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We have investigated the effects of the global monopole on a spin-1/2 particle. In this sense, we analyze the relativistic quantum dynamics, where we determine the eigenfunctions in terms of Bessel functions. In order to determine bound state solutions, we impose two possible scenarios that characterize the confinement of the particle in the presence of the topological defect, from which we obtain the energy profile for both scenarios, in which we can perceive the influences of the background on the levels relativistic energy of fermionic particle. [ABSTRACT FROM AUTHOR]

Topological phase transitions of a generalized two dimensional tight-binding Chern insulator with periodic δ -function kicks applied in x, y and z direction defined by the pseudo spin in the two-band systems, have been studied in this paper. The rich phase diagram characterized by Chern numbers as well as the critical lines in such system have been analyzed. This is an extended study about δ -function periodic kicks on topological systems as profound influences on periodic driven quantum systems. [ABSTRACT FROM AUTHOR]

Dynamic topological photonics is a novel research field, combining the time-domain optics and topological physics. In this review, the recent progress and realization platforms of dynamic topological photonics have been well introduced. The definition, measurement methods and the evolution process of the dynamic topological photonics are demonstrated to better understand the physical diagram. This review is meant to bring the readers a different perspective on topological photonics, grasp the advanced progress of dynamic topology, and inspire ideas about future prospects. [ABSTRACT FROM AUTHOR]

To understand the importance of the interference effect of non-physical non-cyclic phases difference on the expectation value of physical operators that do not commute with the time-dependent adiabatic Hamiltonian, we compare the value of ⟨ ψ (t) | s z | ψ (t) ⟩ of the exact soluble two-level model with its adiabatic approximation in a non-cyclic evolution. This expectation value is calculated in different orders of magnitude of time periods. For time intervals of the same order as the adiabatic Hamiltonian’s period, the inability to account for the contribution of non-physical, non-cyclic adiabatic phases in the temporal evolution of this quantum system may introduce a percentage disagreement of up to 60 % with the precise result of measurable physical quantities. The results obtained in the article are independent of the Hamiltonian instantaneous eigenstate basis that we use to decompose the vector state in adiabatic evolution. For times greater than any integer number of periods T 0 , in which the classical parameters return to their initial values, we only obtain the correct result of the expected value of the physical operators in state vectors with adiabatic evolution when we include in the vector state its Berry phase plus the non-cyclic phase acquired in the elapsed time interval after this integer number of periods T 0 . This simple model emphasizes the relevance of the interference effects of physical or non-physical adiabatic phases in calculating the time evolution of the expectation value of physical operators in an adiabatically evolving quantum state with non-cyclic development. [ABSTRACT FROM AUTHOR]

Spavieri effect in noncommutative space is studied by applying two different methods. One is the Bopp shift and the other is the Seiberg-Witten map. We show that up to the first order of the noncommutative parameter, both methods lead to the same conclusion that the spatial noncommutativity will not lead to corrections to Spavieri effect although the mechanisms of these two methods are very different. Our studies also indicate that the equivalence between Spavieri and Aharonov-Bohm effects is still held in noncommutative space. [ABSTRACT FROM AUTHOR]

Many works on topological insulators have focused on periodic lattice systems; where short- and long-range order is considered. Here we construct a two-dimensional amorphous photonic crystal with short-range order and a controllable level of long-range order and experimentally investigate the transport of topological edge states in this amorphous system. We demonstrate that topology properties remain constant with unidirectional edge state propagation; immune to specific disorder strength. The partition phenomena of edge states are also observed at the intersection of four topological channels in microwave experiments. This proposed amorphous configuration provides new opportunities to explore the relationship between short-range order and topology and may alleviate the fabrication difficulties of topological optical devices for practical applications. [ABSTRACT FROM AUTHOR]

Majorana zero modes (MZMs) have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation (TQC). In addition to the Majorana scheme, some non-Majorana quasiparticles obeying non-Abelian statistics, including topological Dirac fermionic modes, have also been proposed and therefore become new candidates for TQC. In this review, we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes, emphasizing the recent progress on topological Dirac fermionic modes. A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry, which can be realized in a number of platforms, including the one-dimensional topological insulator, higher-order topological insulator, and spin superconductor. This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin, such as superconductivity-free and larger gaps. Therefore, it provides a new avenue for investigating non-Abelian physics and possible TQC. [ABSTRACT FROM AUTHOR]

Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC), enabled by real-space superconducting proximity effect, reciprocal-space superconducting proximity effect, and intrinsic TSC. Whereas the first scheme has so far been most extensively explored, the subtle difference between the other two remains to be fully substantiated. We then move on to candidate intrinsic or p-wave superconductors, including Sr2RuO4,UTe2,Pb3Bi, and graphene-based systems. For TSC systems that rely on proximity effects, the emphases are mainly on the coexistence of superconductivity and nontrivial band topology, as exemplified by transition metal dichalcogenides, cobalt pnictides, and stanene, all in monolayer or few-layer regime. The review completes with discussions on the three dominant tuning schemes of strain, gating, and ferroelectricity in acquiring one or both essential ingredients of the TSC, and optimizations of such tuning capabilities may prove to be decisive in our drive towards braiding of Majorana zero modes and demonstration of topological qubits. [ABSTRACT FROM AUTHOR]

We study theoretically the nonadiabatic geometric phase of a doubly driven two-level system with an additional relative phase between the two driving modes introduced in. It is shown that the time evolution of the system strongly depends on this relative phase. The condition for the system returning to its initial state after a single period is given by the means of the Landau–Zener–Stückelberg–Majorana destructive interference. The nonadiabatic geometric phase accompanying a cyclic evolution is shown to be related to the Stokes phase as well as this relative phase. By controlling the relative phase, the geometric phase can characterize two distinct phases in the adiabatic limit. [ABSTRACT FROM AUTHOR]

In this paper, we study the quantum motions of the non-relativistic particles under the influence of the flux field in the background of a point-like global monopole with Kratzer plus generalised Yukawa potential. The solutions of the quantum system under consideration are obtained using the parametric Nikiforov–Uvarov method by employing the Greene–Aldrich approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation. Afterwards, we use another approximation called the Taylor series expansion up to the first order in the exponential terms and solve the radial equation analytically using the confluent hypergeometric function. It is shown that the topological defect of a point-like global monopole influences the eigenvalue solutions of the non-relativistic particles and gets modified by this defect compared to the flat space result with this superposed potential. We also show that the energy eigenvalue of the particles depends on the quantum flux field and thus gets shifted. Finally, we compare the eigenvalue solutions obtain for these two approximations scheme used here and show graphically that the results are different in these schemes. [ABSTRACT FROM AUTHOR]

The non-Hermitian systems with the non-Hermitian skin effect (NHSE) are very sensitive to the imposed boundary conditions and lattice sizes, which lead to size-dependent non-Hermitian skin effects. Here, we report the experimental observation of NHSE with different boundary conditions and different lattice sizes in the unidirectional hopping model based on a circuit platform. The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary. Meanwhile, our experimental results show how the lattice sizes and boundary terms together affect the strength of NHSE. Therefore, our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems. [ABSTRACT FROM AUTHOR]

In this analysis, we investigate the quantum motions of a non-relativistic particle confined by the Aharonov–Bohm flux field with Hellmann potential (Coulomb plus Yukawa potential) in a topological defect space-time produced by a point-like defect. We employ a suitable approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation and determine the eigenvalue solution using the parametric Nikiforov–Uvarov method. Afterwards, we study the quantum system with an attractive Coulomb potential and obtained the eigenvalue solution using the same NU-method. These eigenvalue solutions are analysed and see the effects of topological defects produced by a point-like defect and the AB-flux field with these potentials. We also see that in addition to the topological effects, the energy levels shift more by the magnetic flux field, which gives us an analogue of the Aharonov–Bohm effect for the bound state. Finally, we plot a few graphs of the energy levels and the radial wave function with different parameters, such as the topological defect, the magnetic flux field, and the screening parameter, and discuss the results. [ABSTRACT FROM AUTHOR]

An attempt is made to quantum simulate the topological characterisations, such as winding number, geometric phase and symmetry properties for a quantum-simulated Kitaev chain. We find that α (ratio between the spin–orbit coupling and magnetic field) and the range of momentum space of consideration, play crucial roles in topological classification. We show explicitly that, for this quantum-simulated Kitaev chain, the topological quantum phase transition occurs for finite range of momentum. We observe that the quasiparticle mass of the fermion plays a significant role in topological quantum phase transition. We also show that the symmetry properties of the simulated Kitaev chain is the same as that of the original Kitaev chain. The exact solution of the simulated Kitaev chain is given. This work provides a new perspective on new emerging quantum simulator and also for the topological state of matter. [ABSTRACT FROM AUTHOR]

Multi-qubit controlled gates are frequently used in quantum information processing. Although they can be built with gates from the universal set of one- and two-qubit gates, this procedure typically becomes very demanding as the number of such gates rapidly grows with the size of the computational problem. Thus, finding a way to realize them with fewer steps and therefore with reduced decoherence errors is important. Particularly, quantum information is entering noisy intermediate-scale quantum era and in this era, quantum computers do not have enough resources for full fault tolerance and therefor can only support the computation with a short duration. This makes the reduction of the steps even more important. Here, we propose the realization of multi-qubit controlled nonadiabatic holonomic gates with connecting systems. Our proposal can efficiently reduce the operation steps of the realization, thereby reducing the affection from decoherence and increasing the precision of the computation. So, it is useful to realize efficient and robust quantum information processors. [ABSTRACT FROM AUTHOR]

In this paper, we determine the approximate eigenvalue bound state solution of the radial Schrodinger equation in three-dimension in the presence of the Aharonov-Bohm flux field with two-term diatomic molecular potential in point-like global monopole (PGM) defect. We analyse the effects of factors, such as topological defects, background curvature associated with topological defects as well as the potential. We also show that the energy levels shift due to the presence of the magnetic flux which gives us an analogue of the Aharonov-Bohm effect for the bound state. Finally, we apply the quantum system for some known potential models, such as q-deformed Hulthen-type potential and Manning-Rosen potential, and discussed the effects of various factors on the eigenvalue solutions. [ABSTRACT FROM AUTHOR]

We present a semiclassical explanation for the morphology of the surface Fermi arcs of Weyl semimetals. Viewing the surface states as a two-dimensional Fermi gas subject to band bending and Berry curvatures, we show that it is the non-parallelism between the velocity and the momentum that gives rise to the spiral structure of Fermi arcs. We map out the Fermi arcs from the velocity field for a single Weyl point and a lattice with two Weyl points. We also investigate the surface magnetoplasma of Dirac semimetals in a magnetic field, and find that the drift motion, the chiral magnetic effect and the Imbert-Fedorov shift are all involved in the formation of surface Fermi arcs. Our work not only provides an insightful perspective on the surface Fermi arcs and a practical way to find the surface dispersion, but also paves the way for the study of other physical properties of the surface states of topological semimetals, such as transport properties and orbital magnetization, using semiclassical methods. [ABSTRACT FROM AUTHOR]

The CoSi family hosts unconventional topological nodes with nonzero Chern numbers. The nontrivial topology is manifested by conspicuous surface Fermi arcs connecting surface projections of the nodes. Here, using angle-resolved photoemission spectroscopy, we have systematically investigated the (001) surface states of pristine and Ni-doped CoSi. The surface states form saddle-like band structures at/near the time-reversal invariant point near the Fermi level. The Fermi arcs undergo consecutive Lifshitz transitions at the saddle points X ¯ , leading to changes of the Fermi arc configuration. As the density of states has a van Hove singularity at the saddle points, exotic many-body physical phenomena may emerge accompanied by the topological transitions of surface Fermi arcs. [ABSTRACT FROM AUTHOR]

As an intrinsic nature of light, polarization plays a critical role in the vectorial characteristic of optical fields. Vector optical fields with an inhomogeneous polarization distribution show many exotic phenomena and applications not existing in scalar optical fields. Existing polarization optics, however, mainly focuses on the manipulation of polarization distribution on a single transverse plane. Here, we propose a synthetic approach to realize polarization manipulation with spatial and temporal degrees. The underlying mechanism relies on decoupling two orthogonal polarization states through asymmetric photonic spin-orbit interactions to obtain customer-tailored phase and amplitude difference in both transverse and longitudinal space, thereby changing the resulting polarization distribution at will in three-dimensional (3D) space. Remarkably, a longitudinally varied cylindrical vector field is experimentally demonstrated by a monolayer metasurface, in which the polarization distribution switches continuously and periodically between radial and azimuthal polarization. Furthermore, the vector field can be dynamically tuned by rotating the incident polarization state. Our work extends polarization optics from two-dimensional space to 3D space, allowing the arbitrary generation and manipulation of 3D vector optical fields with temporal tunability. [ABSTRACT FROM AUTHOR]

We propose a built-in fault-tolerant geometric operation to realize fast remote entanglement between superconducting qubits anchored to a 15 mK plate and Rydberg-atom qubits trapped near a 1 K plate via thermal coupled cavities. We show that this operation is robust against the detrimental effects of the thermal mode states and fluctuations in the control parameters. The operation can generate a high-fidelity entanglement between superconducting and atomic qubits under realistic experimental parameters, comparable to the results of the existing methods using auxiliary cooling systems. The scheme proposed here will promote the development of quantum network and distributed superconducting quantum computation. [ABSTRACT FROM AUTHOR]

We show that the photonic crystal (PhC) made of dielectric cuboids with their centers forming a honeycomb lattice is characterized by a ℤ2${\mathbb{ℤ}}_{2}$ topological index when the longer sides of six cuboids point towards the center of hexagonal unit cell. While the C6v symmetry regarding the center of unit cell is preserved, the C3 symmetry regarding honeycomb sites is broken, which opens a bandgap in the Dirac dispersion of honeycomb structure and induces a band inversion between p modes and d modes. Rotating cuboids around their individual centers closes the bandgap and reopens a trivial bandgap. We discuss that this feature can be exploited for realizing a reconfigurable topological waveguide.

The review is aimed at highlighting the aspects of topological superconductivity in the absence of spin–orbit interaction in two-dimensional systems with long-range noncollinear spin ordering or magnetic skyrmions. Another purpose is to give a brief introduction to the new concept of topological superconductivity, i.e. higher-order topology in two-dimensional systems including spin–orbit coupled structures. The formation of Majorana modes due to magnetic textures is discussed. The role of effective triplet pairings and odd fermion parity of the ground state wave function in different systems is emphasized. We describe the peculiarities of the magnetic skyrmions, leading to the formation of the Majorana modes and defects on which the modes are localized. The problem of braiding in the two-dimensional systems, especially in higher-order topological superconductors, is considered. [ABSTRACT FROM AUTHOR]

We study and present the results of curvature for different symmetry classes (BDI, AIII and A) of model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to the other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behaviour for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret–Frenet equations for all model Hamiltonians in R 3 space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter. [ABSTRACT FROM AUTHOR]

Topological crystalline insulator (TCI) is one of the symmetry-protected topological states. Any TCI can be deformed into a simple product state of several decoupled two-dimensional (2D) topologically nontrivial layers in its lattice respecting its crystalline symmetries called the layer construction (LC) limit. In this work, based on first-principles calculations we have revealed that both tetragonal LaSbTe (t-LaSbTe) and orthorhombic LaSbTe (o-LaSbTe) can be interpreted as stacking of 2D topological insulators in each lattice space. The structural phase transition from t-LaSbTe to o-LaSbTe due to soft phonon modes demonstrates how the real space change can lead to the modification of topological states. Their symmetry-based indicators and topological invariants have been analyzed based on LC. We propose that LaSbTe is an ideal example demonstrating the LC paradigm, which bridges the crystal structures in real space to the band topology in momentum space. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Schrödinger'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. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse algorithms for constructing presentations of graph braid groups from the point of view of anyonic quantum statistics on graphs. In the first part of this paper, we provide a comprehensive review of an algorithm for constructing so-called minimal Morse presentations of graph braid groups that relies on discrete Morse theory. Next, we introduce the notion of a physical presentation of a graph braid group as a presentation whose generators have a direct interpretation as particle exchanges. We show how to derive a physical presentation of a graph braid group from its minimal Morse presentation. In the second part of the paper, we study unitary representations of graph braid groups that are constructed from their presentations. We point out that algebraic objects called moduli spaces of flat bundles encode all unitary representations of graph braid groups. For 2-connected graphs, we conclude the stabilisation of moduli spaces of flat bundles over graph configuration spaces for large numbers of particles. Moreover, we set out a framework for studying locally abelian anyons on graphs whose non-abelian properties are only encoded in non-abelian topological phases assigned to cycles of the considered graph. [ABSTRACT FROM AUTHOR]

Majorana fermion (MF), an exotic particle that is identical to its own antiparticle, was recently found in solid matter as a quasiparticle excitation, the Majorana zero mode (MZM), in the vortex of an artificial topological superconductor (TSC). This artificial TSC, first proposed by Fu and Kane in 2008, is a heterostructure made of a topological insulator BiTe and an s-wave superconductor NbSe. This paper will briefly review the experimental progresses based on the BiTe/NbSe heterostructure. All evidences are self-consistent and reveal that the MZM exists in the center of vortex. Those experimental results are also supported by theory. This finding is a milestone in the research of Majorana fermions in solid state physics and a starting point of MZM's application in topological quantum computation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce useful scheme of the atom–atom interaction in the case of absence and presence of the atomic motion effect. The quantum entanglement between the two two-level atoms based on concurrence quantifier will be investigated. The dependence atom–atom entanglement on the different system parameters will be examined. Moreover, the influence of the atomic motion and initial state setting on the dynamical behavior of the entanglement between two atoms will be discussed. Furthermore, we have explored some important phenomena related to the entanglement between two atoms such as entanglement sudden death (ESD) and entanglement sudden birth (ESB). Finally, we have obtained a high amount of the atom–atom entanglement by a proper choice of the system parameters in the case of stationary and moving atoms. [ABSTRACT FROM AUTHOR]

Topological insulators possess time reversal symmetry protected metallic surface states over the insulating bulk, where these surface states are expected to be immune to small disorder, chemical passivation of the surface or temperature change. However, significant discrepancy from such behavior has been found experimentally in various materials. Here, we review some of our recent results on the electronic structure of a typical topological insulator, Bi 2 Se 3 . Both, the band structure results and high-resolution angle resolved photoemission data reveal significantly different surface electronic structure for different surface terminations. Furthermore, oxygen impurity on Se terminated surface exhibits an electron doping scenario, while oxygen on Bi terminated surface corresponds to a hole-doping scenario. The intensity of the Dirac states reduces with aging indicating fragility of the topological order due to surface impurities. [ABSTRACT FROM AUTHOR]

The dynamic phase transitions and dynamic phase diagrams are studied, within a mean-field approach, in the kinetic Ising model on the Shastry-Sutherland lattice under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The time-dependence behavior of order parameters and the behavior of average order parameters in a period, which is also called the dynamic order parameters, as a function of temperature, are investigated. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions as well as to obtain the dynamic phase transition temperatures. We present the dynamic phase diagrams in the magnetic field amplitude and temperature plane. The phase diagrams exhibit a dynamic tricritical point and reentrant phenomena. The phase diagrams also contain paramagnetic (P), Néel (N), Collinear (C) phases, two coexistence or mixed regions, (N+C) and (N+P), which strongly depend on interaction parameters. [ABSTRACT FROM AUTHOR]

We investigate the behavior of quantum particles in the cosmic string space-time in the presence of Pöschl-Teller double-ring-shaped Coulomb and double-ring-shaped oscillator potentials. We obtain energy levels and finally compare the results with the Minkowski space-time. To do this, we solve the Schrödinger equation in spherical coordinates. [ABSTRACT FROM AUTHOR]

The possibility of realizing fractional quantum Hall liquids in photonic systems has attracted a great deal of interest of late. Unlike electronic systems, interactions in photonic systems must be engineered from nonlinear elements and are thus subject to positional disorder. The stability of the topological liquid relies on repulsive interactions. In this paper we investigate the stability of fractional quantum Hall liquids to impurities which host attractive interactions. Employing the Bose–Hubbard model with a magnetic field, we find that for sufficiently strong attractive interactions these impurities can destroy the topological liquid. However, we find that the liquid is quite robust to these defects, a fact which bodes well for the realization of topological quantum Hall liquids in photonic systems.

We present the results of low lying collective mode of coupled optical cavity arrays. We derive the Dirac equation for this system and explain the existence of Majorana fermion mode in the system. We present quite a few analytical relations between the Rabi frequency oscillation and the atom–photon coupling strength to explain the different physical situation of our study and also the condition for massless collective mode in the system. We present several analytical relations between the Dirac spinor field, order and disorder operators for our systems. We also show that the Luttinger liquid physics is one of the intrinsic concepts in our system. [ABSTRACT FROM AUTHOR]

Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such schemes are typically associated with space-dependent effective masses (tunneling amplitudes) and non-uniform flux patterns. In this work we investigate this phenomenon theoretically, by computing the effective Hamiltonians and quasienergy spectra associated with several kinds of lattice-shaking protocols. A detailed comparison with a method based on moving lattices, which are added on top of a main static optical lattice, is provided. This study allows the identification of novel shaking schemes, which simultaneously provide uniform effective mass and magnetic flux, with direct implications for cold-atom experiments and photonics.

A possible scenario of the Lorentz symmetry violation is discussed based on the arising of geometric quantum phases yielded by the effects of the Lorentz symmetry violation in the CPT-even gauge sector of Standard Model Extension. Analogues of the Anandan quantum phase and the scalar Aharonov-Bohm effect for a neutral particle [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained from the parity-odd sector of the tensor [ABSTRACT FROM AUTHOR]

We show that Bose–Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose–Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.

We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in Zhai et al (2013 Phys. Rev. A http://dx.doi.org/10.1103/PhysRevA.87.063638 87 http://dx.doi.org/10.1103/PhysRevA.87.063638 ), in which populating d bands with a 99 $\%$ fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete ${{\mathbb{Z}}_{2}}$ -symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate anti-symmetric spin interactions that can give rise to novel effects like spin canting.

We theoretically explore quench dynamics in a finite-sized topological fermionic p -wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick’s theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities—the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term ‘parity blocking’. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

Coupling Majorana qubits with other qubits is absolutely essential for storing, manipulating and transferring information for topological quantum computing. We theoretically propose a manner to couple Majorana qubits with solitons, another kind of topological impurity, which was first studied in the spinless Su–Schrieffer–Heeger model. We present a NOT operation on the Majorana qubit by moving the soliton through a heterostructure adiabatically. Based on these two topological impurities, the operation is robust against local disorder. Furthermore, we find that the soliton may carry nonuniversal fractional electric charge instead of fractional charge $1/2$ , because of the breaking of gauge invariance induced by superconducting proximity.

When the electromagnetic potentials are expressed in the Coulomb gauge in terms of the electric and magnetic fields rather than the sources responsible for these fields they have a simple form that is nonlocal (i.e., the potentials depend on the fields at every point in space). It is this nonlocality of classical electrodynamics that is primarily responsible for the puzzle associated with the static Aharonov-Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters. [ABSTRACT FROM AUTHOR]

A mathematical formalism for describing geometric phases is presented. A development of the geometric phase is given, which is valid for noncyclic nonadiabatic processes. The result is used to calculate exactly the geometric phase for a quantum system that is made up of a spin one-half system in a rotating magnetic field. [ABSTRACT FROM AUTHOR]

Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The k th-order deviations are governed by a k th-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the k th-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.

We present a robust practical scheme for measuring the topological invariants of non-interacting tight-binding models realized in arrays of coupled photonic cavities. More specifically, we aim to focus on the implementation of a single unit cell with tunable twisted boundary conditions in order to access the bulk topological properties of much larger systems experimentally. We illustrate our method in a two-dimensional integer quantum Hall model, demonstrating that the associated topological invariants can be measured to a high degree of accuracy despite the driven-dissipative bosonic nature of the system, and discuss the robustness of our scheme against various sources of disorder.