By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted ${\mathrm{WSe}}_2$ bilayers using large-scale molecular dynamics simulations. Our single-parameter theory is valid in graphene bilayers for twist angles $\theta \gtrsim 0.7°$, and in twisted ${\mathrm{WSe}}_2$ for $\theta \gtrsim 1.6°$. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this Letter, we propose a classical system of weakly nonlinear parametrically driven coupled oscillators as a test bed to understand these phases. Such a system of parametric oscillators can be used to model period-doubling instabilities of Josephson junction arrays as well as semiconductor lasers. To show that this instability leads to a discrete time crystal we first show that a certain limit of the system is close to Langevin dynamics in a symmetry breaking potential. We numerically show that this phase exists even in the presence of Ising symmetry breaking using a Glauber dynamics approximation. We then use a field theoretic argument to show that these results are robust to other approximations including the semiclassical limit when applied to dissipative quantum systems.

The combination of an in-plane honeycomb potential and of a photonic spin-orbit coupling (SOC) emulates a photonic or polaritonic analog of bilayer graphene. We show that modulating the SOC magnitude allows us to change the overall lattice periodicity, emulating any type of moiré-arranged bilayer graphene with unique all-optical access to the moiré band topology. We show that breaking the time-reversal symmetry by an effective exciton-polariton Zeeman splitting opens a large topological gap in the array of moiré flat bands. This gap contains one-way topological edge states whose constant group velocity makes an increasingly sharp contrast with the flattening moiré bands.

Anisotropy is a fundamental property of both material and photonic systems. The interplay between material and photonic anisotropies, however, has hardly been explored due to the vastly different length scales. Here we demonstrate exciton polaritons in a 2D antiferromagnet, CrSBr, coupled with an anisotropic photonic crystal cavity, where the spin, atomic, and photonic anisotropies are strongly correlated. Atomic anisotropy led to exceptionally strong coupling between anisotropic exciton and optical modes, which are stable against excitation densities a few orders of magnitude higher than polaritons in isotropic materials. The resulting polaritons feature anisotropic polarizations determined by the interplay of not only the anisotropies but also the dissipations and coupling of both exciton and photon modes, tunable by tens of degrees via many parameters. The work provides insights of excitons in CrSBr and demonstrates a prototype where atomic- and photonic-scale orders strongly couple, giving rise to unconventional properties in quantum materials and photonic devices.

Chiral phonons have been proposed to be involved in various physical phenomena, yet the chirality of molecular normal modes has not been well defined mathematically. Here we examine two approaches for assigning and quantifying the chirality of molecular normal modes in double-helical molecular wires with various levels of twist. First, associating with each normal mode a structure obtained by imposing the corresponding motion on a common origin, we apply the continuous chirality measure (CCM) to quantitatively assess the relationship between the chirality-weighted normal mode spectrum and the chirality of the underlying molecular structure. We find that increasing the amount of twist in the double helix shifts the mean normal mode CCM to drastically higher values, implying that the chirality of molecular normal modes is strongly correlated with that of the underlying molecular structure. Second, we assign to each normal mode a pseudoscalar defined as the product of atomic linear and angular momentum summed over all atoms, and we analyze the handedness of the normal mode spectrum with respect to this quantity. We find that twisting the double-chain structure introduces asymmetry between right- and left-handed normal modes so that in twisted structures different frequency bands are characterized by distinct handedness. This may give rise to global phenomena such as thermal chirality.

The efficient readout of the relevant information is pivotal for quantum simulation experiments. Often only single observables are accessed by performing standard projective measurements. In this work, we implement an atomic beam splitter by controlled outcoupling that enables a generalized measurement scheme. This gives us simultaneous access to number imbalance and relative phase in a system of two tunnel-coupled 1D Bose gases, which realize a quantum simulator of the sine-Gordon field theory. We demonstrate that the scheme is quantum limited by accessing number squeezing as a sensitive probe for added noise; further, we show that we can track Josephson oscillation dynamics with the generalized measurements. Finally, we show that the scheme allows the extraction of atoms while maintaining the system’s coherent dynamics, which opens up the door to accessing multitime correlation functions. Our scheme constitutes a step towards accessing quantum properties of the sine-Gordon field theory and, in the future, studying spatially extended systems under continuous monitoring.

The tomography of photonic quantum states is key in quantum optics, impacting quantum sensing, computing, and communication. Conventional detectors are limited in their temporal and spatial resolution, hampering high-rate quantum communication and local addressing of photonic circuits. Here, we propose to utilize free electron-photon interactions for quantum state tomography, introducing electron homodyne detection with potential for femtosecond-temporal and nanometer-spatial resolutions. The detectable quantum information level depends on the electron-photon interaction strength. Our Letter opens avenues for free-electron-based photodetection utilizing the ultrafast, subwavelength, nondestructive nature of free electrons.

Developing high-precision models of the nuclear force and propagating the associated uncertainties in quantum many-body calculations of nuclei and nuclear matter remain key challenges for ab initio nuclear theory. In this Letter, we demonstrate that generative machine learning models can construct novel instances of the nucleon-nucleon interaction when trained on existing potentials from the literature. In particular, we train the generative model on nucleon-nucleon potentials derived at second and third order in chiral effective field theory and at three different choices of the resolution scale. We then show that the model can be used to generate samples of the nucleon-nucleon potential drawn from a continuous distribution in the resolution scale parameter space. The generated potentials are shown to produce high-quality nucleon-nucleon scattering phase shifts. This work provides an important step toward a comprehensive estimation of theoretical uncertainties in nuclear many-body calculations that arise from the arbitrary choice of nuclear interaction and resolution scale.

Superdiffusion is surprisingly easily observed even in systems without the integrability underpinning this phenomenon. Indeed, the classical Heisenberg chain—one of the simplest many-body systems, and firmly believed to be nonintegrable—evinces a long-lived regime of anomalous, superdiffusive spin dynamics at finite temperature. Similarly, superdiffusion persists for long timescales, even at high temperature, for small perturbations around a related integrable model. Eventually, however, ordinary diffusion is believed to be asymptotically restored. We examine the timescales governing the lifetime of the superdiffusive regime, and argue that it diverges algebraically fast—both in deviation from the integrable limit, and at low temperature, where we find $t^{*}\sim T^{-\zeta }$ with an exponent possibly as large as $\zeta =8$. This can render the crossover to ordinary diffusion practically inaccessible.

Recently, it was proposed that the chiral central charge of a gapped, two-dimensional quantum many-body system is proportional to a bulk ground state entanglement measure known as the modular commutator. While there is significant evidence to support this relation, we show in this Letter that it is not universal. We give examples of lattice systems that have vanishing chiral central charge, which nevertheless give nonzero “spurious” values for the modular commutator for arbitrarily large system sizes, in both one and two dimensions. Our examples are based on cluster states and utilize the fact that they can generate nonlocal modular Hamiltonians.

Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. We show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.

Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.

A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early Universe and in particle colliders, starting from the standard model of particle physics. Classical computing methods, via the framework of lattice gauge theory, have experienced limited success in this mission. Quantum simulation of lattice gauge theories holds promise for overcoming computational limitations. Because of local constraints (Gauss’s laws), lattice gauge theories have an intricate Hilbert-space structure. This structure complicates the definition of thermodynamic properties of systems coupled to reservoirs during equilibrium and nonequilibrium processes. We show how to define thermodynamic quantities such as work and heat using strong-coupling thermodynamics, a framework that has recently burgeoned within the field of quantum thermodynamics. Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators. To illustrate our framework, we compute the work and heat exchanged during a quench in a ${\mathbb{Z}}_2$ lattice gauge theory coupled to matter in $1+1$ dimensions. The thermodynamic quantities, as functions of the quench parameter, evidence a phase transition. For general thermal states, we derive a simple relation between a quantum many-body system’s entanglement Hamiltonian, measurable with quantum-information-processing tools, and the Hamiltonian of mean force, used to define strong-coupling thermodynamic quantities.

We investigate the thermoelectric response of an Abrikosov vortex in type-II superconductors in the deep quantum limit. We consider two thermoelectric geometries, a type-II superconductor–insulator–normal-metal ($S\text{−}I\text{−}N$) junction and a local scanning tunneling microscope (STM)-tip normal metal probe over the superconductor. We exploit the strong breaking of particle-hole symmetry in vortex-bound states at subgap energies within the superconducting vortex to realize a giant thermoelectric response in the presence of fluxons. We predict a thermovoltage of a few $\mathrm{mV}/\mathrm{K}$ at subkelvin temperatures using both semianalytic and numerical self-consistent solutions of the Bogoliubov–de Gennes equations. Relevant thermoelectric coefficients and figures of merit $ZT$ are found within our models, both in linear and nonlinear regimes. $ZT$ of the $S\text{−}I\text{−}N$ junction is around 1, rising to above 3 for the STM junction centered at the vortex core. We also discuss how this system can be used as a sensitive low-temperature thermocouple, or a localized bolometer to detect low-energy single photons.

Fano resonance is achieved by tuning two coupled oscillators and has exceptional potential for modulating light dispersion. Here, distinct from the classical Fano resonances achieved through photonics methodologies, we introduce the Fano resonance in epsilon-near-zero (ENZ) media with novel electromagnetic properties. By adjusting the background permeability of the ENZ host, the transmission spectrum exhibits various dispersive line shapes and covers the full range of Fano parameter $q$ morphologies, from negative to positive infinity. Furthermore, owing to the stretched electromagnetic waves in the ENZ media, ENZ Fano resonance has geometry-independent characteristics and can even be attained on a subwavelength scale. With the assistance of the Fabry-Perot mode, the background relative permeability of waveguide ENZ media can be engineered, experimentally validating the concept of ENZ Fano resonance. Our Letter has significant implications for electromagnetic metamaterials and photonic devices, with potential applications in exotic dispersion modulation and synthesis of light.