Chiral bound states in a staggered array of coupled resonators

We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.

Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings

Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.

Theoretical investigation of excited dipole bound states of alkali-containing diatomic anions

Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules.

Coulomb-assisted nonlocal electron transport between two pairs of Majorana bound states in a superconducting island

We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majorana bound state(MBS)is coupled to one lead via a quantum dot with resonant levels.In this device,the nonlocal correlations can be induced in the absence of Majorana energy splitting.We find that the negative differential conductance and giant current noise cross correlation could be induced,due to the interplay between nonlocality of MBSs and dynamical Coulomb blockade effect.This feature may provide a signature for the existence of the MBSs.

Interface state-based bound states in continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system

We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system.We extensively classify and study these BICs and BCR modes,which exhibit high-quality(high-Q)factors,in different regions relative to the interface of the system.These BICs and BCR modes with a high-Q factor have been studied in detail based on distinctive structural parameters and scattering theory.The outcomes of this research break the periodic limitation of interface state-based BICs,and realize more and higher symmetry interface state-based BICs and BCR modes.Moreover,we can control the region where light is captured by adjusting the frequency,and show that the Q factor of BICs is more closely related to the ordinal number of rings and the rotational symmetry number of the system.

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

High-Q resonances governed by the quasi-bound states in the continuum in all-dielectric metasurfaces

The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound in the continuum(BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q factor of more than 3,000 can be easily achieved by optimizing dimensions of the nanostructure. At this sharp resonance, the intensity of the third harmonic generation signal in the patterned structure can be 368 times larger than that of the flat silicon film. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which may promote the development of the potential meta-devices for nonlinearity, lasing action, and sensing.

BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0

Hybrid bound states in the continuum in terahertz metasurfaces

Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical switches.The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor(Q)and asymmetry.Here,we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice.We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6.In the hybrid BIC lattice,modes are transferred toГpoint inherited from high symmetric X,Y,and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing.This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices.

Dual bound states in the continuum enhanced second harmonic generation with transition metal dichalcogenides monolayer

The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room temperature.However,the ultimate atomic-scale interaction length with light makes the SHG of Transition Metal Dichalcogenides(TM-Ds)monolayers naturally weak.Here,we propose coupling a monolayer of TMDs with a photonic grating slab that works with doubly resonant bound states in the continuum(BIC).The BIC slabs are designed to exhibit a pair of BICs,reson-ant with both the fundamental wave(FW)and the second harmonic wave(SHW).Firstly,the spatial mode matching can be fulfilled by tilting FW's incident angle.We theoretically demonstrate that this strategy leads to more than four orders of magnitude enhancement of SHG efficiency than a sole monolayer of TMDs,under a pump light intensity of 0.1 GW/cm^(2).Moreover,we demonstrate that patterning the TMDs monolayer can further enhance the spatial overlap coefficient,which leads to an extra three orders of magnitude enhancement of SHG efficiency.These results demonstrate remarkable pos-sibilities for enhancing SHG with nonlinear 2D materials,opening many opportunities for chip-based light sources,nano-lasers,imaging,and biochemical sensing.

Discrete vortex bound states with a van Hove singularity in the vicinity of the Fermi level

A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS

We consider the following nonlinear Schroodinger equations -ε^2△u ＋ u = Q（x）｜u｜^p-2u in R^N, u ∈ H^1（R^N）,where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3. We prove that this problem has sign-changing（nodal） semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q（x）.Moreover, the number of this type of solutions will go to infinity as ε→ 0^＋.

Instantaneous Formulation for Transitions Between Two Instantaneous Bound States and Its Gauge Invariance

We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.

Quantum Mechanics of Moving Bound States

The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.

BOUND STATES FOR A CLASS OF QUASILINEAR SCALAR FIELD EQUATIONS WITH POTENTIALS VANISHING AT INFINITY

We study the existence and non-existence of bound states （i.e., solutions in W1,P（RN）） for a class of quasilinear scalar field equations of the for -△pu＋V（x）｜u｜p-2u=a（x）｜u｜q-2u,x∈RN,1〈P〈N,mwhen the potentials V（.）≥ 0 and a（.） decay to zero at infinity.

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 e2/2h 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.

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrodinger equation with the mulfiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l （states） quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.

Computing Quantum Bound States on Triply Punctured Two-Sphere Surface

We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms （MCFs） which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.

Exact bound state solutions of the Klein-Gordon particle in Hulthn potential

In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding bound state solutions are expressed in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking（symmetry of sublattices）.We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for ＂local chemical potential＂ and ＂local gap＂.The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states（BSs） has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~＋（r）,g_m~＋（r）,and f_m^-（r）,g_m^-（r）,can be established by SO（2） group.