Reichenbach’s principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach’s principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input $A$ and outputs $B$ and $C$ is compatible with $A$ being a complete common cause of $B$ and $C$, then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach’s principle to a formalism for quantum causal models and provide examples of how the formalism works.

The antiferromagnetic spin-$1/2$ Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large-scale density matrix renormalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum-dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a $\pi$-flux free-fermion model [the parton mean-field ansatz of a $U(1)$ Dirac spin liquid].

Under irradiation, minerals tend to experience an accumulation of structural defects, ultimately leading to a disordered atomic network. Despite the critical importance of understanding and predicting irradiation-induced damage, the physical origin of the initiation and saturation of defects remains poorly understood. Here, based on molecular dynamics simulations of $\alpha$-quartz, we show that the topography of the enthalpy landscape governs irradiation-induced disordering. Specifically, we show that such disordering differs from that observed upon vitrification in that, prior to saturation, irradiated quartz accesses forbidden regions of the enthalpy landscape, i.e., those that are inaccessible by simply heating and cooling. Furthermore, we demonstrate that damage saturates when the system accesses a local region of the enthalpy landscape corresponding to the configuration of an allowable liquid. At this stage, a sudden decrease in the heights of the energy barriers enhances relaxation, thereby preventing any further accumulation of defects and resulting in a defect-saturated disordered state.

Torque can be provided to magnetization in nanomagnets directly by electric current and/or voltage. This technique enables electric current (voltage)-to-spin conversion without electromagnetic induction, and has been intensively studied for memory device applications. Among the various kinds of torque, torque induced by spin-orbit splitting has recently been found. However, quantitative understanding of bulk-related torque and interface-related torque is still lacking because of their identical symmetry for current-in-plane devices. In this paper, we propose that a pure interface-related torque can be characterized by spin-torque ferromagnetic resonance with a current-perpendicular-to-plane tunnel junction. Epitaxial Fe-MgO-V tunnel junctions are prepared to characterize the interface-related torque at Fe-MgO. We find that the current-driven torque is negligible, and a significant enhancement of the voltage-driven torque is observed when the MgO barrier thickness decreases. The maximum torque obtained is as large as $2.8\times {10}^{-5}\mathrm{J}/({\mathrm{Vm}}^2)$, which is comparable to the voltage-controlled magnetic anisotropy of $180\mathrm{fJ}/\mathrm{Vm}$. The voltage-driven torque shows strong dc-bias-voltage dependence that cannot be explained by conventional voltage-controlled magnetic anisotropy. Tunnel anisotropic magnetoresistance spectroscopy suggests that the torque is correlated to an interface state at the Fe-MgO. This surface-state-sensitive electric modulation of magnetic properties provides new insight into the field of interface magnetism.

For nearly a century, the concept of needle radiation has captured the attention of the electromagnetics communities in both physics and engineering, with various types of contributions reoccurring every decade. With the near-term needs for highly directive, electrically small radiators and scatterers for a variety of communications and sensor applications, superdirectivity has again become a topic of interest. While it is well known that superdirective solutions exist and suffer ill-posedness issues in principle, a detailed needle solution has not been reported previously. We demonstrate explicitly, for the first time, how needle radiation can be obtained theoretically from currents driven on an arbitrary spherical surface, and we explain why such a result can only be attained in practice with electrically large spheres. On the other hand, we also demonstrate, more practically, how broadside radiating Huygens source multipoles can be combined into an end-fire array configuration to achieve needle-like radiation performance without suffering the traditional problems that have previously plagued superdirectivity.

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like $(\text{time}{)}^{1/3}$ and are spatially correlated over a distance $\propto (\text{time}{)}^{2/3}$. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Brillouin and Raman scattering spectroscopy are established techniques for the nondestructive contactless and label-free readout of mechanical, chemical, and structural properties of condensed matter. Brillouin-Raman investigations currently require separate measurements and a site-matched approach to obtain complementary information from a sample. Here, we demonstrate a new concept of fully scanning multimodal microspectroscopy for simultaneous detection of Brillouin and Raman light scattering in an exceptionally wide spectral range, from fractions of GHz to hundreds of THz. It yields an unprecedented 150-dB contrast, which is especially important for the analysis of opaque or turbid media such as biomedical samples, and spatial resolution on a subcellular scale. We report the first applications of this new multimodal method to a range of systems, from a single cell to the fast reaction kinetics of a curing process, and the mechanochemical mapping of highly scattering biological samples.

Conventional semiconductor-based logic and nanomagnet-based memory devices are built out of stable, deterministic units such as standard metal-oxide semiconductor transistors, or nanomagnets with energy barriers in excess of $\approx 40–60\mathrm{kT}$. In this paper, we show that unstable, stochastic units, which we call “$p$-bits,” can be interconnected to create robust correlations that implement precise Boolean functions with impressive accuracy, comparable to standard digital circuits. At the same time, they are invertible, a unique property that is absent in standard digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among all possible inputs that are consistent with that output. First, we present a detailed implementation of an invertible gate to bring out the key role of a single three-terminal transistorlike building block to enable the construction of correlated $p$-bit networks. The results for this specific, CMOS-assisted nanomagnet-based hardware implementation agree well with those from a universal model for $p$-bits, showing that $p$-bits need not be magnet based: any three-terminal tunable random bit generator should be suitable. We present a general algorithm for designing a Boltzmann machine (BM) with a symmetric connection matrix [$J$] ($J_{ij}=J_{ji}$) that implements a given truth table with $p$-bits. The [$J$] matrices are relatively sparse with a few unique weights for convenient hardware implementation. We then show how BM full adders can be interconnected in a partially directed manner ($J_{ij}\ne J_{ji}$) to implement large logic operations such as 32-bit binary addition. Hundreds of stochastic $p$-bits get precisely correlated such that the correct answer out of $2^{33}$ ($\approx 8\times 10^9$) possibilities can be extracted by looking at the statistical mode or majority vote of a number of time samples. With perfect directivity ($J_{ji}=0$) a small number of samples is enough, while for less directed connections more samples are needed, but even in the former case logical invertibility is largely preserved. This combination of digital accuracy and logical invertibility is enabled by the hybrid design that uses bidirectional BM units to construct circuits with partially directed interunit connections. We establish this key result with extensive examples including a 4-bit multiplier which in inverted mode functions as a factorizer.

We present a tensor network especially suited for multi-orbital Anderson impurity models and as an impurity solver for multi-orbital dynamical mean-field theory (DMFT). The solver works directly on the real-frequency axis and yields high spectral resolution at all frequencies. We use a large number $\mathbf{(}\mathcal{O}(100)\mathbf{)}$ of bath sites and therefore achieve an accurate representation of the bath. The solver can treat full rotationally invariant interactions with reasonable numerical effort. We show the efficiency and accuracy of the method by a benchmark for the three-orbital test-bed material ${\mathrm{SrVO}}_3$. There we observe multiplet structures in the high-energy spectrum, which are almost impossible to resolve by other multi-orbital methods. The resulting structure of the Hubbard bands can be described as a broadened atomic spectrum with rescaled interaction parameters. Additional features emerge when $U$ is increased. Finally, we show that our solver can be applied even to models with five orbitals. This impurity solver offers a new route to the calculation of precise real-frequency spectral functions of correlated materials.

Single-photon subtraction plays important roles in optical quantum information processing as it provides a non-Gaussian characteristic in continuous-variable quantum information. While the conventional way of implementing single-photon subtraction based on a low-reflectance beam splitter works properly for a single-mode quantum state, it is unsuitable for a multimode quantum state because a single photon is subtracted from all multiple modes without maintaining their mode coherence. Here, we experimentally implement and characterize a mode-tunable coherent single-photon subtractor based on sum-frequency generation. It can subtract a single photon exclusively from one desired time-frequency mode of light or from a coherent superposition of multiple time-frequency modes. To experimentally characterize the time-frequency modes of the single-photon subtractor, we employ quantum process tomography based on coherent states. The mode-tunable coherent single-photon subtractor will be an essential element for realizing non-Gaussian quantum networks necessary to get a quantum advantage in information processing.

The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, it also diagnoses the chaotic behavior of many-body quantum systems and characterizes information scrambling. Based on OTOCs, three different concepts—quantum chaos, holographic duality, and information scrambling—are found to be intimately related to each other. Despite its theoretical importance, the experimental measurement of the OTOC is quite challenging, and thus far there is no experimental measurement of the OTOC for local operators. Here, we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and nonintegrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for nonintgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.

The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba $\alpha$ and renormalized Dresselhaus $\beta$ couplings to equal fixed strengths $\alpha =\beta$, the total SO field becomes unidirectional, thus rendering the electron spins immune to decay due to momentum scattering. A robust persistent spin helix (PSH), i.e., a helical spin-density wave excitation with constant pitch $P=2\pi /Q$, $Q=4m\alpha /{\hslash }^2$, has already been experimentally realized at this singular point $\alpha =\beta$, enhancing the spin lifetime by up to 2 orders of magnitude. Here, we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with independent electrical control over the SO couplings via top gate voltage $V_T$ and back gate voltage $V_B$ to extract all SO couplings when combined with detailed numerical simulations. We demonstrate for the first time the gate control of the renormalized $\beta$ and the continuous locking of the SO fields at $\alpha =\beta$; i.e., we are able to vary both $\alpha$ and $\beta$ controllably and continuously with $V_T$ and $V_B$, while keeping them locked at equal strengths. This makes possible a new concept: “stretchable PSHs,” i.e., helical spin patterns with continuously variable pitches $P$ over a wide parameter range. Stretching the PSH, i.e., gate controlling $P$ while staying locked in the PSH regime, provides protection from spin decay at the symmetry point $\alpha =\beta$, thus offering an important advantage over other methods. This protection is limited mainly by the cubic Dresselhaus term, which breaks the unidirectionality of the total SO field and causes spin decay at higher electron densities. We quantify the cubic term, and find it to be sufficiently weak so that the extracted spin-diffusion lengths and decay times show a significant enhancement near $\alpha =\beta$. Since within the continuous-locking regime quantum transport is diffusive (2D) for charge while ballistic (1D) for spin and thus amenable to coherent spin control, stretchable PSHs could provide the platform for the much heralded long-distance communication $\sim 8–25\mu \mathrm{m}$ between solid-state spin qubits, where the spin diffusion length for $\alpha \ne \beta$ is an order of magnitude smaller.

We study spinless electrons in a single-channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire, the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one-dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau-level filling factors. For odd-denominator fillings $\nu =1/(2n+1)$, wires at the Luttinger phase form Laughlin states, while wires in the strongly paired phase form a bosonic fractional quantum Hall state of strongly bound pairs at a filling of $1/(8n+4)$. The transition between the two is of the universality class of Ising transitions in three dimensions. For even-denominator fractions $\nu =1/2n$, the two single-wire phases translate into four quantum Hall states. Two of those states are bosonic fractional quantum Hall states of weakly and strongly bound pairs of electrons. The other two are non-Abelian quantum Hall states, which originate from coupling wires close to their critical point. One of these non-Abelian states is the Moore-Read state. The transitions between all of these states are of the universality class of Majorana transitions. We point out some of the properties that characterize the different phases and the phase transitions.

The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model shows that the boundaries of language dialect regions are controlled by a length minimizing effect analogous to surface tension, mediated by variations in population density which can induce curvature, and by the shape of coastline or similar borders. The predictability of dialect regions arises because these effects will drive many complex, randomized early states toward one of a smaller number of stable final configurations. The model is able to reproduce observations and predictions of dialectologists. These include dialect continua, isogloss bundling, fanning, the wavelike spread of dialect features from cities, and the impact of human movement on the number of dialects that an area can support. The model also provides an analytical form for Séguy’s curve giving the relationship between geographical and linguistic distance, and a generalization of the curve to account for the presence of a population center. A simple modification allows us to analytically characterize the variation of language use by age in an area undergoing linguistic change.

Coupling photons to Rydberg excitations in a cold atomic gas yields unprecedentedly large optical nonlinearities at the level of individual light quanta. Here, the basic mechanism exploits the strong interactions between Rydberg atoms to block the formation of nearby dark-state polaritons. However, the dissipation associated with this mechanism ultimately limits the performance of many practical applications. In this work, we propose a new approach to strong photon interactions via a largely coherent mechanism at drastically suppressed photon losses. Rather than a polariton blockade, it is based on an interaction-induced conversion between distinct types of dark-state polaritons with different propagation characteristics. We outline a specific implementation of this approach and show that it permits us to turn a single photon into an effective mirror with a robust and continuously tunable reflection phase. We describe potential applications, including a detailed discussion of achievable operational fidelities.

A system of Majorana zero modes with random infinite-range interactions—the Sachdev-Ye-Kitaev (SYK) model—is thought to exhibit an intriguing relation to the horizons of extremal black holes in two-dimensional anti–de Sitter space. This connection provides a rare example of holographic duality between a solvable quantum-mechanical model and dilaton gravity. Here, we propose a physical realization of the SYK model in a solid-state system. The proposed setup employs the Fu-Kane superconductor realized at the interface between a three-dimensional topological insulator and an ordinary superconductor. The requisite $N$ Majorana zero modes are bound to a nanoscale hole fabricated in the superconductor that is threaded by $N$ quanta of magnetic flux. We show that when the system is tuned to the surface neutrality point (i.e., chemical potential coincident with the Dirac point of the topological insulator surface state) and the hole has sufficiently irregular shape, the Majorana zero modes are described by the SYK Hamiltonian. We perform extensive numerical simulations to demonstrate that the system indeed exhibits physical properties expected of the SYK model, including thermodynamic quantities and two-point as well as four-point correlators, and discuss ways in which these can be observed experimentally.

Genetic information is stored in a linear sequence of base pairs; however, thermal fluctuations and complex DNA conformations such as folds and loops make it challenging to order genomic material for in vitro analysis. In this work, we discover that rotation-induced macromolecular spooling of DNA around a rotating microwire can monotonically order genomic bases, overcoming this challenge. We use single-molecule fluorescence microscopy to directly visualize long DNA strands deforming and elongating in shear flow near a rotating microwire, in agreement with numerical simulations. While untethered DNA is observed to elongate substantially, in agreement with our theory and numerical simulations, strong extension of DNA becomes possible by introducing tethering. For the case of tethered polymers, we show that increasing the rotation rate can deterministically spool a substantial portion of the chain into a fully stretched, single-file conformation. When applied to DNA, the fraction of genetic information sequentially ordered on the microwire surface will increase with the contour length, despite the increased entropy. This ability to handle long strands of DNA is in contrast to modern DNA sample preparation technologies for sequencing and mapping, which are typically restricted to comparatively short strands, resulting in challenges in reconstructing the genome. Thus, in addition to discovering new rotation-induced macromolecular dynamics, this work inspires new approaches to handling genomic-length DNA strands.

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here, we present the formulation of a general mathematical framework, which could be used to extract, from scattering experiments, the molecular relaxation of deformed polymers. By combining and modestly extending several key conceptual ingredients in the literature, we show how the anisotropic single-chain structure factor can be decomposed by spherical harmonics and experimentally reconstructed from its cross sections on the scattering planes. The resulting wave-number-dependent expansion coefficients constitute a characteristic fingerprint of the macromolecular deformation, permitting detailed examinations of polymer dynamics at the microscopic level. We apply this approach to survey a long-standing problem in polymer physics regarding the molecular relaxation in entangled polymers after a large step deformation. The classical tube theory of Doi and Edwards predicts a fast chain retraction process immediately after the deformation, followed by a slow orientation relaxation through the reptation mechanism. This chain retraction hypothesis, which is the keystone of the tube theory for macromolecular flow and deformation, is critically examined by analyzing the fine features of the two-dimensional anisotropic spectra from small-angle neutron scattering by entangled polystyrenes. We show that the unique scattering patterns associated with the chain retraction mechanism are not experimentally observed. This result calls for a fundamental revision of the current theoretical picture for nonlinear rheological behavior of entangled polymeric liquids.

We achieve the strong-coupling regime between an ensemble of phosphorus donor spins in a highly enriched ${}^{28}\mathrm{Si}$ crystal and a 3D dielectric resonator. Spins are polarized beyond Boltzmann equilibrium using spin-selective optical excitation of the no-phonon bound exciton transition resulting in $N=3.6\times 10^{13}$ unpaired spins in the ensemble. We observe a normal mode splitting of the spin-ensemble–cavity polariton resonances of $2g\sqrt{N}=580\mathrm{kHz}$ (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75 000 ($\gamma \ll \kappa \approx 60\mathrm{kHz}$, where $\gamma$ and $\kappa$ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time ($T_2^{*}=9\mu \mathrm{s}$) providing a wide window for viewing the dynamics of the coupled spin-ensemble–cavity system. The free-induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate $g\sqrt{N}$. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial $Z$ projection of the psuedospin using optical excitation and microwave manipulation, respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt $\pi$-phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model.