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While intense laser irradiation and moir\'e engineering have independently proven powerful for tuning material properties on demand in condensed matter physics, their combination remains unexplored. Here we exploit tilted laser illumination to create spatially modulated light-matter interactions, leading to two striking phenomena in graphene. First, using two lasers tilted along the same axis, we create a quasi-1D supercell hosting a network of Floquet topological states that generate controllable and scalable photocurrents spanning the entire irradiated region. Second, by tilting lasers along orthogonal axes, we establish a 2D polarization moir\'e pattern giving rise to closed orbital propagation of Floquet states, reminiscent of bulk Landau states. These features, imprinted in the bulk of the irradiated region and controlled through laser wavelength and tilt angles, establish a new way for engineering quantum states through spatially modulated light-matter coupling., Comment: 14 pages, 10 figures

Light-induced phenomena in materials can exhibit exotic behavior that extends beyond equilibrium properties, offering new avenues for understanding and controlling electronic phases. So far, non-equilibrium phenomena in solids have been predominantly explored using femtosecond laser pulses, which generate transient, ultra-fast dynamics. Here, we investigate the steady non-equilibrium regime in graphene induced by a continuous-wave (CW) mid-infrared laser. Our transport measurements reveal signatures of a long-lived Floquet phase, where a non-equilibrium electronic population is stabilized by the interplay between coherent photoexcitation and incoherent phonon cooling. The observation of non-equilibrium steady states using CW lasers opens a new regime for low-temperature Floquet phenomena, paving the way toward Floquet engineering of steady-state phases of matter., Comment: 21 pages + supplemental materials

We establish a framework for a mechanism steering state vector collapse through time evolution as described by the Schr\"odinger's equation. Under the premise of a non-Hermitian Hamiltonian dynamics, a main outcome is that collapse has to occur when the Hamiltonian completes a closed loop in the parameter space encoding the interaction with the meter. For two-level systems, we put forward the phenomenon of chiral state conversion as a mechanism effectively eliminating superpositions. Our results open a way to simulate quantum measurements in classical systems that up to now were restricted to the Schr\"odinger part of the quantum dynamics., Comment: 7 pages, 1 figure

Non-reciprocal interactions are ubiquitous in nature, and in Physics this realization has started to push boundaries by making non-hermiticity a fundamental rather than exceptional property. Despite the prevalence of evanescent coupling in physics, little attention has been paid to wavefunction profiles, with reciprocity often assumed for practical reasons. Our work challenges this assumption by demonstrating the origin of non-reciprocity in a photonic platform. We experimentally validate non-reciprocal dynamics on directional couplers fabricated via femtosecond laser writing, and corroborate our findings through continuous simulations. Extending these insights, we observe the topological Non-Hermitian Skin Effect in a Rice-Mele lattice model. Our findings open new avenues of research using simple and scalable configurations, and potentially guiding future developments in Physics and beyond., Comment: 17 pages, 3 figures

We investigate Lorentz invariance breaking in quantum wires due to Rashba spin-orbit interaction and transverse phonons. Using bosonization, we derive an effective action coupling electronic and mechanical degrees of freedom. Stikingly, at a quantum phase transition between straight and bent wire states, we find a gapped phonon mode and a gapless mode with quadratic dispersion, signaling the breaking of Lorentz invariance. We explore stability conditions for general potentials and propose nano-mechanical back-action as a sensitive tool for detecting this transition, with implications for Sliding Luttinger Liquids and dimensional crossover studies., Comment: 6 pages, 5 figures

We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby making the last cell incomplete. We find that an anti-PT transition occurs at exceptional points of edge states at certain parameters, which does not coincide with the conventional topological phase transition characterized by the Berry phase, provided the imaginary on-site potential is large enough. Interestingly, when the potential exceeds a critical value, edge states appear even in the regime with a trivial Berry phase. To characterize these novel edge states we present topological invariants associated with the system's parity. Finally, we analyze the dynamics for initial states with different spatial distributions, which exhibit distinct dynamics for the commensurate and incommensurate cases, depending on the imaginary part of edge state energy., Comment: 10 pages, 8 figures

The interplay of spin and lattice fluctuations in two-dimensional magnets without inversion symmetry is investigated. We find a general form for the magnetoelastic coupling between magnons and existing chiral phonons based on the symmetries of the crystalline lattice. We show that in hexagonal lattices, the coupling of magnons and chiral phonons derives from an anisotropic exchange spin model containing topological phases of magnons. Using the Heisenberg-Kitaev-$\Gamma$ model, we show how magnon-polaron edge states with circular polarization arise from this interaction. Our findings exploit the polarization degrees of freedom in spin-lattice systems, thus setting the ground for the transfer of angular momentum between chiral phonons and magnons., Comment: 7 pages, 2 figures

In the context of the measurement problem, we propose to model the interaction between a quantum particle and an "apparatus" through a non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized quantum state split into two spin components (via a Stern-Gerlach experiment) and that undergoes a wave-function collapse driven by a non-Hermitian Hatano-Nelson Hamiltonian. We further analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function obtained under a Schr\"{o}dinger-type evolution. We finally discuss a thought experiment where manipulation of the apparatus could challenge standard quantum mechanics predictions., Comment: 5 pages, 4 figures

Advancements in photonics technologies have significantly enhanced their capability to facilitate experiments involving quantum light, even at room temperature. Nevertheless, fully integrating photonic chips that include quantum light sources, effective manipulation and transport of light minimizing losses, and appropriate detection systems remains an ongoing challenge. Topological photonic systems have emerged as promising platforms to protect quantum light properties during propagation, beyond merely preserving light intensity. In this work, we delve into the dynamics of non-classical light traversing a Su-Schrieffer-Heeger photonic lattice with topological domain walls. Our focus centers on how topology influences the quantum properties of light as it moves across the array. By precisely adjusting the spacing between waveguides, we achieve dynamic repositioning and interaction of domain walls, facilitating effective beam-splitting operations. Our findings demonstrate high-fidelity transport of non-classical light across the lattice, replicating known results that are now safeguarded by the topology of the system. This protection is especially beneficial for quantum communication protocols with continuous variable states. Our study enhances the understanding of light dynamics in topological photonic systems and paves the way for high-fidelity, topology-protected quantum communication., Comment: 8 pages, 5 figures

We report on a theoretical study of a Cs$_2$ molecule illuminated by two lasers and show how it can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming Light-Induced Conical Intersections and modifiable avoided crossings. Our findings show how laser field orientation and strength, along with initial phase differences, can control molecular state transitions, especially on the micromotion scale. We also discuss extensively how the interaction of radiation with matter gives rise to the emergence of potential energy surfaces of hybrids of radiation and molecular states. This research advances a technique for manipulating photoassociation processes in Cs$_2$ molecules, offering potential new avenues in quantum control., Comment: 12 pages, 4 figures

The starting point for much of multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. Some multivariate data sets, however, may be best conceptualized not as $n$ discrete $p$-variate observations, but as $p$ curves or functions defined on a common time interval. Here we introduce a framework for extending techniques of multivariate analysis to such settings. The proposed continuous-time multivariate analysis (CTMVA) framework rests on the assumption that the curves can be represented as linear combinations of basis functions such as $B$-splines, as in the Ramsay-Silverman representation of functional data; but whereas functional data analysis extends MVA to the case of observations that are curves rather than vectors -- heuristically, $n\times p$ data with $p$ infinite -- we are instead concerned with what happens when $n$ is infinite. We present continuous-time extensions of the classical MVA methods of covariance and correlation estimation, principal component analysis, Fisher's linear discriminant analysis, and $k$-means clustering. We show that CTMVA can improve on the performance of classical MVA, in particular for correlation estimation and clustering, and can be applied in some settings where classical MVA cannot, including variables observed at disparate time points. CTMVA is illustrated with a novel perspective on a well-known Canadian weather data set, and with applications to data sets involving international development, brain signals, and air quality. The proposed methods are implemented in the publicly available R package \texttt{ctmva}.

We report on the theoretical investigation of the topological properties of a periodically quenched one-dimensional dimerized lattice where a piece-wise constant Hamiltonian switches from $h_1$ to $h_2$ at a partition time $t_p$ within each driving period $T$. We examine different dimerization patterns for $h_1$ and $h_2$ and the interplay with the driving parameters that lead to the emergence of topological states both at zero energy and at the edge of the Brillouin-Floquet quasi-energy zone. We illustrate different phenomena, including the occurrence of both edge states in a semimetal spectrum, the topological transitions, and the generation of zero-energy topological states from trivial snapshots. The role of the different symmetries in our results is also discussed., Comment: 13 pages, 10 figures

Recently, the applications of the methodologies of Reinforcement Learning (RL) to NP-Hard Combinatorial optimization problems have become a popular topic. This is essentially due to the nature of the traditional combinatorial algorithms, often based on a trial-and-error process. RL aims at automating this process. At this regard, this paper focuses on the application of RL for the Vehicle Routing Problem (VRP), a famous combinatorial problem that belongs to the class of NP-Hard problems. In this work, first, the problem is modeled as a Markov Decision Process (MDP) and then the PPO method (which belongs to the Actor-Critic class of Reinforcement learning methods) is applied. In a second phase, the neural architecture behind the Actor and Critic has been established, choosing to adopt a neural architecture based on the Convolutional neural networks, both for the Actor and the Critic. This choice resulted in effectively addressing problems of different sizes. Experiments performed on a wide range of instances show that the algorithm has good generalization capabilities and can reach good solutions in a short time. Comparisons between the algorithm proposed and the state-of-the-art solver OR-TOOLS show that the latter still outperforms the Reinforcement learning algorithm. However, there are future research perspectives, that aim to upgrade the current performance of the algorithm proposed., Comment: This version is really preliminary and the possibility of errors and typos is high

Unlike the chirality of electrons, the intrinsic chirality of phonons has only surfaced in recent years. Here we report on the effects of the interaction between electrons and chiral phonons in two-dimensional materials by using a non-perturbative solution. We show that chiral phonons introduce inelastic \textit{Umklapp} processes resulting in copropagating edge states which coexist with a continuum. Transport simulations further reveal the robustness of the edge states. Our results hint on the possibility of having a metal embedded with hybrid electron-phonon states of matter., Comment: 8 pages, 6 figures

Three-dimensional topological gapless phases have attracted significant attention due to their unique electronic properties. A flagship example are Weyl semimetals, which require breaking time-reversal or inversion symmetry. In two dimensions, the dimensionality reduction requires imposing an additional symmetry, thereby weakening the phase. Like its three-dimensional counterpart, these two-dimensional Weyl semimetals present edge states directly related to Weyl nodes. The direct comparison with the edge states in zigzag-like terminated graphene ribbons is unavoidable, offering the question of how robust these states are and their differences. Here we benchmark the robustness of the edge states in two-dimensional Weyl semimetals without inversion symmetry with those present in zigzag graphene ribbons. Our results show that, despite having a similar electronic band structure, the edge states of two-dimensional Weyl semimetal are more robust against vacancies than graphene ribbons. We attribute this enhanced robustness to a crucial role of the spin degree of freedom in the former case, Comment: 8 pages, 6 figures

What is the role of topology in the propagation of quantum light in photonic lattices? We address this question by studying the propagation of squeezed states in a topological one-dimensional waveguide array, benchmarking our results with those for a topologically trivial localized state, and studying their robustness against disorder. Specifically, we study photon statistics, one-mode and two-mode squeezing, and entanglement generation when the localized state is excited with squeezed light. These quantum properties inherit the shape of the localized state but, more interestingly, and unlike in the topologically trivial case, we find that propagation of squeezed light in a topologically protected state robustly preserves the phase of the squeezed quadrature as the system evolves. We show how this latter topological advantage can be harnessed for quantum information protocols., Comment: Main text: 11 pages and 6 figures, appendix: 3 pages and 3 figures, 1 ancillary file (mp4)

In recent years, the notion of Quantum Materials has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and cold atom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moire materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry., Comment: 93 pages, 27 figures

We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multi-terminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at $\pm\,\hbar\Omega/2$ lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, where two terms cancel out exactly. More interestingly, we show that near the Dirac point changing the laser polarization (circular right or circular left) controls the Hall conductance, by allowing to switch it on or off, or even by flipping its sign, thereby reversing the chirality of the edge states. This might lead to new avenues to fully control topologically protected transport., Comment: 19 pages, 19 figures

Harnessing the unique features of topological materials for the development of a new generation of topological based devices is a challenge of paramount importance. Using Floquet scattering theory combined with atomistic models we study the interplay between laser illumination, spin and topology in a two-dimensional material with spin-orbit coupling. Starting from a topological phase, we show how laser illumination can selectively disrupt the topological edge states depending on their spin. This is manifested by the generation of pure spin currents and spin-polarized charge photocurrents under linearly and circularly polarized laser-illumination, respectively. Our results open a path for the generation and control of spin-polarized photocurrents., Comment: 7 pages, 4 figures

Patients undergoing physical rehabilitation therapy must perform series of exercises regularly over a long period of time to improve, or at least not to worsen, their condition. Rehabilitation can easily become boring because of the tedious repetition of simple exercises, which can also cause mild pain and discomfort. As a consequence, patients often fail to follow their rehabilitation schedule with the required regularity, thus endangering their recovery. In the last decade, video games have become largely popular and the availability of advanced input controllers has made them a viable approach to make physical rehabilitation more entertaining while increasing patients motivation. In this paper, we present a framework integrating serious games for the lower-limb rehabilitation of children suffering from Juvenile Idiopathic Arthritis (JIA). The framework comprises games that implement parts of the therapeutic protocol followed by the young patients and provides modules to tune, control, record, and analyze the therapeutic sessions. We present the result of a preliminary validation we performed with patients at the clinic under therapists supervision. The feedback we received has been overall very positive both from patients, who enjoyed performing their usual therapy using video games, and therapists, who liked how the games could keep the children engaged and motivated while performing the usual therapeutic routine.

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits rich transport and topological properties. By varying the detuning coefficient we find a regime where bands become flatter (with reduced transport) and, a second regime, where both bands connect on at a gap-closing transition (with enhanced transport). We detect an asymmetric transport due to the asymmetric inter-mode coupling and a linear energy exchange mechanism between modes. Further analysis show that the bands have a topological transition with a non-trivial Zak phase which leads to the appeareance of edge states in a finite system. Finally, for zero detuning, we found a symmetric condition for coupling constants, where the linear spectrum becomes completely flat, with states fully localized in space occupying only two lattice sites., Comment: 8 pages, 5 figures

In this article, we calculate the magnon spectrum of Kitaev-Heisenberg magnets. This model has been recently proposed as a spin Hamiltonian to model $\text{CrI}_3$ and other two-dimensional magnets. It is a minimal spin Hamiltonian that includes a contribution stemming from a Heisenberg, isotropic exchange, and a contribution arising from a Kitaev interaction, anisotropic and frustrated exchange. Our calculations reveal the topological nature of the magnons and a gap that opens at the $K$ and $K^\prime$ points. These topological properties give rise to effects such as thermal Hall effect. In addition to the bulk properties, we calculate the magnon spectrum of nanoribbons illustrating the corresponding edge states., Comment: 5 pages, 4 figures

We report on the effect of laser illumination with circularly polarized light on the electronic structure of AB-stacked graphite samples. By using Floquet theory in combination with Green's function techniques, we find that the polarized light induces band-gap openings at the Floquet zone edge $\hbar\Omega/2$, bridged by chiral boundary states. These states propagate mainly along the borders of the constituting layers as evidenced by the time-averaged local density of states and the probability current density in several geometries. Semianalytic calculations of the Chern number suggest that these states are of topological nature, similar to those found in illuminated 2D samples like monolayer and bilayer graphene. These states are promising candidates for the realization of a three-dimensional version of the quantum Hall effect for Floquet systems., Comment: 16 pages, 8 figures

Topological states require the presence of extended bulk states, as usually found in the picture of energy bands and topological states bridging the bulk gaps. But in driven systems this can be circumvented, and one can get topological states coexisting with fully localized bulk states, as in the case of the anomalous Floquet-Anderson insulator. Here, we show the fingerprints of this peculiar topological phase in the transport properties and their dependence on the disorder strength, geometrical configuration (two-terminal and multiterminal setups) and details of the driving protocol., Comment: 7 pages, 5 figures

The search of topological states in non-Hermitian systems has gained a strong momentum over the last two years climbing to the level of an emergent research front. In this Perspective we give an overview with a focus in connecting this topic to others like Floquet systems. Furthermore, using a simple scattering picture we discuss an interpretation of concepts like the Hamiltonian's defectiveness, i.e. the lack of a full basis of eigenstates, crucial in many discussions of topological phases of non-Hermitian Hamiltonians., Comment: 22 pages, 4 figures, invited article to appear in Journal of Physics: Materials, special issue

We propose a directional switching effect in a metallic device. To such end we exploit a graphene-based device with a three-terminal geometry in the presence of a magnetic field. We show that unidirectional charge and valley currents can be controlled by the Fermi energy and the magnetic field direction in the active device. Interestingly, unidirectional transport of charge and valley is generated between two-terminals at the same bias voltage. Furthermore, we quantify the valley depolarization as a function of disorder concentration. Our results open a way for active graphene-based valleytronics devices.

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the context of photonic systems, where one needs to account for gain and loss, circuits of resonators, and also when modeling the lifetime due to interactions in condensed matter systems. Here we provide a brief overview of this rapidly growing subject, the search for topological states and a bulk-boundary correspondence in non-Hermitian systems., Comment: Invited short review for the special issue "Topological States of Matter: Theory and Applications"

Rehabilitation is a painful and tiring process involving series of exercises that patients must repeat over a long period. Unfortunately, patients often grow bored, frustrated, and lose motivation making rehabilitation less effective. In the recent years video games have been widely used to implement rehabilitation protocols so as to make the process more entertaining, engaging and to keep patients motivated. In this paper, we present an integrated framework we developed for the wrist rehabilitation of patients affected by Juvenile Idiopathic Arthritis (JIA) following a therapeutic protocol at the Clinica Pediatrica G. e D. De Marchi. The framework comprises four video games and a set modules that let the therapists tune and control the exercises the games implemented, record all the patients actions, replay and analyze the sessions. We present the result of a preliminary validation we performed with four poliarticular JIA patients at the clinic under the supervision of the therapists. Overall, we received good feedback both from the young patients, who enjoyed performing known rehabilitation exercises using video games, and therapists who were satisfied with the framework and its potentials for engaging and motivating the patients.

The search of new means of generating and controlling topological states of matter is at the front of many joint efforts, including bandgap engineering by doping and light-induced topological states. Most of our understading, however, is based on a single particle picture. Topological states in systems including interaction effects, such as electron-electron and electron-phonon, remain less explored. By exploiting a non-perturbative and non-adiabatic picture, here we show how the interaction between electrons and a coherent phonon mode can lead to a bandgap hosting edge states of topological origin. Further numerical simulations witness the robustness of these states against different types of disorder. Our results contribute to the search of topological states, in this case in a minimal Fock space., Comment: 11 pages, 6 figures

Shift current---a photocurrent induced by light irradiating noncentrosymmetric materials in the absence of any bias voltage or built-in electric field---is one of the mechanisms of the so-called bulk photovoltaic effect. It has been traditionally described as a nonlinear optical response of periodic solids to continuous wave light using a perturbative formula, which is linear in the intensity of light and which involves Berry connection describing the shift in the center of mass position of the Wannier wave function associated with the transition between the valence and conduction bands. We analyze realistic two-terminal devices, where paradigmatic Rice-Mele model is sandwiched between two metallic electrodes, using recently developed time-dependent nonequilibrium Green function algorithms scaling linearly in the number of time steps and capable of treating nonperturbative effects in the amplitude of external time-dependent fields. This unveils novel features: superballistic transport, signified by time dependence of the displacement, $\sim t^\nu$ with $\nu > 1$, of the photoexcited charge carriers from the region where the femtosecond light pulse is applied toward the electrodes; and photocurrent quadratic in light intensity at subgap frequencies of light due to two-photon absorption processes that were missed in previous perturbative analyses. Furthermore, frequency dependence of the DC component of the photocurrent reveals shift currents as a realization of nonadiabatic quantum charge pumping enabled by breaking of left-right symmetry of the device structure. This demonstrates that a much wider class of systems, than the usually considered polar noncentrosymmetric bulk materials, can be exploited to generate nonzero DC component of photocurrent in response to unpolarized light and optimize shift-current-based solar cells and optoelectronic devices., Comment: 8 pages, 6 figures, PDFLaTeX; two additional movies, depicting spatial profiles of local shift current in clean and disordered systems during application of fs light pulse, are available from https://wiki.physics.udel.edu/qttg/Publications