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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.

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.

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.

With inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

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.

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.

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.

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.

The evolutions of polarization and orbital angular momentum (OAM) states of light in helically twisted birefringent photonic crystal fibers (TB-PCFs) are analyzed. It is shown that a circular polarization (CP) component ( S 3 of a Stokes parameter) is periodically excited when usual linearly polarized (LP) modes of PCF are launched. The excitation originates from a geometric phase in TB-PCFs. The S 3 excitation is larger for larger linear birefringence for a fixed twisting rate. If the linear birefringence is large enough, a CP filtering behavior can be seen in addition to the S 3 excitation. From the analytical consideration of the sign of the geometric phase, the TB-PCF with periodical inversion of twisting is proposed to generate arbitrary polarization state on the Poincaré sphere. Next, an OAM state generation in multimode TB-PCFs is shown for higher-order LP mode input. By observing a far-field interference pattern from TB-PCF mixed with LP 01 mode, a vortex associated with the OAM state can be seen. Similar to the single-mode case, by using periodical twisting inversion, efficient OAM generation is possible. These results indicate that by simply launching fiber’s LP mode into TB-PCF, arbitrary polarization and OAM states can be generated, leading to a novel mechanism for the manipulation of the spatial state of light.

We study axion strings of hyperlight axions coupled to photons. Hyperlight axions -- axions lighter than Hubble at recombination -- are a generic prediction of the string axiverse. These axions strings produce a distinct quantized polarization rotation of CMB photons which is $\mathcal{O}(\alpha_{\rm em})$. As the CMB light passes many strings, this polarization rotation converts E-modes to B-modes and adds up like a random walk. Using numerical simulations we show that the expected size of the final result is well within the reach of current and future CMB experiments through the measurement of correlations of CMB B-modes with E- and T-modes. The quantized polarization rotation angle is topological in nature and can be seen as a geometric phase. Its value depends only on the anomaly coefficient and is independent of other details such as the axion decay constant. Measurement of the anomaly coefficient by measuring this rotation will provide information about the UV theory, such as the quantization of electric charge and the value of the fundamental unit of charge. The presence of axion strings in the universe relies only on a phase transition in the early universe after inflation, after which the string network rapidly approaches an attractor scaling solution. If there are additional stable topological objects such as domain walls, axions as heavy as $10^{-15}$ eV would be accessible. The existence of these strings could also be probed by measuring the relative polarization rotation angle between different images in gravitationally lensed quasar systems., Comment: 35 pages, 10 figures, published in JHEP

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.

The unusual electromagnetic responses of nanostructured metasurfaces endow them with an ability to manipulate the four fundamental properties (amplitude, phase, polarization, and frequency) of lightwave at the subwavelength scale. Based on this, in the past several years, a lot of innovative optical elements and devices, such as metagratings, metalens, metaholograms, printings, vortex beam generators, or even their combinations, have been proposed, which have greatly empowered the advanced research and applications of metasurfaces in many fields. Behind these achievements are scientists’ continuous exploration of new physics and degrees of freedom in nanostructured metasurface design. This review will focus on the progress on the design of different nanostructured metasurfaces for lightwave manipulation, including by varying/fixing the dimensions and/or orientations of isotropic/anisotropic nanostructures, which can therefore provide various functionalities for different applications. Exploiting the design degrees of freedom of optical metasurfaces provides great flexibility in the design of multifunctional and multiplexing devices, which can be applied in anticounterfeiting, information encoding and hiding, high-density optical storage, multichannel imaging and displays, sensing, optical communications, and many other related fields.

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

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass de...

The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take advantage of the geometric phase to sense the corrections induced while a neutral particle travels at constant velocity in front of an imperfect sheet in quantum vacuum. As it is already known, two bodies in relative motion at constant velocity experience a quantum contactless dissipative force, known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. However, we give details of an innovative experiment designed to track traces of the quantum friction by measuring the velocity dependence of corrections to the geometric phase. We notice that the environmentally induced corrections can be decomposed in different contributions: corrections induced by the presence of the dielectric sheet and the motion of the particle in quantum vacuum. As the geometric phase accumulates over time, its correction becomes relevant at a relative short timescale, while the system still preserves purity. The experimentally viable scheme presented would be the first one in tracking traces of quantum friction through the study of decoherence effects on a NV center in diamond., version published in npj quantum informtion 2020

In this article, we study the geometric phase in a system formed by two spatially separated cavities interacting with the environment. Each cavity is lled by a linear optical medium and contains a quantum well. For different initial states, the robustness of the generated geometric phase is analyzed under the effects of the optical susceptibility, the dissipation of the cavities, the exciton-cavity and ber-cavity couplings. Our results show that the geometric phase is extremely sensitive to the effects of the cavity-exciton and the ber-cavity couplings as well as to the optical susceptibility. This opens new routes to understand the storage and manipulation of quantum data in a quantum network.

Inc, Mustafa/0000-0003-4996-8373; Korpinar, Zeliha/0000-0001-6658-131X We introduce the theory of optical spherical Heisenberg ferromagnetic spin of timelike spherical normal magnetic flows of particles by the spherical frame in de Sitter space. Also, the concept of timelike spherical normal magnetic particles is investigated, which may have evolution equations. Afterward, we reveal new relationships with some integrability conditions for timelike spherical normal magnetic flows in de-Sitter space. In addition, we obtain total phases for spherical normal magnetic flows. We also acquire perturbed solutions of the nonlinear Schrodinger's equation that governs the propagation of solitons in de-Sitter space S-1(2). Finally, we provide some numerical simulations to supplement the analytical outcomes.

In order to improve the transmitted efficiency of metasurfaces, the three-layer unit cell structure with coupling characteristics between layers was proposed. Using these Pancharatnam-Berry phase element particles with three-layer structure, we constructed encoded metasurfaces with different sequences to control the transmitted scattered waves. However, the manipulation of continuous transmission angle requires the continuous change of encoding metasurface period. Since the size of encoding particles in the coded metasurfaces cannot be designed to be infinitesimally small, it is impossible to obtain the continuously changing period of coded metasurfaces. In order to obtain the continuous manipulation of transmission scattering angles, we introduced the principle of Fourier convolution operation in digital signal processing on encoding metasurface sequences. By performing the addition and subtraction operation between two different encoding metasurface sequences, a new encoding metasurface sequence can be obtained with different scattering angle. The transmission scattering angles can be obtained continuously, and the terahertz wave can be manipulated freely. Moreover, by using the proposed three-layer highly efficient Pancharatnam-Berry phase encoding meta-atoms, these coded particles with different rotation angles can be precisely arranged to build the generators of the orbital angular momentum beam with different topological charges.

The capability to manipulate the polarization state of light at the nanoscale is of paramount importance in many emerging research areas ranging from optical communication to quantum information processing. Gap-surface plasmon (GSP) metasurfaces, which provide advantages and abilities of molding reflected fields, have been demonstrated excellently suited for integration of multifunctional polarization optics into a single device. Here, we establish a versatile GSP metasurface platform based on nanoscale quarter-wave plates (nano-QWPs) that enable efficient circular-to-linear polarization conversion along with the complete phase control over reflected fields. Capitalizing on the nano-QWP design, we demonstrate, both theoretically and experimentally, how resonance and geometric phases can be used in concert to achieve independent and simultaneous phase modulation of both co- A nd cross-polarized circularly polarized (CP) waves by realizing arbitrary beam steering of co- A nd cross-polarized CP channels in a broadband near-infrared range. The GSP metasurface platform established in our work provides versatile and flexible solutions to enrich multiple functionalities for diversified metasurface-based polarization optics exploited in modern integrated photonic devices and systems.

The proximity-coupling of a chiral non-collinear antiferromagnet (AFM)1–5 with a singlet superconductor allows spin-unpolarized singlet Cooper pairs to be converted into spin-polarized triplet pairs6–8, thereby enabling non-dissipative, long-range spin correlations9–14. The mechanism of this conversion derives from fictitious magnetic fields that are created by a non-zero Berry phase15 in AFMs with non-collinear atomic-scale spin arrangements1–5. Here we report long-ranged lateral Josephson supercurrents through an epitaxial thin film of the triangular chiral AFM Mn3Ge (refs. 3–5). The Josephson supercurrents in this chiral AFM decay by approximately one to two orders of magnitude slower than would be expected for singlet pair correlations9–14 and their response to an external magnetic field reflects a clear spatial quantum interference. Given the long-range supercurrents present in both single- and mixed-phase Mn3Ge, but absent in a collinear AFM IrMn16, our results pave a way for the topological generation of spin-polarized triplet pairs6–8 via Berry phase engineering15 of the chiral AFMs.

In [5] (2018), Capolupo et al. calculate the noncyclic geometric phases associated with neutrino flavor transitions in the two-neutrino scenario, and claim that the results depend on the choice of representations of neutrino mixing matrix thus can be used to distinguish between Dirac and Majorana neutrinos. In this paper, we show that their calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. Their results are neither gauge invariant nor lepton field rephasing invariant. We present an alternative calculation, which is solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. We point out that the seemingly nontrivial dependence of geometric phase on Majorana CP-violating phase presented in Capolupo et al. (2018) [5] is unphysical and thus unmeasurable.

In this article, we obtain the multistable macroscopic quantum states and quantum tricritical behavior in generalized Dicke model (DM) analytically by means of spin-coherent-state (SCS) variational method for a finite atom number N . The quantum phase transition (QPT) is characterized by the ground state from the normal phase (NP) to the superradiant phases (SP). The second-order QPT turns to the first-order one at the tricritical point of phase boundary. The tricritical behavior of QPT emerges when the coupling strength of the symmetry breaking mechanism increases to a certain extent, which leads to an additional dimension of phase diagram. Beyond the ground state the symmetry-breaking coupling can manipulate the pseudospin flip of higher-level macroscopic states. The critical property of QPT is also demonstrated from the average photon-number, the atomic population as well as Berry phase.

While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs' unique properties: At large scale, due to the absence of global magnetization, AFMs may appear to behave like any non-magnetic material; However, such a seemingly mundane macroscopic magnetic property is highly nontrivial at microscopic level, where opposite spin alignment within the AFM unit cell forms a rich internal structure. In topological AFMs, such an internal structure leads to a new possibility, where topology and Berry phase can acquire distinct spatial textures. Here, we study this exciting possibility in an AFM Axion insulator, even-layered MnBi$_2$Te$_4$ flakes, where spatial degrees of freedom correspond to different layers. Remarkably, we report the observation of a new type of Hall effect, the layer Hall effect, where electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under no net electric field, even-layered MnBi$_2$Te$_4$ shows no anomalous Hall effect (AHE); However, applying an electric field isolates the response from one layer and leads to the surprising emergence of a large layer-polarized AHE (~50%$\frac{e^2}{h}$). Such a layer Hall effect uncovers a highly rare layer-locked Berry curvature, which serves as a unique character of the space-time $\mathcal{PT}$-symmetric AFM topological insulator state. Moreover, we found that the layer-locked Berry curvature can be manipulated by the Axion field, E$\cdot$B, which drives the system between the opposite AFM states. Our results achieve previously unavailable pathways to detect and manipulate the rich internal spatial structure of fully-compensated topological AFMs. The layer-locked Berry curvature represents a first step towards spatial engineering of Berry phase, such as through layer-specific moir\'e potential., Comment: A revised version of this article is published in Nature

The polarization singularities are directly generated by using plasmonic metasurfaces with the geometric phase profiles designed to form the Poincaré beams. Different morphologies of polarization topological structures of lemon, star, monstar, spiral, dipole and quadrupole are created by the superpositions of Laguerre–Gauss modes with different orders under orthogonal circular or linear polarization basis. The polarization ellipse patterns and topological features of the produced optical vector fields are analyzed to reveal the properties of the polarization singularities of C-points and L-lines, and the orbital angular momentum states are also measured. The demonstrated polarization singularities generated from the geometric metasurfaces will promise many potential applications related to optical polarization imaging, metrology, optical trapping and quantum information processing.

In this manuscript, we present a system consisting of a three-level atom interacting with optical field. We investigate qualitatively the entanglement and atomic (field) geometric phase under the effect of cavity damping. The atom–field entanglement is measured by the negativity. We show that these quantifiers depend strongly on the variations of the initial settings of the atom, and this exhibits substantial phenomena that depend on the cavity damping effect. Finally, we explore the link between the entanglement and atomic (field) geometric phase of different physical parameters within the presence and absence of the cavity damping effect.

A method based on the tracking of the peaks of interference fringes as a function of time-dependent analyzer setting is used to detect the Pancharatnam phase of light. The advantage of this method is demonstrated by observations of the nonlinearity of the Pancharatnam phase for certain paths on Poincare sphere where the fringe visibility reduces to almost zero. We also describe variations of this experiment with structured light beams, where the Pancharatnam phase leads to linear or nonlinear rotation of flower-pattern or spiral-shape interference fringes.

Elastic strain engineering is an important strategy to design material properties in semiconductor and emerging advanced manufacturing industries. Recently, peak-pair method has drawn great attention compared to geometric phase analysis, owing to its precise determination of atom position at real space. Most current strain characterization methods estimate the local strain by comparing it with the related information from unstrained areas as reference. However, peak-pair method generated large errors in some cases because of the complexity of lower symmetric crystal structures, such as hexagonal structure. In this study, we introduce a new algorithm to overcome this limitation by directly comparing the atom positions with multiple references with different lattice symmetries. Furthermore, this new method is validated through several complicated crystal systems such as hexagonal, orthorhombic, monoclinic, and tetragonal structure, and returns expected values. This finding is essential to reliably determine the localized elastic strain with various crystal structures.

Motivated by J. Larson’s work (Crespi et al., 2012), in which vacuum induced non-trivial Berry phases for Jaynes–Cummings (JC) model were considered to be the results from the application of rotating wave approximation (RWA) and become vanishing in the quantum Rabi model without RWA. Besides a counterpart relation between the trivialness or non-trivialness of Berry phases and the existence of conical intersections (CIs) of adiabatic potentials is illustrated by introducing semi-classical energy surface. We argue that there exist no definite connections between the trivialness or not of Berry phase and the CIs of adiabatic potentials because the CIs are fully controllable for the generalized JC and Rabi models discussed in this text by adjusting the dispersive non-linear interacting parameter.

In this paper, we relate the evolution equation of the electric field and magnetic field vectors of the polarized light ray traveling along with a coiled optical fiber on the unit 2-sphere S² into the nonlinear Schrödinger's equation by proposing new kinds of binormal motions and new kinds of Hasimoto functions in addition to commonly known formula of the binormal motion and Hasimoto function. All these operations have been conducted by using the orthonormal frame of spherical equations that is defined along with the coiled optical fiber lying on the unit 2-sphere S². We also propose perturbed solutions of the nonlinear Schrödinger's evolution equation that governs the propagation of solitons through electric field (E) and magnetic field (M) vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes.

The probability distribution of the magnitude C of the curvature 2-form, that underlies the quantum geometric phase and the reaction force of geometric magnetism, is calculated for an ensemble of three-parameter Hamiltonians represented by the gaussian unitary ensemble of N × N matrices. The distributions are determined analytically: exactly for N = 2 and approximately for N ≥ 3, and compared with simulations. The distributions decay asymptotically as 1/C5/2; this is a consequence of the codimension of energy-level degeneracies in the ensemble.

2-s2.0-85073970823 In this work, we first present the theory of Heisenberg ferromagnetic model of directional velocity magnetic flows of particles with the help of the quasi-frame in ordinary space. Afterward, we give new integrability conditions of directional velocity magnetic flows by using quasi-frame fields. Additionally, we derive the total phase for quasi-vector fields. Finally, we obtain new constructions for quasi-curvatures of directional velocity magnetic flows by Heisenberg ferromagnetic model. © 2019, Indian Association for the Cultivation of Science.

We propose a quantum two-level system interacting with a two-mode nondegenerate entangled states (TMNESs). The dynamical properties of entropy squeezing component is investigated based on atomic density matrix in the absence and presence of classical field effect. Moreover, the dynamical properties of the nonlocal correlation between the atom and TMNESs are studied and compared with geometric phase. We examine the influence of the initial interaction conditions and classical field on the evolution of nonlocal correlation, linear entropy and geometric phase. Furthermore, we discuss the link between the geometric phase, field purity and nonlocal correlation during the time dynamics. Finally, the results clarified that a geometric phase and entanglement are strongly affected by the classical field and detuning parameter.

When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on the material’s properties. Seminal examples include the anomalous Hall and spin Hall effects from the momentum-space Berry phases in homogeneous crystals. Here, we explore a conjugate form of the electron Berry phase arising from the moiré pattern: the texture of atomic configurations in real space. In homobilayer transition metal dichalcogenides, we show that the real-space Berry phase from moiré patterns manifests as a periodic magnetic field with magnitudes of up to hundreds of Tesla. This quantity distinguishes moiré patterns from different origins, which can have an identical potential landscape, but opposite quantized magnetic flux per supercell. For low-energy carriers, the homobilayer moirés realize topological flux lattices for the quantum-spin Hall effect. An interlayer bias can continuously tune the spatial profile of the moiré magnetic field, whereas the flux per supercell is a topological quantity that can only have a quantized jump observable at a moderate bias. We also reveal the important role of the non-Abelian Berry phase in shaping the energy landscape in small moiré patterns. Our work points to new possibilities to access ultra-high magnetic fields that can be tailored to the nanoscale by electrical and mechanical controls.

Nanoscale optical antennas mediate frequency mixing processes via their optical modes. Within arrays, metasurfaces provide unique opportunities to control nonlinear processes. Macroscopic interpret...

An augmented-reality (AR) device which presents virtual volumetric images to switchable integrated spaces is proposed and demonstrated. A bi-focal geometric phase (GP) lens can project the integrated volumetric images to switchable integrated spaces by switching the polarization of them. For that purpose, a combination of GP lens and an active polarization switching device has been adopted. A demonstration of an AR display with switchable integrations is also provided to verify the proposed concept.

We examine the noncommutation of Pancharatnam–Berry phase elements in the generation of vector beams. Any desirable vector beams on the two high-order Poincare spheres can be generated by incorporating the noncommutation and certain input polarization states. We show that the vector polarization states can be switched between two different high-order Poincare spheres by simply exchanging the order of two Pancharatnam–Berry phase elements. More importantly, the point-to-point conversion of vector beams makes our scheme highly flexible and easy to operate.

A simple combination of density functional theory/time-dependent density functional theory (DFT/TDDFT) and configuration interaction is presented to fix the incorrect topology of the S0- S1 conical intersection (CI) and allow a description of bond making and bond breaking in photoinduced dynamics. The proposed TDDFT-1D method includes one lone optimized doubly excited configuration in addition to the DFT/TDDFT singly excited states within the context of a large configuration interaction Hamiltonian. Results for ethylene and stilbene are provided to demonstrate that this ansatz can yield physically meaningful potential energy surfaces near S0- S1 avoided crossings without changing the vertical excitation energies far from the relevant crossings. We also investigate the famous linear water example to show that the algorithm calculates the correct topology of the S0- S1 CI and yields the correct geometric phase.

In modern theory of solids, many-electron correlations can give rise to superconductivity, while the Berry or geometric phase is responsible for non-trivial topology. So far, these two physical ingredients have been taken into account only in a simple additive manner. Here, we carry out a systematic study of the interplay between geometric phase and electron correlation as well as their combined effects on topological and superconducting properties. Based on first-principles studies of Pb3Bi/Ge(111) as a prototypical system, we develop a generic two-dimensional effective formalism that respects hexagonal symmetry with Rashba spin–orbit coupling, displays a van Hove singularity and includes geometric phase-decorated electron correlations. Our functional renormalization group analysis shows that superconductivity dominates the competing orders in the weak interaction regime, with two consequences. First, the renormalized geometric phase flows to three stable fixed points, favouring chiral (px ± ipy)-wave and f-wave superconducting states. Second, the corresponding superconductivity can be substantially enhanced. We construct the phase diagram of the topological quantum states, and identify hole-doped Pb3Bi/Ge(111) as an appealing platform for realizing chiral topological superconductivity in two-dimensional systems that are highly desirable for detecting and braiding Majorana fermions. Renormalization group calculations incorporate band structure and interaction effects on an equal footing. Applying this methodology to Ge-doped Pb3Bi shows that this material is a chiral topological superconductor and hosts Majorana fermions.

Three different methods of experimental mesoscopic physics, namely, weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations, have been used to extract the electron phase-coherence scattering rate in two-dimensional gas of InGaAs/AlInAs heterostructures. The Aharonov-Bohm oscillations reveal strong beating effects, indicating the existence of two similar periodicities of the flux dependencies. As suggested by certain theoretical models, such a behavior might be expected from the so-called Berry phase acquired by electrons with different spin orientations in the presence of strong spin-orbit coupling and Zeeman splitting. In our paper we deduce the experimental values of the dephasing length and try to compare the observed beating pattern with possible scenarios for the appearance of the Berry phase.

The transverse and longitudinal magnetoresistances of GaSb microcrystals with tellurium doping concentration of 1.7 × 1017 cm−3 under the influence of uniaxial compression strain were studied in high magnetic fields of 0–14 T. Low-temperature Shubnikov–de Haas oscillations were observed for unstrained and strained n-type conductivity GaSb microcrystals in the whole range of the magnetic fields. The magnetoresistance oscillation amplitude decreases with the temperature increasing in the range of 4.2–30 K. The Shubnikov–de Haas oscillation period was changed due to the strain influence, and it was found to be 0.039 T−1. The emergence of the splitting at a magnetic field of about 7 T was revealed in the longitudinal magnetoresistance of GaSb microcrystals doped to a concentration in the vicinity of the metal–insulator transition. The value of the g-factor was found in the strained samples, and it has a value of 53. The strain influence on the effective mass of the electron mc and the Dingle temperature TD were also studied. The appearance of the Berry phase caused by the strain was revealed in GaSb microcrystals allowing their transition to the topological insulator state.

Polarized light passing through twisted wave plates shows entangled state of both SAM and OAM. The polarization matrix and the polarized state are constructed on OAM sphere for l = 1 where m varies between l, 0, − l. The twisted birefringent matrix develops the twisted quarter- and half-wave plates which in turn identify various retarders. The variable circular and linear retarders (VCR and VLR) are studied here from the viewpoint of quantum processing of entangled states. Interestingly, the geometric phase in association with the gain of OAM has been studied here for the phase shifter of an antenna array.

In this paper, we introduce the notion of the Heisenberg ferromagnetic model for directional inextensible flows of spacelike curves by using the quasi-frame in the Minkowski space. Furthermore, we study some integrability conditions for quasi-frame fields. With this new concept, we derive the necessary and sufficient condition for the given curve to be the inextensible flow. Finally, we give some new characterizations for quasi-curvatures of the spacelike curve by Heisenberg ferromagnetic model and we obtain total phase for quasi-vector fields. © 2019, Indian Association for the Cultivation of Science.

The state vector representing a quantum system acquires a phase factor following an adiabatic evolution along a closed trajectory in phase space. This is the traditional example of a geometric phase, or Pancharatnam–Berry phase, a concept that has now been generalized beyond cyclic adiabatic evolutions to include generalized quantum measurements, and that has been experimentally measured in a variety of physical systems. However, a clear description of the relationship between the emergence of a geometric phase and the effects of a series of generalized quantum measurements on a quantum system has not yet been provided. Here we report that a sequence of weak measurements with continuously variable measurement strengths in a quantum optics experiment conclusively reveals that the quantum measurement back-action is the source of the geometric phase—that is, the stronger a quantum measurement, the larger the accumulated geometric phase. We furthermore find that in the limit of strong (projective) measurement there is a direct connection between the geometric phase and the sequential weak value, ordinarily associated with a series of weak quantum measurements. Following a closed evolution in the Hilbert space, the state vector of a quantum system accumulates a geometric phase factor. A series of weak measurements reveal the origin of this in the back-action of any quantum measurement.