Aharonov-Bohm Interferometer in a T-Shaped Quantum Dot Embedded in Majorana Bound States *

We theoretically study the spin-dependent transport properties of anAharonov-Bohm (AB) interferometer composed by a T-shaped quantum dot (QD)embedded in Majorana bound states (MBS). We use the equation of motion method tocalculate the conductance across the interferometer. We note that the conductance exhibitssensitive dependence on the MBS-QD coupling strength as well as the polarization strengthof the leads when the phase factor of AB ring changes periodically. The conductance shows a transitionfrom resonance to anti-resonance when the MBS-QD coupling strength changes from small to large. Also, there is different p-dependence conductance when the leads alignment changesfrom parallel to anti-parallel. These findings suggest that such a model could be used for a sensitivedetection of MBS interactions, exploiting the high sensitivity of conductance to the AB phase in theinterferometer.     

耦合Majorana束缚态T形双量子点中的Andreev反射

研究了连接在正常金属电极和超导电极之间的耦合Majorana束缚态(MBSs)T形双量子点结构中的Andreev反射.研究发现,对于T形双量子点结构,当入射能量等于边耦合量子点能级时Andreev反射电导出现Fano振荡,连接MBSs之后,零费米能附近出现一对新的Fano型振荡峰.如果忽略两个MBSs之间的相互作用,零费米能点的Andreev反射电导为定值1/2G_0(G_0=2e~2/h),不受量子点能级、双量子点之间耦合强度以及量子点与MBSs之间的耦合强度的影响.此外,在没有耦合MBSs的T形双量子点结构中,调节双量子点间的耦合强度可以使零费米能附近的Andreev反射电导出现由共振带向反共振带的转变,而耦合MBSs之后,又可以使反共振消失转而出现新的共振峰.     

Resonant Andreev reflection in a normal-metal/quantum-dot/superconductor system with coupled Majorana bound states

Andreev reflection(AR) in a normal-metal/quantum-dot/superconductor(N–QD–S) system with coupled Majorana bound states(MBSs) is investigated theoretically. We find that in the N–QD–S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD–MBS coupling or MBS–MBS coupling. The AR conductance is always e~2/2h at the zero Fermi energy point when only QD–MBSs coupling is considered. In addition, the resonant AR occurs when the MBS–MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD–MBS coupling and the MBS–MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.     

Fano‐Majorana Effect and Bound States in the Continuum on a Crossbar‐Shaped Quantum Dot Hybrid Structure

Transport properties are investigated through a crossbar‐shaped structure formed by a quantum dot (QD) coupled to two normal leads and embedded between two 1D topological superconductors (TSCs). Each TSC hosts Majorana‐bound states (MBSs) at its ends, which can interact between them with an effective coupling strength. A signature of bound states in continuum (BIC) is found in the MBSs spectral function. By allowing finite inter MBSs coupling, BICs splitting is observed and shows projection in transmission for asymmetric coupling case as quasi‐BICs. As a consequence, it is also shown that the Fano effect, arising from interference phenomena between MBSs hybridization trough QD, is observed with a half‐integer amplitude modulation. It is believed that the findings can help to better understand the properties of MBSs and their interplay with QDs.     

Influence of Majorana Bound States in Quantum Rings

A quantum ring coupled to a 1D topological superconductor hosting Majorana bound states (MBSs) is investigated. The MBSs effects over the spectrum and persistent current along the quantum ring are studied. The spectra of the system are obtained by an exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian in the Majorana representation. In addition, Green's function formalism is implemented for analytical calculations and obtained a switching condition in the MBSs fermionic parity. Three different patterns that could be obtained for the spatial separation of the MBSs, named: bowtie, diamond, and asymmetric, are reported here, which are present only in odd parity in the quantum ring, while only a single pattern (bowtie) is obtained for even parity. Those patterns are subject strictly to the switching condition for the MBSs. Besides, quantum ring with the presence of a Majorana zero mode presents gapped/gapless spectra in odd/even parity showing in the even case a subtle signature in the persistent current.     

超导邻近效应在正常金属层中引起的反常小能隙现象

将散射矩阵方法推广到超导双结系统，对正常金属/正常金属/超导结的隧道电导进行了研究.中间正常金属层中的电子和其Andreev反射空穴之间的相位相干性导致了隧道电导出现反常小能隙现象.综合考虑相干和顺序遂穿，计算结果理想的解释了最近Gupta等人在实验中观测到的反常小能隙现象.     

电子型FeSe基高温超导体的磁通束缚态与Majorana零能模

作为凝聚态物理中一类新奇准粒子态,Majorana零能模(Majorana zero mode)由于可用来实现拓扑量子计算而成为当前的研究热点.理论预言,Majorana零能模可作为特殊的束缚态出现在一些拓扑超导体的磁通涡旋中.但实际超导体磁通中还可能存在其他低能束缚态或杂质态,这给Majorana零能模的辨别和具体应用带来了困难.目前实验上寻找合适的拓扑超导体系、分辨出清晰的Majorana零能模仍然是十分迫切的.本文主要介绍最近利用高能量分辨的扫描隧道显微镜,对电子掺杂铁硒类超导体(Li,Fe)OHFeSe和单层FeSe/SrTiO3磁通态进行的研究.实验上在前者的自由磁通中观测到清晰的零能模,并进一步测量到Majorana零能模的重要特征—量子化电导.而在后者磁通中只发现常规Caroli-de Gennes-Matricon(CdGM)束缚态,反映出s波对称性的特征.这系列实验既为Majorana零能模物性的进一步研究提供了合适平台,也为澄清铁基超导体中拓扑超导电性的来源提供了线索.     

Bound States in Quantum Electrodynamics: Theory and Application

The basic methods that have been used for describing bound-state quantum electrodynamics are described and critically discussed. These include the external field approximation, the quasi-potential approaches, the effective potential approach, the Bethe–Salpeter method, and the three-dimensional equations of Lepage and other workers. Other methods less frequently used but of some intrinsic interest such as applications of the Duffin–Kemmer equation are also described. A comparison of the strengths and shortcomings of these various approaches is included.     

Modifications of Electron States,Magnetization, and Persistent Current in a Quantum Dot by Controlled Curvature

The thin‐layer quantization procedure is used to study the physical implications due to curvature effects on a quantum dot in the presence of an external magnetic field. Among the various physical implications due to the curvature of the system, the absence of the $m=0$ state is the most relevant one. This absence affects the Fermi energy and consequently the thermodynamic properties of the system. In the absence of magnetic fields, it is verified that the rotational symmetry in the lateral confinement is preserved in the electronic states of the system and its degeneracy concerning the harmonicity of the confining potential is broken. In the presence of a magnetic field, however, the energies of the electronic states in a quantum dot with curvature are greater than those obtained for a quantum dot in a flat space, and the profile of degeneracy changes when the field is varied. It is shown that the curvature of the surface modifies the number of subbands occupied in the Fermi energy. In the study of both magnetization and persistent currents, it is observed that Aharonov–Bohm‐type oscillations are present, whereas de Haas–van Alphen‐type oscillations are not well defined.     

Transferring and Bounding Single Photon in Waveguide Controlled by Quantum Node Based on Atomic Ensemble

We study the scattering process of photons confined in a one-dimensional optical waveguide by a laser controlled atomic ensemble. The investigation leads to an alternative setup of quantum node controlling the coherent transfer of single photon in such one dimensional continuum. To exactly solve the effective scattering equations by using the discrete coordinate approach, we simulate the linear waveguide as a coupled resonator array at the high energy limit. We generally calculate the transmission eoet~cients and its vanishing at resonance reflects the good controllability of our scheme. We also show that there exist two bound states to describe the localize photons around the cavity.     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Energy-resolved spin filtering effect and thermoelectric effect in topological-insulator junctions with anisotropic chiral edge states

Topological edge states have crucial applications in the future nano spintronics devices. In this work, circularly polarized light is applied on the zigzag silicene-like nanoribbons resulting in the anisotropic chiral edge modes. An energy-dependent spin filter is designed based on the topological-insulator (TI) junctions with anisotropic chiral edge states. The resonance transmission has been observed in the TI junctions by calculating the local current distributions. And some strong Fabry−Perot resonances are found leading to the sharp transmission peaks. Whereas, the weak and asymmetric resonance corresponds to the broad transmission peaks. In addition, a qualitative relation between the resonant energy separation T_R and group velocity v_f is derived: T_R=πhv_fn/L, that indicated T_R is proportional to v_f and inversely proportional to the length L of the conductor. The different T_R between the spin-up and spin-down cases results in the energy-resolved spin filtering effect. Moreover, the intensity of the circularly polarized light can modulate the group velocity v_f. Thus, the intensity of circularly polarized light, as well as the conductor-length, play very vital roles in designing the energy-dependent spin filter. Since the transmission gap root in the Fabry−Perot resonances, the thermoelectric (TE) property can be enhanced by adjusting the gap. A schedule to enhance the TE performance in the TI-junction is proposed by modulating the electric field (E_z). The TE dependence on E_z in the nanojunction is investigated, where the appropriate E_z leads to a very high spin thermopower and spin figure of merit. These TI junctions have potential usages in the nano spintronics and thermoelectric devices.     

磁场和库仑场对抛物量子点中弱耦合极化子激发态性质的影响

采用线性组合算符和幺正变换方法研究了磁场和库仑场对抛物量子点中极化子激发态性质的影响。导出了抛物量子点中弱耦合束缚磁极化子的振动频率、第一内部激发态能量、激发能量与量子点的有效受限长度、库仑束缚势和磁场的回旋频率之间的变化关系。通过数值计算,结果表明:抛物量子点中弱耦合束缚极化子的振动频率、第一内部激发态能量、激发能量均随量子点的有效受限长度减小而迅速增大。随库仑束缚势增大而增大。随磁场的回旋频率的增加而增大。     

Polarization States of Light and Their Quantum Tomography

The notion and main features of polarization states of light are discussed within the framework of classical and quantum optics. This notion is shown to be correctly defined for arbitrary light beams only within quantum optics by using the P-quasispin formalism developed earlier. Polarization states of quantum light are shown to be fully described by a polarization density operator (PDO) obtained via reducing the total field density operator. Theoretical foundations are given for quantum tomography of polarization states of light fields considered as a way of measuring PDO. Herewith, the main attention is paid to a method where proper polarization tomographic observables (PDO “measurers”) are used. The method is shown to be adequately formulated by means of quasi-spectral tomographic expansions of PDO in special operator bases (given by finite sums of partially orthogonal projectors), which determine probability distributions of tomographic observables as expansion coefficients. Matrix versions of such “tomographic” PDO representations are obtained. In particular, projections of these expansions on quasiclassical operator bases, determining polarization quasiprobability functions, are given. An example of experimental implementation of polarization tomography of unpolarized light (biphoton radiation with hidden polarization) is analyzed.     

Surface barrier and magnetic hysteresis of ac permeability in YBaCuO single crystal

The nature of hysteretic behavior of the flux line lattice (FLL) contribution to ac magnetic permeability (μ_v) is analyzed for the case of YBa₂Cu₃O_x single crystal (at applied magnetic field Hc axis). It is shown that hysteresis loops μ_v(H) corresponding to different temperatures (T=70–84 K) are scaled to a universal curve in normalized coordinates. Such a behavior is interpreted in terms of the FLL interaction with the crystal surface. The explicit relationship between μ_v and magnetic induction B is found for the near-surface region of the superconductor. It is shown that the μ_v(H) loops are closely related to the hysteresis of B at cycling of applied magnetic field. The latter hysteresis stems from the Bean–Livingston surface barrier. The estimates demonstrate strong suppression of the surface barrier in YBa₂Cu₃O_x crystal in comparison to that expected for the ideal surface. As a result, the lower branch of the hysteresis loop corresponding to the increasing field is very close to the equilibrium μ_v(H) curve and the surface barrier appreciably affects only the upper branch when magnetic flux leaves the sample. The comparison of theoretical predictions and experimental data provides an opportunity to refine the actual range of stability H_max(B)–H_min(B) for the FLL at fixed B for YBa₂Cu₃O_x crystal in the case of Hc.     

Fission and Fusion in the New Localized Structures to the Integrable (2 + 1)-Dimensional Higher-Order Broer–Kaup System

By means of the Weiss–Tabor–Carnevale (WTC) truncation method and the general variable separation approach (GVSA), analytical investigation of the integrable (2+1)-dimensional higher-order Broer–Kaup (HBK) system shows, due to the possibility of selecting three arbitrary func.tions, the existence of interacting coherent excitations such as dromions, solitons, periodic solitons, etc. The interaction between some of the localized solutions are elastic because they pass through each other and preserve their shapes and velocities, the only change being the phase shift. However, as for some soliton models, completely non-elastic interactions have been found in this model. These non-elastic interactions are characterized by the fact that, at a specific time, one soliton may fission to two or more solitons; or on the contrary, two or more solitons will fuse to one soliton.     

1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating the external potential well in the three-dimensional (3D) Gross–Pitaevskii equation (GPE). Within the framework of this method, under suitable conditions, the GPE can be exactly decomposed into a pair of coupled equations: a transverse two-dimensional (2D) linear Schr?dinger equation and a one-dimensional (1D) longitudinal nonlinear Schr?dinger equation (NLSE) with, in a general case, a time-dependent nonlinear coupling coefficient. We review the general idea how to filter and control localized solutions of the GPE. Then, the 1D longitudinal NLSE is numerically solved with suitable non-ideal controlling potentials that differ from the ideal one so as to introduce relatively small errors in the designed spatial profile. It is shown that a BEC with an asymmetric initial position in the confining potential exhibits breather-like oscillations in the longitudinal direction but, nevertheless, the BEC state remains confined within the potential well for a long time. In particular, while the condensate remains essentially stable, preserving its longitudinal soliton-like shape, only a small part is lost into “radiation”.     

Derivation of the Evans Wave Equation from the Lagrangian and <Emphasis Type="Italic">Action</Emphasis>: Origin of the Planck Constant in General Relativity

No Heading The Evans wave equation is derived from the appropriate Lagrangian and action, identifying the origin of the Planck constant in general relativity. The classical Fermat principle of least time, and the classical Hamilton principle of least action, are expressed in terms of a tetrad multiplied by a phase factor exp(iS/), where S is the action in general relativity. Wave (or quantum) mechanics emerges from these classical principles of general relativity for all matter and radiation fields, giving a unified theory of quantum mechanics based on differential geometry and general relativity. The phase factor exp(iS/) is an eigenfunction of the Evans wave equation and is the origin in general relativity and geometry of topological phase effects in physics, including the Aharonov-Bohm class of effects, the Berry phase, the Sagnac effect, related interferometric effects, and all physical optical effects through the Evans spin field B⁽³⁾ and the Stokes theorem in differential geometry. The Planck constant is thus identified as the least amount possible of action or angular momentum or spin in the universe. This is also the origin of the fundamental Evans spin field B⁽³⁾, which is always observed in any physical optical effect. It originates in torsion, spin and the second (or spin) Casimir invariant of the Einstein group. Mass originates in the first Casimir invariant of the Einstein group. These two invariants define any particle.