent of the measurement scheme that is employed to probe them.

A remarkable aspect of quantum theory is that certain measurement outcomes are entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. We formally introduce, design, and experimentally demonstrate an ultrafast optical quantum random number generator that uses a totally untrusted photonic source. While considering completely general quantum attacks, we certify and generate in real time random numbers at a rate of $8.05\mathrm{Gb}/\mathrm{s}$ with a composable security parameter of ${10}^{-10}$. Composable security is the most stringent and useful security paradigm because any given protocol remains secure even if arbitrarily combined with other instances of the same, or other, protocols, thereby allowing the generated randomness to be utilized for arbitrary applications in cryptography and beyond. This work achieves the fastest generation of composably secure quantum random numbers ever reported.