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Macroscopic responses of magnets are often governed by magnetization and, thus, have been restricted to ferromagnets. However, such responses are strikingly large in the newly developed topological magnets, breaking the conventional scaling with magnetization. Taking the recently discovered antiferromagnetic (AF) Weyl semimetals as a prime example, we highlight the two central ingredients driving the significant macroscopic responses: the Berry curvature enhanced because of nontrivial band topology in momentum space, and the cluster magnetic multipoles in real space. The combination of large Berry curvature and multipoles enables large macroscopic responses such as the anomalous Hall and Nernst effects, the magneto-optical effect, and the novel magnetic spin Hall effect in antiferromagnets with negligible net magnetization, but also allows us to manipulate these effects by electrical means. Furthermore, nodal-point and nodal-line semimetallic states in ferromagnets may provide the strongly enhanced Berry curvature near the Fermi energy, leading to large responses beyond the conventional magnetization scaling. These significant properties and functions of the topological magnets lay the foundation for future technological development such as spintronics and thermoelectric technology.

International audience; The Berry phase of wave functions is a key quantity to understand various low-energy propertiesof matter, among which electric polarisation, orbital magnetism, as well as topological and ultra-relativisticphenomena. Standard approaches to probe the Berry phase in solids rely on the electron dynamics inresponse to electromagnetic forces. In graphene, probing the Berry phase π of the massless relativisticelectrons requires an external magnetic field. Here, we show that the Berry phase also affects the staticresponse of the electrons to a single atomic scatterer, through wavefront dislocations in the surroundingstanding-wave interference. This provides a new experimental method to measure the graphene Berry phasein the absence of any magnetic field and demonstrates that local disorder can be exploited as probe oftopological quantum matter in scanning tunnelling microscopy experiments.; Les interférences de quasiparticules observées par microscopie à effet tunnel sont particulièrementutiles pour étudier les propriétés électroniques de matériaux en surfaces. Ces interférences possèdent desinformations sur la surface de Fermi du système et leur résolution en énergie permet, dans certains cas,de reconstruire la relation dispersion. Nous montrons ici que les images d’interférences de quasiparticulespeuvent aussi contenir une information sur la phase de Berry qui caractérise la structure de bande dumatériau. La phase de Berry est une phase géométrique que les fonctions d’onde electroniques acquièrentlors d’une évolution cyclique dans un espace de paramètres. Elle est quantifiée lorsque la trajectoire del’évolution enserre une singularité des fonctions d’onde. Il s’agit alors d’une propriété topologique de lastructure de bande. La phase de Berry dans les solides est traditionnellement mesurée en appliquant deschamps électromagnétiques pour forcer les particules à former de trajectoires fermées. L’utilisation de lafigure d’interférence de quasiparticules permet de s’extraire de ce paradigme car la phase de Berry peutaffecter la réponse statique des électrons au désordre en l’absence de champ électromagnétique.

Perovskite functional ceramics have been widely applied for thermal protection owing to their unique physical properties. However, formation of oxygen vacancies under external stimuli usually limits their performance in practical applications. Therefore, the mechanism of the effect of oxygen vacancy on the layer structure of perovskite La0.9Sr0.1TiO3+δ was investigated by experiments and first-principles simulations. The experimental results showed that the lattice distortion occurred in oxygen-deficient environment to give a longer c-axis, along with a significant adjustment in the modes of A/B–O bond vibration, resulting in lower reflectivity. Advanced transmission electron microscopy studies revealed that oxygen vacancies induced localized atomic rearrangements via [TiO6] layer movements to adapt to the lattice distortion. This eventually restructured a part of the layer interfaces by expanding the overlapping projection of atoms in the c-axial direction. The specific transformation process was described as a compendious process, while geometric phase analysis effectively clarified how oxygen vacancies can inhibit reflectivity on the layer structure. Thus, this study provides effective approaches for researching the effects of oxygen vacancy on the physical properties of orthorhombic layer perovskite structures, which may facilitate the development of perovskite-based functional devices.

Traditional methods of generating vortex beams based on metasurfaces consist mainly in modulating propagation phase or geometric phase. Here, by introducing detour phase, we propose the construction of dual-polarized vortex beam generators in the form of metasurface and metagrating (MG). The phase is modulated through moving the position of meta-atoms instead of varying the geometrical parameters or rotating the unit cells. To use detour phase, two kinds of unit cells are designed to achieve specific diffraction order. Each unit can arbitrarily and independently adjust the operation frequency and diffraction angle of transverse electric (TE) and transverse magnetic (TM) polarizations. Two vortex beam generators are designed and fabricated with different topological charges carried by orthogonal polarizations. To demonstrate the ability to independently manipulate, two polarizations of the generator based on MG are designed in different frequency bands. Both the simulation and experimental results validate the proposed method, showing great potential for polarization division multiplexing in orbital angular momentum (OAM) communication systems.

As a classical or quantum system undergoes a cyclic evolution governed by slow change in its parameter space, it acquires a topological phase factor known as the geometric or Berry phase. One popular manifestation of this phenomenon is the Gouy phase which arises when the radius of curvature of the wavefront changes adiabatically in a cyclic manner, for e.g., when focused by a lens. Here, we report on a new manifestation of the Berry phase in 3D structured light which arises when its polarization state adiabatically evolves along the optical path. We show that such a peculiar evolution of angular momentum, which occurs under free space propagation, is accompanied by an accumulated phase shift that elegantly coincides with Berry’s prediction. Unlike the conventional dynamic phase, which accumulates monotonically with propagation, the Berry phase observed here can be engineered on demand, thereby enabling new possibilities; such as spin-dependent spatial frequency shifts, and modified phase matching in resonators and nonlinear interactions. Our findings expand the laws of wave propagation and can be applied in optics and beyond.

Charged particles subjected to magnetic fields form Landau levels (LLs). Originally studied in the context of electrons in metals1, fermionic LLs continue to attract interest as hosts of exotic electronic phenomena2,3. Bosonic LLs are also expected to realize novel quantum phenomena4,5, but, apart from recent advances in synthetic systems6,7, they remain relatively unexplored. Cooper pairs in superconductors—composite bosons formed by electrons—represent a potential condensed-matter platform for bosonic LLs. Under certain conditions, an applied magnetic field is expected to stabilize an unusual superconductor with finite-momentum Cooper pairs8,9 and exert control over bosonic LLs10–13. Here we report thermodynamic signatures, observed by torque magnetometry, of bosonic LL transitions in the layered superconductor Ba6Nb11S28. By applying an in-plane magnetic field, we observe an abrupt, partial suppression of diamagnetism below the upper critical magnetic field, which is suggestive of an emergent phase within the superconducting state. With increasing out-of-plane magnetic field, we observe a series of sharp modulations in the upper critical magnetic field that are indicative of distinct vortex states and with a structure that agrees with predictions for Cooper pair LL transitions in a finite-momentum superconductor10–14. By applying Onsager’s quantization rule15, we extract the momentum. Furthermore, study of the fermionic LLs shows evidence for a non-zero Berry phase. This suggests opportunities to study bosonic LLs, topological superconductivity, and their interplay via transport16, scattering17, scanning probe18 and exfoliation techniques19. Using torque magnetometry, the thermodynamic signatures of bosonic Landau level transitions are observed in a layered superconductor, owing to the formation of Cooper pairs with finite momentum.

Surface waves (SWs) can be coupled by phase gradient metasurfaces (PGMs) with high efficiency, but this methodology still suffers from inherent defects of narrow bandwidth, changeless coupled mode, difficult separation of hybrid modes SWs, and uncontrollable propagation direction. In this article, a series of innovative designs is proposed by combining different Pancharatnam–Berry (PB) PGMs with appointed phase distribution principles to resolve PGMs SWs couplers’ above problems. Both the simulated and measured results verify that the broadband conventional SWs coupler can couple transverse magnetic (TM) mode SWs under $x$ -polarized incidence and the broadband extraordinary SWs coupler can couple TM mode SWs under $y$ -polarized incidence in 8.5–11.5 GHz. By integrating these two SWs couplers, a bifunctional SWs coupler is obtained to couple TM mode SWs to the left and transverse electric (TE) mode SWs to the right simultaneously under $x$ -polarized incidence. Furthermore, another two SWs couplers are designed to excite TM mode SWs with 30° and 45° slant directions under $x$ -polarized incidence in 8.5–11.5 GHz, which indicates that coupled SWs’ wavefront direction can be controlled flexibly in a wide bandwidth. The above SWs couplers are proved to work with relatively high coupling efficiencies and have great potential in engineering applications.

In this article, we investigate new constructions of optical Heisenberg spherical optical ferromagnetic spin of timelike magnetic fluids by de Sitter frame. Also, we approach spherical magnetic flows geometrically. Thus, we get total magnetic spherical phases of magnetic spherical timelike fluids. Finally, we construct new numerical presentations of optical spherical magnetic ferromagnetic particles by analytical spherical traveling wave interpretation. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

The Majorana representation, which provides an intuitive way to represent the quantum state by stars on the Bloch sphere, has drawn considerable attention in the context of many body systems or systems with high-dimensional Hilbert space. In this work, we study Majorana representation for an interacting spin-1/2 composite system and its relation with the quantum correlation between the subsystems. Similar with the Majorana representation, we can define a new intuitive representation for the composite system by defining three stars which represents the dynamics and correlation of the two subsystems. The results show that, these two representations are the same for the separable case. The Berry phase has been found to be directly related to the concurrence between the two subsystems. By study the cases of no correlation and large correlation, the quantum entanglement and the Berry phases of the subsystem and their two representations on the Bloch sphere are discussed. These representations by stars provides a intuitive way to study the dynamics, entanglement and Berry phase composite system and its subsystems.

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems., 15 pages, 5 figures

We present mode conversion between the higher order ${{\bf E}}_{21}^{\boldsymbol{x}}$ and ${{\bf E}}_{12}^{\boldsymbol{x}}$ optical modes in an out-of-plane silicon waveguide exhibiting Berry's phase. Superpositions of the ${{\bf E}}_{21}^{\boldsymbol{x}}$ and ${{\bf E}}_{12}^{\boldsymbol{x}}$ waveguide modes form quasi-Laguerre-Gaussian modes with total angular momentum of $1\hbar $ per photon for a 720 × 600 nm2 silicon waveguide core. When the waveguide is deflected out-of-plane by 22.5°, 50% mode conversion occurs from the ${{\bf E}}_{21}^{\boldsymbol{x}}$ mode to the ${{\bf E}}_{12}^{\boldsymbol{x}}$ mode. The concatenation of a quarter wavelength straight section results in an output with $0.89\hbar $ orbital and $0.15\hbar $ spin angular momentum per photon. Orbital angular momentum generation in a waveguide platform provides a route for on-chip applications that utilize the angular momentum of light for sensing, optical manipulation, non-linear optics, and communications.

Holographic display requires thinner liquid crystal cell for smaller pixels and fast response. In this paper, a continuous geometric phase modulation method realised by electrically tuning a dual i...

Three-dimensional Dirac semimetal Cd3As2 has been considered as an excellent candidate for applications of electronic devices owing to its ultrahigh mobility and air-stability. However, current researches are focused mainly on the use of gate-voltage to control its carrier transport tunability, while the manipulation of transport properties by element-doping is quite limited. Here we report the tunable magneto-transport properties by adjusting Mn-doping in the Cd3As2 compound. We find that Mn-element doping has a strong influence on the Fermi level positions, and the Fermi energy approaches to Dirac point with higher Mn-doping. More importantly, the introduction of Mn atoms transforms diamagnetic Cd3As2 to antiferromagnetic (Cd, Mn)3As2, which provides an approach to control topological protected Dirac materials by manipulating antiferromagnetic order parameters. The Shubnikov-de Hass oscillation originates from the surface states, and the Landau fan diagram yields a nontrivial Berry phase, indicating the existence of massless Dirac fermions in the (Cd1-xMnx)3As2 compounds. Our present results may pave a way for further investigating antiferromagnetic topological Dirac semimetal and expand the potential applications in optoelectronics and spintronics.

In this article, two transmissive metasurfaces with different phase control mechanisms and working polarization condition are proposed to efficiently generate zero order Bessel beams (BBs), respectively. For the linear polarization condition, a dual-mode meta-atom constructed by three layers of dielectric substrate and four layers of metal patch is designed. By changing the size of metal patches of meta-atom along $x$ -axis and $y$ -axis, respectively, the phase shift for $x$ - and $y$ -polarized incident wave can be tuned relative independently of 0–2 $\pi $ while the transmission coefficient keeps high value at 10 GHz. For the circular polarization condition, a sandwich type meta-atom applying geometric phase to realize full phase control while keep high efficiency near 10 GHz is designed. According to the designed phase profile of BBs, select meta-atoms with certain phase and efficiency, then arrange them to construct metasurfaces. Full wave simulation results indicate that the dual-mode metasurface working in linear polarization condition generates BBs with the maximum transmission efficiency 0.79 and 0.85 for $x$ and $y$ polarization wave, respectively, and the geometric phase metasurface working in circular polarization condition generates BBs with the maximum transmission efficiency 0.92. Besides, the propagation characteristics of the excited BBs are studied.

van der Waals crystals exhibit excellent material performance when exfoliated to few-atomic-layer thickness. In contrast, the van der Waals thin films more than 10 nm thick are believed to show bulk properties, in which outstanding material performance is rarely found. Here we report the largest anomalous Hall conductivity observed so far in a 170 nm van der Waals ferromagnetic 1T-CrTe2 flake, which reaches 67,000 Ω-1 cm-1. Such a colossal anomalous Hall conductivity in 1T-CrTe2 is dominated by the extrinsic skew scattering process rather than the intrinsic Berry phase effect, as evidenced by the linear relation between the anomalous Hall conductivity and the longitudinal conductivity. Defying the dilemma of mutually exclusive large anomalous Hall angle and high electric conductivity for most ferromagnets, 1T-CrTe2 achieves both in a thin film sample. Considering the shared physics of the anomalous Hall effect and the spin Hall effect, our finding offers a guideline for searching large spin Hall materials of high conductivity which may overcome the bottleneck of overheating in spintronics devices.

Weakly interacting Fermi liquid can exhibit integer or fractional quantum Hall effect at sufficiently low temperatures, and in the presence of variable applied magnetic and/or electric fields. The ...

The Fresnel–Arago laws of interference are five laws describing the interference of polarized light and published in 1819. The fifth law has been systematically forgotten in almost all available re...

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.

We introduce a quantum scheme where a single five-level atom interacts with a single-mode cavity field by a time-dependent coupling. During the interaction, the temporal behavior of the quantum entropy in the atomic basis is compared with that of the Mandel parameter used to quantify the nonclassical properties of the field. With the field prepared in a squeezed coherent state, the atomic quantum entropy is then used to quantify the entanglement or the nonlocal correlation of the five-level atom (5 LA) – field system. The influence of one- and two-photon transitions and the atomic motion on the degree of entanglement and the Pancharatnam phase is analyzed. The analysis emphasizes that both the time dependence and photon multiplicity play an important role in the evolution of the degree of entanglement, the Pancharatnam phase, and nonclassical properties. This insight may be very useful in various applications in quantum physics and quantum optics.

In this article, the theory, design, and validation of planar array antennas capable of producing dual-circularly-polarized (dual-CP) dual-beam radiation with a single feeding network are reported. Importantly, the properties of the formed CP beams with different handedness can be independently controlled. Such a capability is achieved by exploiting both the in-plane rotation-induced Berry phase and excitation phase for all the linearly polarized array elements, which can be regarded as a generalization of the well-known sequential rotation arrays. Microstrip patch arrays with such single-feed dual-CP dual-beam functionalities can be synthesized through a straightforward analytical approach that accurately predicts the radiation patterns for both right- and left-handed CP beams. The proposed technique and design methodology were verified by two proof-of-concept microstrip arrays consisting of $8 \times 8$ linearly polarized circular patch elements operating in the $K$ -band, one with uniform excitation amplitudes and the other with tapered excitations for sidelobe suppression. Both arrays were fabricated and measured, experimentally achieving a joint $S_{11} dB, axial ratio < 3 dB, and 3 dB gain bandwidth of more than 22.5%/20.0% and 16.7%/15.8%, respectively, for the right- and left-handed CP beams. Within this broad operational band, the beam squinting is on average within ±3°. The proposed dual-CP dual-beam arrays have fully planarized structures, low profiles, wide operational bandwidths, and high polarization purity, making them useful candidates for applications including satellite communications, point-to-multipoint communications, and so on.

The Berry phase, which reveals the intimate geometrical structure underlying quantum mechanics, plays a central role in the anomalous Hall effect. In this work, we observed a sign change of Berry curvatures at the interface between the ferromagnet SrRuO3 (SRO) layer and the SrIrO3 (SIO) layer with strong spin-orbit coupling. The negative Berry curvature at the interface, induced by the strongly spin-orbit-coupled Ir 5d bands near the Fermi level, makes the SRO/SIO interface different from the SRO layer that has a positive Berry curvature. These opposite Berry curvatures led to two anomalous Hall effect (AHE) channels with opposite signs at the SRO/SIO interface and in the SRO layer, respectively, resulting in a hump-like feature in the Hall resistivity loop. This observation offers a straightforward explanation of the hump-like feature that is usually associated with the chiral magnetic structure or magnetic skyrmions. Hence, this study provides evidence to oppose the widely accepted claim that magnetic skyrmions induce the hump-like feature.

Quantum state preparation has drawn great attention to physical community. In order to solve this challenge, the protocol of counterdiabatic driving was put forward. In this paper, the idea was applied to two important models, Coherent states and Spin coherent states, which had played important roles in the development of quantum optic and atomic physics. If their parameters vary slowly, the evolution can be studied by the adiabatic perturbation theory. Furthermore, their non-adiabatic response are investigated respectively. Specifically, we build the relationship between the generalized force and Berry curvature of coherent states and spin coherent states. And the leading corrections to energy are also been researched, which lead to the mass and moment of inertia renormalization respectively. In addition, we also calculate the broadening of the energy distribution (energy variance), which determined by the metric tensor. Finally, in order to suppress transition and speed up the evolution, the counterdiabatic Hamiltonians are designed, which would have potential use in the field of quantum manipulation.

Based on the principle of equivalence of the general theory of relativity and the definition of the non-Euclidean metric of space in a non-inertial frame of reference associated with rotation, a geometric (topological) phase is found that occurs when traversing any closed loop. This approach made it possible to establish a deep physical analogy between various wave effects (both classical and quantum) in closed waveguides that arise under the conditions of their rotation. Due to the coherence of the wave function of spinless charge carriers (Cooper pairs of conduction electrons with oppositely directed spins) in superconductors in the ground quantum state (superconducting state), the appearance of a geometric phase in closed loops under rotation conditions can lead to interference effects in the presence of weak bonds in the loop. To register interference effects, it was proposed to use superconducting quantum interferometers placed in the electric field of a cylindrical or spherical capacitor. In accordance with the general theory of the geometric phase of rotation, the study obtained the basic relations between the geometric phase of rotation and the phase of the wave function induced by an external magnetic field, and an estimate of their values was obtained for acceptable values of the angular velocity of rotation, dimensions of superconducting quantum interferometers, and voltages on the capacitor. The errors in measuring the magnetic flux during the rotation of the measuring complex are determined. Taking into account the dependence of the magnitude of the geometric phase of rotation on the voltage across the capacitor and the size of the superconducting quantum interferometers, and also taking into account the specific range of angular velocities of rotation, the sensitivity of superconducting quantum interferometers to the angular velocity can be regulated by a rational choice of these parameters. Based on the results obtained, a new method for measuring magnetic fields was proposed using two superconducting quantum interferometers with different values of areas bounded by closed contours under conditions of rotational movements, which makes it possible to compensate for the disturbing influence of rotations on magnetic measurements, as well as to simultaneously determine the magnetic induction and angular velocity of rotation.

In this study, we firstly introduce a different type of directional Fermi-Walker transportations along with vortex lines of a non-vanishing vector field in three-dimensional Minkowski space. Then we consider some geometric quantities, which are used to characterize vortex lines, in order to express angular velocity vector (Darboux vector) of the system in terms of these quantities. Later we present timelike directional magnetic vortex lines by computing the Lorentz force. Hence, we reach a remarkable relation between timelike directional magnetic vortex lines and angular velocity vector of vortex lines with a nonrotating frame in Minkowski space. We also determine the timelike directional electric vortex lines by considering the electromagnetic force equation. We finally investigate the conditions of being uniform for magnetic fields of timelike directional magnetic vortex lines and we improve such a remarkable approach to find the electromagnetic curvature which contains many geometrical features belonging to timelike directional magnetic and electric vortex line.

Geometric metasurfaces have shown great potential in holography due to their straightforward geometric nature of phase control. The incident angles, spins, and wavelengths of the light provide various degrees of freedom to multiplex metasurface holographic images, which, however, are usually interrelated and hence challenging to be fully decoupled. Here, we report a synergetic recipe to break such seemingly inevitable interrelation by incorporating an effective point source (a pinhole), with which the spin, wavelength, and coordinate of the point source can be fully decoupled in meta-holograms. We experimentally demonstrate spin-decoupled, full-colored metasurface holography and dynamic holography controlled with the position of the point source. The significance of this work is not merely to offer an alternative approach to break the interrelation limitations of the geometric metasurface, but more importantly, it provides a promising route for point sources in reality to realize advanced functionalities with meta-optics, such as single-photon holography, fluorescence holography, etc.

At the interface of classical and quantum physics, the Maxwell and Schrodinger equations describe how optical fields drive and control electronic phenomena to enable lightwave electronics at terahertz or petahertz frequencies and on ultrasmall scales1-5. The electric field of light striking a metal interacts with electrons and generates light-matter quasiparticles, such as excitons6 or plasmons7, on an attosecond timescale. Here we create and image a quasiparticle of topological plasmonic spin texture in a structured silver film. The spin angular momentum components of linearly polarized light interacting with an Archimedean coupling structure with a designed geometric phase generate plasmonic waves with different orbital angular momenta. These plasmonic fields undergo spin-orbit interaction and their superposition generates an array of plasmonic vortices. Three of these vortices can form spin textures that carry non-trivial topological charge8 resembling magnetic meron quasiparticles9. These spin textures are localized within a half-wavelength of light, and exist on the timescale of the plasmonic field. We use ultrafast nonlinear coherent photoelectron microscopy to generate attosecond videos of the spatial evolution of the vortex fields; electromagnetic simulations and analytic theory confirm the presence of plasmonic meron quasiparticles. The quasiparticles form a chiral field, which breaks the time-reversal symmetry on a nanometre spatial scale and a 20-femtosecond timescale (the 'nano-femto scale'). This transient creation of non-trivial spin angular momentum topology pertains to cosmological structure creation and topological phase transitions in quantum matter10-12, and may transduce quantum information on the nano-femto scale13,14.

Materials, where charge carriers have a linear energy dispersion, usually exhibit a strong nonlinear optical response in the absence of disorder scattering. This nonlinear response is particularly interesting in the terahertz frequency region. We present a theoretical and numerical investigation of charge transport and nonlinear effects, such as the high harmonic generation in topological materials including Weyl semimetals (WSMs) and α-T(3) systems. The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix. We show that the nonlinear response is strongly dependent on temperature and topological parameters, such as the Weyl point (WP) separation b and Berry phase ϕ(B). A finite spectral gap opening can further modify the nonlinear effects. Under certain parameters, universal behaviors of both the linear and nonlinear response can be observed. Coupled with experimentally accessible critical field values of 10(4)–10(5) V/m, our results provide useful information on developing nonlinear optoelectronic devices based on topological materials. [Image: see text]

One compound metalens with the multiple functions is benefit to the optical integration. A bifocal metalens with diverse polarization combination is proposed by using the optical metasurface. This metalens consists of nanometer rectangular holes etched on a silver film. Two focusing spots result respectively from the propagation phase introduced by nanoholes with different sizes and the geometric phase caused by the rotation of nanoholes. Two focal spots for one designed compound metalens take on different polarization combination under different polarization light illumination. The interference between them is effectively controlled through the ingenious design. Theoretic analysis and calculation simulations give the powerful verification for the diverse polarization combination of the bifocal matelens. This focusing metalens with diverse polarization combination can expand the wide applications of metalenses.

Achieving independent control of the amplitude and phase of the electromagnetic (EM) wave by a thin flat device is very important in wireless and photonic communications. However, most of the reported metasurfaces, so far, have realized only the simultaneous control of the amplitude and phase of the linearly polarized EM wave. This communication presents a strategy to realize the independent and arbitrary control of the amplitude and phase responses for the circularly polarized EM wave by using a dual-phase hybrid metasurface that integrates both geometric and propagation phases. A beam deflector with a tailorable amplitude is then designed to verify the proposed strategy. As a proof of concept of its practical application, a circularly polarized reflector antenna with a high gain and an extremely low sidelobe is implemented by the proposed metasurface. Experimental results are in good accordance with the simulation ones, demonstrating that the sidelobe of the designed antenna can be reduced by 8 dB compared with a reflector antenna actualized by the phase-only metasurface. The proposed methodology and the metasurface can provide a new degree of freedom in controlling the circularly polarized waves by simultaneous phase and amplitude modulations, which may trigger many interests in EM/optical integration and complex EM-wave manipulations, as well as advanced metadevices for real-world applications.

In this work, we study the adiabatic phases and shortcut for a pseudo-Hermitian interacting spin-1/2 composite system in which one system is driven by a non-Hermitian magnetic field. The biorthonormal eigenbasis and the condition for real eigenvalues have been derived and discussed. By studying the Berry phases and the transitionless quantum driving (TQD) Hamiltonian, the roles of correlation between the subsystems and the non-Hermicity are discussed. The non-Hermitian dynamics and the Berry phases of the subsystem, as well as their influences on the TQD Hamiltonian are studied in both no correlation and large correlation cases. These results mean that we can modify the correlation between the subsystems to control the adiabatic shortcuts of the subsystems. These schemes can provide a feasible way for studying the adiabatic shortcuts of the composite system and the non-Hermitian system.

We review the geometric evolution of a linearly polarized light wave coupling into an optical fiber and the rotation of the polarization plane in a three dimensional ordinary space. We demonstrate that the evolution of a linearly polarized light wave is associated with the Berry phase or the geometric phase. We define other Fermi-Walker parallel transportation laws and connect them with the famous Rytov parallel transportation law for an electric field E, which is considered as the direction of the state of the linearly polarized light wave in the optical fiber in the 3D space. Later, we define a special class of magnetic curves called by quasi electromagnetic curves (qE M-curves), which are generated by the electric field E along the linearly polarized monochromatic light wave propagating in the optical fiber. In this way, not only we define a special class of linearly polarized point-particles corresponding to qE M-curves of the electromagnetic field along with the optical fiber in the 3D space, but we also calculate, both numerically and analytically, the electromagnetic force, Poynting vector, energy-exchanges rate, optical angular and linear momentum, and optical magnetic-torque experienced by the linearly polarizable point-particles along with the optical fiber in the 3D space.

The intriguing quasiparticles in solids, known as Dirac, Weyl, and Majorana fermions, etc. with properties akin to those theoretically predicted but never realized in high-energy physics, have excited intensive research activities in recent years. The transition metal dipnictides are attractive because of their extremely large magnetoresistance that is usually attributed to the carrier compensation effect. We briefly review herein the crystal growth, magneto-transport measurements, and theoretical studies of tantalum dipnictides TaAs2 and TaP2, with the emphasis being put on discussion of the nontrivial topological states in both materials. The analysis of quantum oscillations of the magnetoresistance unveils nonzero Berry phase. The chiral negative longitudinal magnetoresistance further points to possible Weyl state, which was recently theoretically suggested as the result of the magnetic field-induced Zeeman splitting effect no matter how large the field is. The analysis of these intriguing behaviors could brush up our understanding about the family of materials and would be valuable for future work on investigating the magnetic field-induced topological phase transition in such semimetals.

Semiclassical quantization of electronic states under a magnetic field, as proposed by Onsager, describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field1-5. Even in graphene with relativistic energy dispersion, Onsager's rule correctly describes the π Berry phase, as well as the unusual Landau level spectrum of Dirac particles6,7. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of dispersionless flat bands called 'singular flat bands'8. The singular flat band has a band crossing with another dispersive band that is enforced by the band-flatness condition, and shows anomalous magnetic responses. The Landau levels of a singular flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual 1/n dependence on the Landau level index n, which results in diverging orbital magnetic susceptibility. The total energy spread of the Landau levels of a singular flat band is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert-Schmidt quantum distance. We show that there is a universal and simple relationship between the total Landau level spread of a flat band and the maximum Hilbert-Schmidt quantum distance, which can be verified in various candidate materials. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.

Nanoscale Kirkendall effect has been widely used for rationally fabricating high-quality hollow nanocrystals, but often requires the intrinsic diffusion coefficient of out-diffusion materials higher than that of in-diffusion components. Here we demonstrate an unexpected Kirkendall effect that occurs in diffusing intrinsically faster Cu atoms into Pd icosahedra, leading to the formation of PdCu alloyed hollow nanocrystals. The control experiment with Pd octahedra replacing icosahedra indicates the critical role of twin boundaries in facilitating such unexpected Kirkendall effect. In addition, geometric phase analysis and density functional theory calculation show that out-diffusion of Pd atoms in the icosahedra is faster than in-diffusion of Cu atoms, particularly through the twin boundaries, upon the strain gradient with an inward distribution from tensile to compressive strains. The unexpected Kirkendall effect is also found in the interdiffusion of Ag and Pd atoms in Pd icosahedra. Our finds break the limitation of the intrinsic diffusion coefficient for the synthesis of hollow nanocrystals through Kirkendall effect and are expected to enormously enrich the family of hollow nanocrystals which have shown great potential in broad areas, such as fine chemical production, energy storage and conversion, and environmental protection. This work also provides a deep understanding in the diffusion behavior of atoms upon the strain gradient.

Controlling spin electromagnetic waves by ultra-thin Pancharatnam-Berry (PB) metasurfaces show promising prospects in the optical and wireless communications. One of the major challenge is to precisely control over the complex wavefronts and spatial power intensity characteristics without relying on massive algorithm optimizations, which requires independent amplitude and phase tuning. However, traditional PB phase can only provide phase control. Here, by introducing the interference of dual geometric phases, we propose a metasurface that can provide arbitrary amplitude and phase manipulations on meta-atom level for spin waves, achieving direct routing of multi-beams with desired intensity distribution. As the experimental demonstration, we design two microwave metasurfaces for respectively controlling the far-field and near-field multi-beam generations with desired spatial scatterings and power allocations, achieving full control of both sophisticated wavefronts and their energy distribution. This approach to directly generate editable spatial beam intensity with tailored wavefront may pave a way to design advanced meta-devices that can be potentially used in many real-world applications, such as multifunctional, multiple-input multiple-output and high-quality imaging devices.

The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of the quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under electron spin states in Nitrogen-Vacancy(NV ) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compared with the previous method, we can implement both the one- and two-qubit gates by varying the amplitude and phase of the microwave pulse applied to control the non-Abelian geometric phase acquired by NV centers. We also found that our proposed scheme may be implemented in the current experiment to discuss the gate fidelity with the experimental parameters. Therefore, the scheme adopts a new method to achieve high-fidelity non-adiabatic holonomic quantum computation.

In this work, we introduce a model of a two-atom interacting with a multi-level atom governed by su(2) Lie algebra in the presence of external classical field. The influence of the classical field on the system is discussed in detail for certain values for the classical terms. The atomic density matrix of the proposed system is obtained. The dynamical behavior of the atomic Fisher information as an indicator of the nonlocal correlation between a two-atom and su(2) field is discussed. Moreover, we examine the effect of classical field on the evolution of entropy squeezing and the geometric phase induced between the initial and final state of the proposed system. The results outlined some important phenomena as sudden death and sudden birth of entanglement in presence of the classical terms is observed through the dynamics of atomic Fisher information in the presence of classical field for the large number of levels.

In this paper, we proposed and fabricated a liquid crystal random-phase plate (LCRPP) for laser beam phase smoothing, while the simulation and experimental verification of LCRPP applied to laser be...

Intriguing interference mechanism Quantum interference (QI) effects play a fundamental role in the dynamics of chemical reactions. Xie et al. detected unusual QI oscillations in the differential cross section measured in the recoil scattering direction of the prototypical elementary reaction H + HD → H 2 + D (see the Perspective by Aoiz). Topological analysis showed that this pattern originates from the QI between a direct abstraction and previously unknown rebounding insertion pathways, which are affected by the geometric phase at energies far below the conical intersection. The QI observed between these two distinctive pathways in the three-atom system is a clear example of the quantum nature of chemical reactivity. Science , this issue p. 767 ; see also p. 706

Two superconducting (SC) qubits interacting with a radiation field in the coherent state (CS) in the presence of Stark shift are investigated. The density matrix is expressed in terms of the wave function to describe the proposed system. Physical properties, such as the geometric phase, linear entropy, and negativity are used to describe the behavior of the system. The effects of the Stark shift and the initial state on the linear entropy, geometric phase, and nonclassical correlation are discussed. Thermal and magnetic field interactions are also examined during the time evolution of the two SC qubits. By raising the temperature and decreasing the qubit–qubit entanglement, the nonclassical connection between the CS field and the two SC qubits is strengthened. Moreover, the Stark shift considerably affects the dynamical and physical properties of both types of entanglement.

In this paper, we propose a scheme for realizing controlled phase gate of transmon qubits by combining the unconventional geometric phase and the inverse Hamiltonian engineering. The scheme possesses built-in fault tolerance and can be implemented in only one step without additional single qubit operations on each transmon qubit. In addition, the Rabi frequencies of the designed driving fields are smooth and vanish at boundary, so that the driving fields can be easily turned on and off . Numerical simulations show that the controlled phase gate is robust against several types of noise and the decoherence factors. Thus, the scheme may provide an alternative approach in constructing controlled phase gate with superconducting qubits.

The photonic spin Hall effect, a deep subdiffraction-limited shift between the opposite spin components of light, emerges when light undergoes an evolution of polarization or trajectory that induces the geometric phase. Here, we study a stochastic photonic spin Hall effect arising from space-variant Berry–Zak phases, which are generated by disordered magneto-optical effects. This spin shift is observed from a spatially bounded lattice of ferromagnetic meta-atoms displaying nanoscale disorders. A random variation of the radii of the meta-atoms induces the nanoscale fluctuation. The standard deviation of the probability distribution of the spin shifts is proportional to the fluctuation of the meta-atoms. This enables us to detect a five-nanometre fluctuation by measuring the probability distribution of the spin shifts via weak measurements. Our approach may be used for sensing deep-subwavelength disorders by actively breaking the photonic spin symmetry and may enable investigations of fluctuation effects in magnetic nanosystems. Magneto-optical interaction of light with magnetic metasurfaces can give rise to the photonic spin Hall effect such that the light trajectory depends on the polarization of the light. For disordered systems, the probability distribution of the spin-dependent trajectories is a sensitive tool to detect random nanoscale variations in the metasurface.

We study solutions to the difference equation $\Psi(z+h)=M(z)\Psi(z)$ where $z$ is a complex variable, $h>0$ is a parameter, and $M:\mathbb{C}\mapsto SL(2,\mathbb{C})$ is a given analytic function. We describe the asymptotics of its analytic solutions as $h\to 0$. The asymptotic formulas contain an analog of the geometric (Berry) phase well-known in the quasiclassical analysis of differential equations., Comment: 21 pages

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous, and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states---a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement., 9 pages, 6 figures + 3 pages supplemental material, 2 figures