Bound States in the Continuum (BIC) Protected By Self-Sustained Potential Barriers in a Flat Band System

Mapping Intimacies ◽

10.21203/rs.3.rs-1082419/v1 ◽

2021 ◽

Author(s):

Yi-Cai Zhang

Keyword(s):

Coulomb Potential ◽

Bound States ◽

Band System ◽

Bound State ◽

Attractive Potential ◽

Flat Band ◽

Exponential Potential ◽

Potential Barriers ◽

Strong Potential ◽

The Continuum

Abstract In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system with a potential of type III, which has a unique non-vanishing matrix element in basis |1⟩. It is found that, for such a kind of potential, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Some bound states in the continuum (BIC) can appear for sufficiently strong potential. These bound states (BIC) are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strength, near which the bound state energy can goes to infinite. For a sufficiently strong exponential potential, there exists two different bound states with a same number of wave function nodes. The existences of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for existence of BIC is that the maximum value of potential is larger than two times band gap.

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Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

Physica Scripta ◽

10.1088/1402-4896/ac46f4 ◽

2021 ◽

Author(s):

Yi-Cai Zhang

Keyword(s):

Energy Spectrum ◽

Continuous Spectrum ◽

Bound States ◽

State Energy ◽

Band System ◽

Bound State ◽

Flat Band ◽

Bound State Energy ◽

Type Iii ◽

Potential Strength

Abstract In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $\alpha_c$ at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

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(1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

Open Physics ◽

10.2478/s11534-013-0202-8 ◽

2013 ◽

Vol 11 (4) ◽

Cited By ~ 2

Author(s):

Omar Mustafa

Keyword(s):

Harmonic Oscillator ◽

Bound States ◽

Bound State ◽

One Dimension ◽

Fermi Velocity ◽

Dirac Particles ◽

The Continuum ◽

Oscillator Models

AbstractWe extend Panella and Roy’s [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v F2 (x) = A, where A ≥ 0 is constant. Dirac Pöschl-Teller and harmonic oscillator models are also reported.

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Bound states in the continuum in resonant nanostructures: an overview of engineered materials for tailored applications

Nanophotonics ◽

10.1515/nanoph-2021-0387 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Shereena Joseph ◽

Saurabh Pandey ◽

Swagato Sarkar ◽

Joby Joseph

Keyword(s):

Bound States ◽

Beam Steering ◽

Functional Materials ◽

Bound State ◽

Dielectric Medium ◽

Quality Factors ◽

Theoretical Frameworks ◽

Experimental Realization ◽

Promising Tool ◽

The Continuum

Abstract From theoretical model to experimental realization, the bound state in the continuum (BIC) is an emerging area of research interest in the last decade. In the initial years, well-established theoretical frameworks explained the underlying physics for optical BIC modes excited in various symmetrical configurations. Eventually, in the last couple of years, optical-BICs were exploited as a promising tool for experimental realization with advanced nanofabrication techniques for numerous breakthrough applications. Here, we present a review of the evolution of BIC modes in various symmetry and functioning mediums along with their application. More specifically, depending upon the nature of the interacting medium, the excitations of BIC modes are classified into the pure dielectric and lossy plasmonic BICs. The dielectric constituents are again classified as photonic crystal functioning in the subwavelength regime, influenced by the diffraction modes and metasurfaces for interactions far from the diffraction regime. More importantly, engineered functional materials evolved with the pure dielectric medium are explored for hybrid-quasi-BIC modes with huge-quality factors, exhibiting a promising approach to trigger the nanoscale phenomena more efficiently. Similarly, hybrid modes instigated by the photonic and plasmonic constituents can replace the high dissipative losses of metallic components, sustaining the high localization of field and high figure of merit. Further, the discussions are based on the applications of the localized BIC modes and high-quality quasi-BIC resonance traits in the nonlinear harmonic generation, refractometric sensing, imaging, lasing, nanocavities, low loss on-chip communication, and as a photodetector. The topology-controlled beam steering and, chiral sensing has also been briefly discussed.

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Bound states in the continuum and time evolution of the generalized eigenfunctions

Revista Mexicana de Física ◽

10.31349/revmexfis.64.464 ◽

2018 ◽

Vol 64 (5) ◽

pp. 464 ◽

Cited By ~ 1

Author(s):

David Lohr ◽

Enriqueta Hernandez ◽

Antonio Jauregui ◽

Alfonso Mondragon

Keyword(s):

Time Evolution ◽

Bound States ◽

Scattering Problem ◽

Bound State ◽

The Other ◽

Von Neumann ◽

Generalized Eigenfunctions ◽

Jost Solutions ◽

Type Potential ◽

The Continuum

We study the Jost solutions for the scattering problem of a von Neumann-Wigner type potential, constructed by means of a two times iterated and completely degenerated Darboux transformation. We show that for a particular energy the unnormalizedJost solutions coalesce to give rise to a Jordan cycle of rank two. Performing a pole decomposition of the normalized Jost solutions we find the generalized eigenfunctions: one is a normalizable function corresponding to the bound state in the continuum and the other is a bounded, non-normalizable function. We obtain the time evolution of these functions as pseudo-unitary, characteristic of a pseudo-Hermitian system.

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Quasi-BIC laser enabled by high-contrast grating resonator for gas detection

Nanophotonics ◽

10.1515/nanoph-2021-0368 ◽

2021 ◽

Vol 0 (0) ◽

Cited By ~ 1

Author(s):

Haoran Zhang ◽

Tao Wang ◽

Jingyi Tian ◽

Jiacheng Sun ◽

Shaoxian Li ◽

...

Keyword(s):

Bound States ◽

Signal To Noise Ratio ◽

Bound State ◽

Gain Medium ◽

Gas Detection ◽

Visible Range ◽

High Signal ◽

High Contrast ◽

High Contrast Grating ◽

The Continuum

Abstract In this work, we propose and numerically investigate a two-dimensional microlaser based on the concept of bound states in the continuum (BIC). The device consists of a thin gain layer (Rhodamine 6G dye-doped silica) sandwiched between two high-contrast-grating layers. The structure supports various BIC modes upon a proper choice of topological parameters; in particular it supports a high-Q quasi-BIC mode when partially breaking a bound state in the continuum at Γ point. The optically-pumped gain medium provides sufficient optical gain to compensate the quasi-BIC mode losses, enabling lasing with ultra-low pump threshold (fluence of 17 μJ/cm2) and very narrow optical linewidth in the visible range. This innovative device displays distinguished sensing performance for gas detection, and the emission wavelength sensitively shifts to the longer wavelength with the changing of environment refractive index (in order of 5 × 10−4). The achieved bulk sensitivity is 221 nm/RIU with a high signal to noise ratio, and a record-high figure of merit reaches to 4420 RIU−1. This ultracompact and low threshold quasi-BIC laser facilitated by the ultra-narrow resonance can serve as formidable candidate for on-chip gas sensor.

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Acousto-optic modulation of photonic bound state in the continuum

Light Science & Applications ◽

10.1038/s41377-019-0231-1 ◽

2020 ◽

Vol 9 (1) ◽

Cited By ~ 42

Author(s):

Zejie Yu ◽

Xiankai Sun

Keyword(s):

Refractive Index ◽

Integrated Circuits ◽

Acoustic Waves ◽

Bound States ◽

Quantum Information Processing ◽

Modulation Frequency ◽

Surface Acoustic Waves ◽

High Refractive Index ◽

Bound State ◽

The Continuum

AbstractPhotonic bound states in the continuum (BICs) have recently been studied in various systems and have found wide applications in sensors, lasers, and filters. Applying BICs in photonic integrated circuits enables low-loss light guidance and routing in low-refractive-index waveguides on high-refractive-index substrates, which opens a new avenue for integrated photonics with functional single-crystal materials. Here, we demonstrate high-quality integrated lithium niobate microcavities inside which the photonic BIC modes circulate and further modulate these BIC modes acousto-optically by using piezoelectrically actuated surface acoustic waves at microwave frequencies. With a high acousto-optic modulation frequency, the acousto-optic coupling is well situated in the resolved-sideband regime. This leads to coherent coupling between microwave and optical photons, which is exhibited by the observed electro-acousto-optically induced transparency and absorption. Therefore, our devices serve as a paradigm for manipulating and controlling photonic BICs on a chip, which will enable many other applications of photonic BICs in the areas of microwave photonics and quantum information processing.

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Separability of the Planar 1/ρ2 Potential in Multiple Coordinate Systems

Symmetry ◽

10.3390/sym12081312 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1312

Author(s):

Richard DeCosta ◽

Brett Altschul

Keyword(s):

Schrödinger Equation ◽

Coulomb Potential ◽

Schrodinger Equation ◽

Separation Of Variables ◽

Bound State ◽

Three Dimensions ◽

Attractive Potential ◽

Coordinate Systems ◽

Repulsive Potential ◽

Isotropic Harmonic Oscillator

With a number of special Hamiltonians, solutions of the Schrödinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. Multiply separable Hamiltonians exhibit a number of interesting features, including “accidental” degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schrödinger equation is separable in both cylindrical and parabolic coordinates: A z-independent V∝1/ρ2=1/(x2+y2) in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at ρ=0. When separated in parabolic coordinates, the Schrödinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential—one equation with an attractive potential, the other with an equally strong repulsive potential.

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BOUND STATES IN CONTINUUM GENERATED BY POINT INTERACTION AND SUPERSYMMETRIC QUANTUM MECHANICS

Modern Physics Letters B ◽

10.1142/s0217984912501771 ◽

2012 ◽

Vol 26 (27) ◽

pp. 1250177 ◽

Cited By ~ 7

Author(s):

S. Lj. S. KOČINAC ◽

V. MILANOVIĆ

Keyword(s):

Quantum Mechanics ◽

Kinetic Energy ◽

Bound States ◽

Energy Operator ◽

Bound State ◽

Point Interaction ◽

Supersymmetric Quantum Mechanics ◽

Kinetic Energy Operator ◽

Point Interactions ◽

The Continuum

Four-parameter family of point interactions represent all possible self-adjoint extensions of kinetic energy operator. We demonstrate a method for generating a bound state in the continuum of point interactions which relies on supersymmetric quantum mechanics (SUSYQM). Both zero and nonzero transparency cases are considered.

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Coexistence of a new type of bound state in the continuum and a lasing threshold mode induced by PT symmetry

Science Advances ◽

10.1126/sciadv.abc1160 ◽

2020 ◽

Vol 6 (34) ◽

pp. eabc1160

Author(s):

Qianju Song ◽

Jiashun Hu ◽

Shiwei Dai ◽

Chunxiong Zheng ◽

Dezhuan Han ◽

...

Keyword(s):

Bound States ◽

External Source ◽

Bound State ◽

Pt Symmetry ◽

Lasing Threshold ◽

Symmetric Perturbation ◽

New Type ◽

The Rich ◽

Symmetric Systems ◽

The Continuum

Some photonic systems support bound states in the continuum (BICs) that have infinite lifetimes, although their frequencies and momenta are matched to vacuum modes. Using a prototypical system that can be treated analytically, we show that each of these BICs always splits into a pair of new type BIC and lasing threshold mode when a parity-time (PT)–symmetric perturbation is introduced. The radiation loss at the lasing threshold is exactly balanced by the net gain of the particles. These PT symmetry-induced BICs are different from ordinary BICs, as they can be excited by an external source but do not radiate, and they carry a different quality factor divergence rate from that of the ordinary BICs. While most of the attention of PT-symmetric systems is captured by the coalescence of modes at exceptional points, the splitting of ordinary BICs is a new phenomenon that illustrates the rich physics embedded in PT-symmetric systems.

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