Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.30245

Topological control of third-harmonic generation in a mesoscopic quantum ring with spiral dislocation

Carlos Magno O. Pereira, Denise Assafrão, Edilberto O. Silva

cond-mat.mes-hallquant-phSubmitted Jun 29, 2026• Announced Jun 30, 2026
arXivHTMLPDF

Abstract

We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schrödinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule $Δm=\pm 1$ and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on $β$ and $B$, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.

Comments
14 pages, 12 figures, 1 table. Comments are welcome

Related papers

Torsion-induced confinement and tunable nonlinear optical gain in a mesoscopic electron system

Carlos Magno O. Pereira, Edilberto O Silva

We investigate the optical response of a conduction electron in a helically twisted mesoscopic medium containing a screw dislocation and a uniform torsional background, in the presence of an axial magnetic field and an Aharonov--Bohm flux. We show that the coupling between longitudinal motion and the geometric background produces an effective in-plane confinement, allowing bound states to emerge without the need for an external radial potential. Exact analytical solutions are obtained for the energy spectrum and radial wave functions, and these results are used to evaluate linear and third-order nonlinear absorption, changes in the refractive index, the photoionization cross section, and the oscillator strength. The combined action of torsion, magnetic field, and topological defect increases the interlevel spacing, compresses the radial electronic distribution, and breaks the dynamical symmetry between opposite angular-momentum channels, leading to strongly asymmetric and state-resolved optical spectra. Under intense optical excitation, the nonlinear contribution can overcome linear absorption, driving the system into a negative-absorption regime and enabling geometry-controlled optical gain. These results establish torsion and defect engineering as effective tools for tuning confinement, resonant energies, and selective amplification in mesoscopic nanophotonic platforms operating in the mid-infrared and terahertz ranges.

cond-mat.mes-hallCross-listedarXiv:2604.12664•Apr 15, 2026

Screw-dislocation-engineered quantum dot: geometry-tunable nonlinear optics, orbital qubit addressability, and torsion metrology

Edilberto O. Silva

We study a single electron confined in a uniform-torsion medium, a continuum model of a screw dislocation density, in a perpendicular magnetic field, and in the presence of an Aharonov--Bohm flux. Torsion alone produces radial confinement without any \textit{ad hoc} potential, while the Aharonov--Bohm phase breaks the usual $m\leftrightarrow -m$ symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from $\sim 6.8$ to $\sim 15.5$~meV and whose saturation intensity varies by an order of magnitude, enabling geometry-programmable optical switching; (ii) an Aharonov--Bohm-tunable ``angular pseudospin'' formed by the $m=\pm1$ states, with flux-controlled level splitting and asymmetric oscillator strengths that allow selective optical addressability; and (iii) an approximately linear torsion dependence of the transition energy that enables nanoscale torsion metrology with an estimated resolution of $\sim 10^{5}~\mathrm{m}^{-1}$. In this context, ``torsion'' refers to the experimentally relevant continuum limit of a uniform density of parallel screw dislocations, i.e., a crystal with finite torsion but vanishing curvature, which can, in practice, be engineered and probed in twisted nanowires and strained semiconductor heterostructures. We also show how torsion provides \textit{in situ} control of emitter--cavity detuning and light--matter coupling in cavity QED, in direct analogy with strain tuning of semiconductor quantum dots in nanocavities, but here arising from a purely geometric/topological parameter.

cond-mat.mes-hallCross-listedarXiv:2511.13920•Nov 19, 2025

Second-Harmonic and Third-Harmonic Generation in Nanostructures with Asymmetric Confinement Potential: The Role of Two-level Atom Approximation

Dairo A. Causil, M. P. Urango Baquero, Alfonso A. Portacio

The second harmonic generation (SHG) and third harmonic generation (THG) into a cylindrical quantum dot (CQD) with asymmetric confinement potential is studied theoretically within the framework the two-level atom approximation, by using the matrix density formalism. The energy levels and waves functions of an electron into CQD they were obtained by solving the time-independent Schrodinger equation. The numerical calculations make for a CQD of GaAs/GaAlAs. It was found that the increase in the confinement of the charge carriers produced by the increase of the magnetic field and/or the dimensions of the nanostructure generates a shift to blue in the transition energies of the electrons. Also a multiple resonances in the two-level atom approximation was found. These were associated with transition between excited state and ground state and a second transition getting a change permanent dipole moment.For the English version of the abstract, please be careful with the language.

Revista cubana de física•Dec 15, 2018•0 citations

Mechanisms and modulation of third-order nonlinear optical responses in spherical quantum dots confined by a Mie-type potential

Yue Wu, Xuechao Li

Abstract This paper systematically explores the third-order nonlinear optical properties and modulation mechanisms of a spherical quantum dot system confined by a Mie-type potential. We analytically solve the Schrödinger equation with Nikiforov–Uvarov method based on effective mass approximation to obtain the eigenenergies and wave function of the system. Subsequently, key third-order nonlinear optical parameters, including the third-harmonic generation (THG) coefficient, total optical absorption coefficients, and refractive index changes, are derived via the density matrix formalism. The results indicate that the nonlinear optical responses strongly depend on the geometric dimensions and the microscopic confinement parameters. By adjusting these parameters, effective control over the THG coefficient can be achieved. Furthermore, this study reveals the significant modulation effects of environmental factors. The synergistic influence of quantum dot size, confinement potential, and environmental interactions is systematically analyzed, providing a theoretical basis for designing high-performance nonlinear optical devices based on quantum dots.

Communications in Theoretical Physics•Jul 7, 2026•0 citations

Numerical study of non-relativistic quantum systems and small oscillations induced in a helically twisted geometry

C. F. S. Pereira, R. L. L. Vitória, A. R. Soares +3 more

We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by the Schrödinger equation on a curved spatial background and, when included, by minimal coupling to a magnetic vector potential incorporating an Aharonov--Bohm flux. After separation of variables, the problem reduces to a one-dimensional radial eigenvalue equation governed by an effective potential that combines torsion-induced Coulomb-like and centrifugal-like structures with magnetic/flux-dependent terms and optional model interactions. Because closed-form analytic solutions are not reliable over the parameter ranges required for systematic scans, we compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem and solving it with a finite-difference discretization on a truncated radial domain, with explicit convergence control. We analyze four representative scenarios: (i) no external potential, (ii) Cornell-type confinement, (iii) Kratzer-type interaction, and (iv) the small-oscillation regime around the minimum of a Morse potential. We present systematic trends of the low-lying levels as functions of the torsion parameter, magnetic field, and azimuthal sector, and we show that geometric couplings alone can produce effective confinement even in the absence of an external interaction.

quant-pharXiv:2602.16693•Feb 19, 2026

Third-harmonic generation in cylindrical parabolic quantum wires with an applied electric field

Guanghui Wang

The third-harmonic generation (THG) in $\mathrm{GaAs}∕\mathrm{AlGaAs}$ cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over ${10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}$ can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.

Physical Review B•Oct 27, 2005•129 citations
We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schrödinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule Δm=±1Δm=\pm 1Δm=±1 and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on βββ and BBB, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.
We investigate the optical response of a conduction electron in a helically twisted mesoscopic medium containing a screw dislocation and a uniform torsional background, in the presence of an axial magnetic field and an Aharonov--Bohm flux. We show that the coupling between longitudinal motion and the geometric background produces an effective in-plane confinement, allowing bound states to emerge without the need for an external radial potential. Exact analytical solutions are obtained for the energy spectrum and radial wave functions, and these results are used to evaluate linear and third-order nonlinear absorption, changes in the refractive index, the photoionization cross section, and the oscillator strength. The combined action of torsion, magnetic field, and topological defect increases the interlevel spacing, compresses the radial electronic distribution, and breaks the dynamical symmetry between opposite angular-momentum channels, leading to strongly asymmetric and state-resolved optical spectra. Under intense optical excitation, the nonlinear contribution can overcome linear absorption, driving the system into a negative-absorption regime and enabling geometry-controlled optical gain. These results establish torsion and defect engineering as effective tools for tuning confinement, resonant energies, and selective amplification in mesoscopic nanophotonic platforms operating in the mid-infrared and terahertz ranges.
We study a single electron confined in a uniform-torsion medium, a continuum model of a screw dislocation density, in a perpendicular magnetic field, and in the presence of an Aharonov--Bohm flux. Torsion alone produces radial confinement without any \textit{ad hoc} potential, while the Aharonov--Bohm phase breaks the usual m↔−mm\leftrightarrow -mm↔−m symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from ∼6.8\sim 6.8∼6.8 to ∼15.5\sim 15.5∼15.5~meV and whose saturation intensity varies by an order of magnitude, enabling geometry-programmable optical switching; (ii) an Aharonov--Bohm-tunable ``angular pseudospin'' formed by the m=±1m=\pm1m=±1 states, with flux-controlled level splitting and asymmetric oscillator strengths that allow selective optical addressability; and (iii) an approximately linear torsion dependence of the transition energy that enables nanoscale torsion metrology with an estimated resolution of ∼105 m−1\sim 10^{5}~\mathrm{m}^{-1}∼105 m−1. In this context, ``torsion'' refers to the experimentally relevant continuum limit of a uniform density of parallel screw dislocations, i.e., a crystal with finite torsion but vanishing curvature, which can, in practice, be engineered and probed in twisted nanowires and strained semiconductor heterostructures. We also show how torsion provides \textit{in situ} control of emitter--cavity detuning and light--matter coupling in cavity QED, in direct analogy with strain tuning of semiconductor quantum dots in nanocavities, but here arising from a purely geometric/topological parameter.
The second harmonic generation (SHG) and third harmonic generation (THG) into a cylindrical quantum dot (CQD) with asymmetric confinement potential is studied theoretically within the framework the two-level atom approximation, by using the matrix density formalism. The energy levels and waves functions of an electron into CQD they were obtained by solving the time-independent Schrodinger equation. The numerical calculations make for a CQD of GaAs/GaAlAs. It was found that the increase in the confinement of the charge carriers produced by the increase of the magnetic field and/or the dimensions of the nanostructure generates a shift to blue in the transition energies of the electrons. Also a multiple resonances in the two-level atom approximation was found. These were associated with transition between excited state and ground state and a second transition getting a change permanent dipole moment.For the English version of the abstract, please be careful with the language.
Abstract This paper systematically explores the third-order nonlinear optical properties and modulation mechanisms of a spherical quantum dot system confined by a Mie-type potential. We analytically solve the Schrödinger equation with Nikiforov–Uvarov method based on effective mass approximation to obtain the eigenenergies and wave function of the system. Subsequently, key third-order nonlinear optical parameters, including the third-harmonic generation (THG) coefficient, total optical absorption coefficients, and refractive index changes, are derived via the density matrix formalism. The results indicate that the nonlinear optical responses strongly depend on the geometric dimensions and the microscopic confinement parameters. By adjusting these parameters, effective control over the THG coefficient can be achieved. Furthermore, this study reveals the significant modulation effects of environmental factors. The synergistic influence of quantum dot size, confinement potential, and environmental interactions is systematically analyzed, providing a theoretical basis for designing high-performance nonlinear optical devices based on quantum dots.
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by the Schrödinger equation on a curved spatial background and, when included, by minimal coupling to a magnetic vector potential incorporating an Aharonov--Bohm flux. After separation of variables, the problem reduces to a one-dimensional radial eigenvalue equation governed by an effective potential that combines torsion-induced Coulomb-like and centrifugal-like structures with magnetic/flux-dependent terms and optional model interactions. Because closed-form analytic solutions are not reliable over the parameter ranges required for systematic scans, we compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem and solving it with a finite-difference discretization on a truncated radial domain, with explicit convergence control. We analyze four representative scenarios: (i) no external potential, (ii) Cornell-type confinement, (iii) Kratzer-type interaction, and (iv) the small-oscillation regime around the minimum of a Morse potential. We present systematic trends of the low-lying levels as functions of the torsion parameter, magnetic field, and azimuthal sector, and we show that geometric couplings alone can produce effective confinement even in the absence of an external interaction.
The third-harmonic generation (THG) in GaAs∕AlGaAs\mathrm{GaAs}∕\mathrm{AlGaAs}GaAs∕AlGaAs cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over ${10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}$ can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.