From a semiclassical perspective, the Bohr-Sommerfeld quantization of the closed cyclotron orbits for charged particles such as electrons in an external magnetic field gives rise to discrete Landau levels and a series of fascinating quantum Hall phenomena. Here, we consider topologically nontrivial physics from a distinct origin, where the cyclotron orbits take nontrivial knotting structures such as a trefoil knot. We present a scenario of a Weyl semimetal with a slab geometry, where the Fermi arcs on the opposing surfaces can cross without interfering with each other and form a knot together with the bulk Weyl nodes, and in an external magnetic field, the resulting chiral Landau levels. We provide a microscopic lattice model to realize a cyclotron orbit with an unconventional geometry of a trefoil knot and study the corresponding quantum oscillations. Interestingly, unlike the conventional ring-shaped cyclotron orbit, a trefoil knot is self-threading, allowing the magnetic field line along the cyclotron orbit to contribute to the overall Berry phase and therefore altering the external magnetic field for each quantization level. The cyclotron orbit knot offers an arena of the nontrivial knot theory in three spatial dimensions and its subsequent physical consequences.

Recent progress in nanoscale optics is driven by the physics of electric and magnetic resonances supported by high-index dielectric nanoparticles. Here, we exploit optical bound states in the continuum in a subwavelength particle enhanced by an engineered substrate undergoing an epsilon-near-zero transition from an insulator to a conductor, and uncover how to boost dramatically high-order parametric nonlinear effects. Our strategy makes feasible an observation of a variety of multistep cascaded and multifrequency nonlinear effects in an individual subwavelength resonator. This would expand substantially the range of applications of Mie-resonant dielectric metaphotonics for highly efficient subwavelength optical circuitry, nonlinear metadevices, ultrasensitive hyperspectral sensing, and quantum nanophotonics.

The first indication of a pseudogap in cuprates came from a sudden decrease of the NMR Knight shift at a doping-dependent temperature $T^{*}\left(\delta \right)$. Since then, experiments have found phase transitions at a lower $T_{\text{phase}}^{*}\left(\delta \right)$. Using plaquette cellular dynamical mean field for the square-lattice Hubbard model at high temperature, where the results are reliable, we show that $T^{*}\left(\delta \right)$ shares many features of $T_{\text{phase}}^{*}\left(\delta \right)$. The remarkable agreement with several experiments, including quantum critical behavior of the electronic specific heat, supports the view that the pseudogap is controlled by a finite-doping extension of the Mott transition. We propose further experimental tests.

Interaction of electromagnetic radiation with time-variant objects is a fundamental problem whose study involves foundational principles of classical electrodynamics. Such study is a necessary preliminary step for delineating the novel research field of linear time-varying metamaterials and metasurfaces. A closer look to the literature, however, reveals that this crucial step has not been addressed and important simplifying assumptions have been made. Before proceeding to studies of linear time-varying metamaterials and metasurfaces with their effective parameters, we need to rigorously describe the electric and magnetic responses of a temporally modulated meta-atom. Here, we introduce a theoretical model which describes a time-variant meta-atom and its interaction with incident electromagnetic waves in time domain. The developed general approach is specialized for a dipole emitter/scatterer loaded with a time-varying reactive element. We confirm the validity of the theoretical model with full-wave simulations. Our study is of major significance also in the area of nanophotonics and nano-optics because the optical properties of all-dielectric and plasmonic nanoparticles can be varied in time in order to achieve intriguing scattering phenomena.

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry-breaking phase transitions in systems with open boundaries. Recently, it has been shown that a correct description requires one to extend Bloch band theory into the complex plane. A still open question is whether the non-Hermitian skin effect and non-Bloch symmetry-breaking phase transitions can be probed by real-space wave dynamics far from edges, which is entirely governed by ordinary Bloch bands. Here it is shown that the Lyapunov exponent in the long-time behavior of bulk wave dynamics can generally reveal non-Bloch symmetry-breaking phase transitions and the existence of the non-Hermitian skin effect.

Broadband spin-photon interfaces for the long-lived storage of photonic quantum states are key elements for quantum information technologies. Yet, the reliable operation of such memories in the quantum regime is challenging due to photonic noise arising from technical and/or fundamental limitations in the storage-and-recall processes controlled by strong electromagnetic fields. Here, we experimentally implement a single-photon-level spin-wave memory in a laser-cooled rubidium gas, based on the recently proposed Autler-Townes splitting (ATS) protocol. We demonstrate the storage of 20-ns-long laser pulses, each containing an average of 0.1 photons, for 200 ns with an efficiency of $12.5\%$ and a signal-to-noise ratio above 30. Notably, the robustness of ATS spin-wave memory against motional dephasing allows for an all-spatial filtering of the control-field noise, yielding an ultralow unconditional noise probability of $3.3\times {10}^{-4}$, without the complexity of spectral filtering. These results highlight that broadband ATS memory in ultracold atoms is a preeminent option for storing quantum light.

Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically, in two dimensions, repeating an isotropic rotation twice maps a given point on the two-dimensional unit sphere (the unit circle) uniformly at random to any point on the unit sphere, reflecting a statistical symmetry as expected. In contrast, in three and higher dimensions, a point is mapped more often closer to the original point than a uniform distribution predicts. Curiously, in the limit of the dimension $d\to \infty$, a symmetric distribution is approached again. We intuitively explain the emergence of this asymmetry and why it disappears in higher dimensions by disentangling isotropic rotations into a sequence of partial actions. The asymmetry emerges in two qualitatively different forms and for a wide range of general random operations relevant in complex systems modeling, including repeated continuous and discrete rotations, roto-reflections and general orthogonal transformations.

The recent discovery of a nonmagnetic nematic quantum critical point (QCP) in the iron chalcogenide family ${\mathrm{FeSe}}_{1\text{−}x}{\mathrm{S}}_x$ has raised the prospect of investigating, in isolation, the role of nematicity on the electronic properties of correlated metals. Here we report a detailed study of the normal state transverse magnetoresistance (MR) in ${\mathrm{FeSe}}_{1\text{−}x}{\mathrm{S}}_x$ for a series of S concentrations spanning the nematic QCP. For all temperatures and $x$ values studied, the MR can be decomposed into two distinct components: one that varies quadratically in magnetic field strength ${\mu }_0\mathit{H}$ and one that follows precisely the quadrature scaling form recently reported in metals at or close to a QCP and characterized by a $H$-linear MR over an extended field range. The two components evolve systematically with both temperature and S substitution in a manner that is determined by their proximity to the nematic QCP. This study thus reveals the coexistence of two independent charge sectors in a quantum critical system. Moreover, the quantum critical component of the MR is found to be less sensitive to disorder than the quadratic (orbital) MR, suggesting that detection of the latter in previous MR studies of metals near a QCP may have been obscured.

Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. This research offers a comprehensive solution to a long-standing challenge regarding the lattice-based materials: how to systematically construct a lattice and transform it among different symmetric configurations in a predictable, scalable, and reversible way. By bridging the lattice geometry and rigid-folding kinematics of a group of origamis consisting of generic degree-4 vertices, we successfully construct all types of two- and three-dimensional Bravais lattices, and demonstrate that they can undergo all diffusionless phase transformations via rigid folding (i.e., dilation, extension, contraction, shear, and shuffle). Such folding-induced lattice transformations can trigger fundamental lattice-symmetry switches, which can either maintain or reconstruct the nearest-neighbor relationships according to a continuous symmetry measure. This study can foster the next generation of transformable lattice structures and materials with on-demand property tuning capabilities.

We present a topological characterization of time-periodically driven two-band models in $2+1$ dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three-dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.

A continuous transition for a system moving in a three-dimensional (3D) space to moving in a lower-dimensional space, 2D or 1D, can be made by means of an external squeezing potential. A squeeze along one direction gives rise to a 3D to 2D transition, whereas a simultaneous squeeze along two directions produces a 3D to 1D transition, without going through an intermediate 2D configuration. In the same way, for a system moving in a 2D space, a squeezing potential along one direction produces a 2D to 1D transition. In this work we investigate the equivalence between this kind of confinement procedure and calculations without an external field, but where the dimension $d$ is taken as a parameter that changes continuously from $d=3$ to $d=1$. The practical case of an external harmonic oscillator squeezing potential acting on a two-body system is investigated in detail. For the three transitions considered, $3\mathrm{D}\to 2\mathrm{D}, 2\mathrm{D}\to 1\mathrm{D}$, and $3\mathrm{D}\to 1\mathrm{D}$, a universal connection between the harmonic oscillator parameter and the dimension $d$ is found. This relation is well established for infinitely large 3D scattering lengths of the two-body potential for $3\mathrm{D}\to 2\mathrm{D}$ and $3\mathrm{D}\to 1\mathrm{D}$ transitions, and for infinitely large 2D scattering length for the $2\mathrm{D}\to 1\mathrm{D}$ case. For finite scattering lengths size corrections must be applied. The traditional wave functions for external squeezing potentials are shown to be uniquely related to the wave functions for specific noninteger dimension parameters, $d$.

We construct $n$ levels of nested, self-similar winnerless competition dynamics of which we explicitly work out the first three levels in the framework of generalized Lotka-Volterra equations. We choose microscopic rules such that the competition in the form of rock-paper-scissors is played between metapopulations, populations, and individuals at the same time. The trajectory of individual activities moves through a hierarchically structured heteroclinic network in a desired way. The hierarchy in structure is able to induce a separation of timescales that translates into nested spirals if the heteroclinic networks are coupled via diffusion on a spatial grid. For sufficiently strong diffusion the dynamics of interacting heteroclinic networks gets synchronized between the sites, which amounts to a large dimensional reduction of phase space. Possible applications lie in ecology and in brain dynamics. Our model reproduces in particular chunking dynamics with slow oscillations modulating fast oscillations modulating faster ones as observed in brain dynamics.

For two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous ($2+1$)-dimensional [($2+1$)-d] Chern-Simons (CS) response for the background gauge potential of the electromagnetic U(1) field. The Hall conductance is given by the quantized prefactor of the CS term, which is a momentum-space topological invariant. Here, we show that three-dimensional crystalline topological insulators with no other symmetries are described by a topological ($3+1$)-dimensional [($3+1$)-d] mixed CS term. In addition to the electromagnetic U(1) gauge field, this term contains elasticity tetrad fields $E_{\mu }^a(\mathbf{r},t)={\partial }_{\mu }{X}^a(\mathbf{r},t)$ which are gradients of crystalline U(1) phase fields $X^a(\mathbf{r},t)$ and describe the deformations of the crystal. For a crystal in three spatial dimensions $a=1,2,3$ and the mixed axial-gravitational response contains three parameters protected by crystalline symmetries: the weak momentum-space topological invariants. The response of the Hall conductance to the deformations of the crystal is quantized in terms of these invariants. In the presence of dislocations, the anomalous ($3+1$)-d CS term describes the Callan-Harvey anomaly inflow mechanism. The response can be extended to all odd spatial dimensions. The elasticity tetrads, being the gradients of the lattice U(1) fields, have canonical dimension of inverse length. Similarly, if such tetrad fields enter general relativity, the metric becomes dimensionful, but the physical parameters, such as Newton's constant, the cosmological constant, and masses of particles, become dimensionless.

We consider a simple, physically and biologically motivated model of transient subdiffusion having different exponents in the mean squared displacement at short and long times. For this purpose, the sum of two independent stable processes (with different indexes) as subordinators is used. Based on their infinitely divisible properties, the probability density function of particle displacements and the Fokker-Planck-type equation are obtained. Manifesting different origins of inhomogeneities (traps) in the system, the subordinators' indexes affect the asymptotic behavior of the mean squared displacement for a particle walking in the environment. Links to the Jonscher universal relaxation law and the Prabhakar-type memory functions are given.

Domains of finite topological charge density can exist in chiral materials and chiral matter. Spatial and temporal variation of the average topological charge density, represented by the $\theta$ field, induces anomalous currents that are responsible for the chiral magnetic effect, the anomalous Hall effect, and other phenomena that are intimately related to the chiral anomaly. We consider domains with constant average topological charge density. We argue that even though the Maxwell equations in the bulk are not altered, the chiral anomaly manifests itself by the way of the boundary conditions. This is illustrated by several examples. The first example deals with the refraction of plane electromagnetic waves on a surface of a constant-$\theta$ domain. We derive the modified Fresnel equations and discuss the effect of the chiral anomaly on the amplitude and polarization of the reflected and transmitted waves. In particular, we argue that the Brewster's angle is sensitive to the value of $\theta$. In the second example we compute the spectrum of the transition radiation at high frequencies and show that it is enhanced at finite $\theta$.

Lee-Yang zeros are points in the complex plane of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on the real axis, where a phase transition occurs. Partition function zeros have for many years been considered a purely theoretical concept; however, the situation is changing now as Lee-Yang zeros have been determined in several recent experiments. Motivated by these developments, we here devise a direct pathway from measurements of partition function zeros to the determination of critical points and universal critical exponents of continuous phase transitions. To illustrate the feasibility of our approach, we extract the critical exponents of the Ising model in two and three dimensions from the fluctuations of the total energy and the magnetization in lattices of finite size. Importantly, the critical exponents can be determined even if the system is away from the phase transition. Moreover, in contrast to standard methods based on Binder cumulants, it is not necessary to drive the system across the phase transition. As such, our method provides an intriguing perspective for investigations of phase transitions that may be hard to reach experimentally, for instance at very low temperatures or at very high pressures.

We report on spectroscopic and time-domain measurements on a fixed-frequency concentric transmon qubit in an applied in-plane magnetic field to explore its limits of magnetic field compatibility. We demonstrate quantum coherence of the qubit up to field values of $B=40\text{mT}$, even without an optimized chip design or material combination of the qubit. The dephasing rate ${\mathrm{\Gamma }}_{\phi }$ is shown to be unaffected by the magnetic field in a broad range of the qubit transition frequency. For the evolution of the qubit transition frequency, we find the unintended second junction created in the shadow angle evaporation process to be non-negligible and deduce an analytic formula for the field-dependent qubit energies. We discuss the relevant field-dependent loss channels, which cannot be distinguished by our measurements, inviting further theoretical and experimental investigation. Using well-known and well-studied standard components of the superconducting quantum architecture, we are able to reach a field regime relevant for quantum sensing and hybrid applications of magnetic spins and spin systems.

Most of the non-Abelian string vortices studied so far are characterized by two-dimensional $\mathbb{CP}\left(N\right)$ models with various degrees of supersymmetry on their worldsheet. We generalize this construction to “composite” non-Abelian strings supporting the Grassmann $\mathcal{G}(L,M)$ models (here $L+M=N$). The generalization is straightforward and provides, among other results, a simple and transparent way for counting the number of vacua in $\mathcal{N}=(2,2)$ Grassmannian model.

The notion of stringy naturalness—that an observable ${\mathcal{O}}_2$ is more natural than ${\mathcal{O}}_1$ if more (phenomenologically acceptable) vacua solutions lead to ${\mathcal{O}}_2$ rather than ${\mathcal{O}}_1$—is examined within the context of the Standard model (SM) and various supersymmetric models (SUSY) extensions: Constrained minimal supersymmetric standard model (CMSSM)/minimal supergravity model (mSUGRA), high-scale SUSY, and radiatively driven natural SUSY (RNS). Rather general arguments from string theory suggest a (possibly mild) statistical draw towards vacua with large soft SUSY breaking terms. These vacua must be tempered by an anthropic veto of nonstandard vacua or vacua with too large a value of the weak scale $m_{\mathrm{weak}}$. We argue that the SM, the CMSSM and various high-scale SUSY models are all expected to be relatively rare occurrences within the string theory landscape of vacua. In contrast, models with TeV-scale soft terms but with $m_{\mathrm{weak}}\sim 100\mathrm{GeV}$ and consequent light higgsinos (SUSY with radiatively driven naturalness) should be much more common on the landscape. These latter models have a statistical preference for $m_h\simeq 125\mathrm{GeV}$ and strongly interacting sparticles beyond current LHC reach. Thus, while conventional naturalness favors sparticles close to the weak scale, stringy naturalness favors sparticles so heavy that electroweak symmetry is barely broken and one is living dangerously close to vacua with charge-or-color breaking minima, no electroweak breaking or pocket universe weak-scale values too far from our measured value. Expectations for how landscape SUSY would manifest itself at collider and dark matter search experiments are then modified compared to usual notions.

We theoretically study the effect of a magnetic field on quasicrystalline superconductors, by modeling them as an attractive Hubbard model on a Penrose-tiling structure. We find that at low temperatures and under a high magnetic field there appears an exotic superconducting state with the order parameter changing its sign in real space. We discuss the state in comparison with the Fulde-Ferrell-Larkin-Ovchinnikov state proposed many years ago for periodic systems, clarifying commonalities and differences. It is remarkable that, even in the absence of periodicity, the electronic system finds a way to keep a coherent superconducting state with a spatially sign-changing order parameter compatible with the underlying quasiperiodic structure.