Search Results (112)

We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality at which Ehrenfest atomic instability emerges, where the Schrödinger equation describing the wavefunction of a single electron orbiting around an atom becomes scale-free, and discuss the potential of observing this phenomena in laboratory settings. We then study the Rydberg states of stable atoms using the Wentzel–Kramers–Brillouin approximation, along with a proposed extension for the Langer modification, in general fractal dimensionalities. We show that fractal space atoms near instability explode in size even at low-number excited state, making them highly suitable to induce strong entanglements and foster long-range many-body interactions. We argue that atomic physics in fractal spaces—“fractatomic physics”—is a rich research avenue deserving of further theoretical and experimental investigations. Full article

We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the transverse direction relative to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed for parallel emission, we deduce analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interhalf- and intrahalfcycle interference contributions, the latter modulating the intercycle pattern responsible for sideband formation. We identify the intrahalfcycle interference arising from trajectories released within the same half cycle as the mechanism governing attosecond phase delays in the perpendicular geometry. Our results reveal the suppression of even-order sidebands due to destructive interhalfcycle interference, leading to a characteristic spacing between adjacent peaks that doubles the standard spacing observed along the polarization axis. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation confirm the accuracy of the semiclassical description. This work provides a unified framework for understanding quantum interferences in attosecond chronoscopy, bridging the cases of parallel and perpendicular electron emission in RABBIT-like protocols. Full article

This study presents a comprehensive numerical investigation of excitonic states in GaAs quantum wells embedded in ${\mathrm{Al}}_x$${\mathrm{Ga}}_{1-x}$As barriers, incorporating the effects of donor and acceptor impurities, external electric and magnetic fields, and varying well widths. The electron and hole wavefunctions are computed by directly solving the Schrödinger equation using the finite element method in cylindrical coordinates, without assuming trial forms. To evaluate the exciton binding energy, the implementation and comparison of two independent approaches were performed: a numerical integration method based on elliptic function corrections, and a novel finite element electrostatic formulation using COMSOL Multiphysics v5.6. The latter computes the Coulomb interaction by solving Poisson’s equation with the hole charge distribution and integrating the resulting potential over the electron density. Both methods agree within 1% and capture the spatial and field-induced modifications in excitonic properties. The results show that quantum confinement enhances binding in narrow wells, while donor impurities and electric fields reduce binding via spatial separation of carriers. Magnetic fields counteract this effect by providing radial confinement. The FEM-based electrostatic method demonstrates high spatial accuracy, computational efficiency, and flexibility for complex heterostructures, making it a promising tool for exciton modeling in low-dimensional systems. Full article

In this work, a theoretical study on the combined effects of an external electric field and a nonresonant intense laser field on the electronic properties of a quantum dot with a truncated cone shape is presented. This quantum dot was made from a type-II CdTe/CdSe heterostructure (core/shell). Using the effective mass approximation with parabolic bands and the finite element method, the Schrödinger equation was solved to analyze the confined states of electron, hole, and exciton. This study demonstrates the potential of combining nonresonant intense laser and electric fields to control confinement properties in semiconductor nanodevices, with potential applications in optoelectronics and quantum mechanics-related technologies. Full article

This is a numerical investigation of optical and electronic characteristics of GaAs spherical quantum dots based on single and double quartic potentials and presenting a hydrogenic impurity at their center. The radial Schrödinger equation was solved using the finite difference method (FDM) to obtain the energy levels and the wavefunctions. These physical quantities were then used to compute the dipole matrix elements, the total optical absorption coefficient (TOAC), and the binding energies. The impact of the structural parameters in the confining potentials on the red and blue shifts of the TOAC is discussed in the presence and absence of hydrogenic impurity. Our results indicate that the structural parameter $k$ in both potentials plays a crucial role in tuning the TOAC. In the case of single quartic potential, increasing $k$ produces a blue shift; however, its augmentation in the case of double quartic potential displays a blue shift at first, and then a red shift. Furthermore, the augmentation of the parameter $k$ can control the binding energies of the two lowest states, ($1s$) and ($1p$). In fact, enlarging this parameter reduces the binding energies and converges them to constant values. In general, the modification of the potential’s parameters, which can engender two shapes of confining potentials (single quartic and double quartic), enables the experimenters to control the desired energy levels and consequently to adjust and select the suitable TOAC between the two lowest energy states (ground ($1s$) and first excited ($1p$)). Full article

The current study presents the results of a methodical investigation into the ionization of rare gas atoms, specifically focusing on argon. In this study, two configurations are examined: ionization via a near-infrared (NIR) laser field alone, and ionization caused by extreme ultraviolet (XUV) radiation in the presence of a strong, synchronized NIR pulse. The theoretical investigation is conducted using an ab initio method to solve the time-dependent Schrödinger equation within the single active electron (SAE) approximation. The simulation results show a sequence of above-threshold ionization (ATI) peaks that shift to lower energies with increasing laser intensity. This behavior reflects the onset of the Stark effect, which modifies atomic energy levels and increases the number of photons required for ionization. An examination of the two-color photoionization spectrum, which includes sideband structures and harmonic peaks, shows how the ionization probability is redistributed between the direct path (single XUV photon absorption) and sideband pathways (XUV ± n × IR) as the intensity of the infrared field increases. Quantum interference between continuum states is further revealed by the photoelectron angular distribution, clearly indicating the control of ionization dynamics by the IR field. Full article

External fields modify the confinement potential and electronic structure in a multiple quantum well system, affecting the light–matter interaction. Here, we present a theoretical study of the modulation of the nonlinear optical response simultaneously employing an intense non-resonant laser field and an electric field. Considering four occupied subbands, we focus on a GaAs/AlGaAs symmetric multiple quantum well system with five wells and six barriers. By solving the Schrödinger equation through the finite element method under the effective mass approximation, we determine the electronic structure and the nonlinear optical response using the density matrix formalism. The laser field dresses the confinement potential while the electric field breaks the inversion symmetry. The combined effect of both fields modifies the intersubband transition energies and the overlap of the wave functions. The results obtained demonstrate an active tunability of the nonlinear optical response, opening up the possibility of designing optoelectronic devices with tunable optical properties. Full article

We discuss an extension of the Single-Active-Electron (SAE) approximation in atoms by allowing the model potential to depend on the angular-momentum quantum number ℓ. We refer to this extension as the ℓ-SAE approximation. The main ideas behind ℓ-SAE are illustrated using the helium atom as a benchmark system. We show that introducing ℓ-dependent potentials improves the accuracy of key quantities in atomic structure computed from the Time-Independent Schrödinger Equation (TISE), including energies, oscillator strengths, and static and dynamic polarizabilities, compared to the standard SAE approach. Additionally, we demonstrate that the ℓ-SAE approximation is suitable for quantum simulations of light−atom interactions described by the Time-Dependent Schrödinger Equation (TDSE). As an illustration, we simulate High-order Harmonic Generation (HHG) and the three-sideband (3SB) version of the Reconstruction of Attosecond Beating by Interference of Two-photon Transitions (RABBITT) technique, achieving enhanced accuracy comparable to that obtained in all-electron calculations. One of the main advantages of the ℓ-SAE approach is that existing SAE codes can be easily adapted to handle ℓ-dependent potentials without any additional computational cost. Full article

This study presents the synthesis of manganese molybdenum tetraoxide (MnMoO₄)-based nanoparticles and then their experimental demonstration as saturable absorbers (SAs) in erbium-doped fiber lasers (EDFLs). The MnMoO₄ nanoparticles were prepared and then embedded between the fiber ferrule to act as an SA to generate Q-switched pulsed operation in EDFLs. For the characterization, scanning electron microscopy (SEM) was employed to confirm the particle size of the prepared MnMoO₄ nanoparticles, and the SA optical properties were further investigated by measuring their modulation depth and saturation intensity. By implementing the prepared SA within the cavity, the measured results revealed that under pump power ranging from 28 to 312.5 mW, the laser exhibited Q-switched pulse durations varying from 15.22 to 2.35 µs and repetition rates spanning from 24.98 to 88.11 kHz. The proposed EDFL system delivered an average output power between 0.128 and 2.95 mW, pulse energies ranging from 5.12 to 33.49 nJ, and peak power from 0.281 to 6.26 mW. The laser stability was also confirmed by continuously noticing the pulse duration, emission wavelengths, and pulse repetition rates for 4 h. Finally, a numerical model based on a nonlinear Schrödinger equation (NLSE) was employed to validate both experimental and theoretical results of the passive Q-switched EDFL. These findings highlight the potential of EDFLs utilizing MnMoO₄-based SAs for potential applications in pulsed laser sources. Full article

It is experimentally established that there is no ground triplet state of the natural $He$ atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot in a magnetic field, as described by the Schrödinger–Pauli equation, we provide theoretical proof of the existence of a ground triplet state by deriving an exact analytical correlated wave function solution to the equation. The state exists in the Wigner high-electron-correlation regime. We further explain that the solution satisfies all requisite symmetry and electron coalescence constraints of a triplet state. Since, due to technological advances, such a Wigner crystal quantum dot can be created, we propose an experimental search for the theoretically predicted ground triplet-state spectral line. We note that there exists an analytical solution to the Schrödinger–Pauli equation for a ground singlet state in the Wigner regime for the same value of the magnetic field. The significance to quantum mechanics of the probable experimental observation of the ground triplet state for an ‘artificial atom’ is discussed. Full article

Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for various geometries of the target molecule, three-dimensional vibrational states of HDO, and the vibrational frame transformation. The vibrational states of the molecule are evaluated by solving the Schrödinger equation numerically, without relying on the normal-mode approximation, which is known to be inaccurate for water molecules. As a result, couplings and transitions between the vibrational states of HDO are accurately accounted for. From the calculated cross sections, thermally averaged rate coefficients and their analytical fits are provided. Significant differences between the results for HDO and H₂O are observed. Additionally, an uncertainty assessment of the obtained data is performed for potential use in modeling non-local thermodynamic equilibrium (non-LTE) spectra of water in various astrophysical environments. Full article

Including an n-doped layer in asymmetric double quantum wells restricts confined carriers into V-shaped potential profiles, forming discrete conduction subbands and enabling intersubband transitions. Most studies on doped semiconductor heterostructures focus on how external fields and structural parameters dictate optical absorption. However, electromagnetically induced transparency remains largely unexplored. Here, we show that the effect of an n-doped layer GaAs/Al_xGa_1−xAs in an asymmetric double quantum well system is quite sensitive to the width and position of the doped layer. By self-consistently solving the Poisson and Schrödinger’s equations, we determine the electronic structure using the finite element method within the effective mass approximation. We found that the characteristics of the n-doped layer can modulate the resonance frequencies involved in the electromagnetically induced transparency phenomenon. Our results demonstrate that an n-doped layer can control the electromagnetically induced transparency effect, potentially enhancing its applications in optoelectronic devices. Full article

We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential operators of the first and second order. We show how to build a Hilbert basis for this space. We study these first- and second-order partial derivation non-self-adjoint operators defined on this space, showing that these operators are defined on dense subspaces of the initial space of smooth curves; we determine their respective adjoints, compute their respective commutators, determine their eigenvalues and, under some normalisation conditions on the eigenvectors, we present examples of a discrete set of eigenvalues. Using these derivation operators, we study a Schrödinger-type equation, building particular solutions given by their representation as smooth curves on the Segal–Bergmann space, and we show the existence of general solutions using an Fourier–Hilbert base of the space of smooth curves. We point out the existence of self-adjoint operators in the space of smooth curves that are obtained by the composition of the partial derivation operators with multiplication operators, showing that these operators admit simple sequences of eigenvalues and eigenvectors. We present two applications of the Schrödinger-type equation studied. In the first one, we consider a wave associated with an object having the mass of an electron, showing that two waves, when considered as having only a free real space variable, are entangled, in the sense that the probability densities in the real variable are almost perfectly correlated. In the second application, after postulating that a usual package of information may have a mass of the order of magnitude of the neutron’s mass attributed to it—and so well into the domain of possible quantisation—we explore some consequences of the model. Full article

We study systems of two and three electrons confined to circular rings. The electrons are considered spinless, and we assume that one electron occupies a single ring. We use the framework of such a model to calculate the linear entropy and, thus, the spatial entanglement between the confined electrons. The geometry of the problem for the case of two electrons incorporates situations in which the planes of the two rings form an arbitrary angle with each other. The resulting Schrödinger’s equation is solved numerically with very high accuracy by means of the exact diagonalization method. We compute the ground state energy and entanglement for all configurations under consideration. We also study the case of three electrons confined to identical, parallel and concentric rings which are located in three different equidistant planes. The vertically separated system of rings is allowed to gradually merge into a single ring geometry, which would represent the equivalent system of a ring with three electrons. It is observed that the system of three electrons gives rise to a richer structure, as the three rings merge into a single one. Full article

This study presents a theoretical investigation into the photovoltaic efficiency of InGaN/GaN quantum well-based intermediate band solar cells (IBSCs) under the simultaneous influence of electric and magnetic fields. The finite element method is employed to numerically solve the one-dimensional Schrödinger equation within the framework of the effective-mass approximation. Our findings reveal that electric and magnetic fields significantly influence the energy levels of electrons and holes, optical transition energies, open-circuit voltages, short-circuit currents, and overall photovoltaic conversion performances of IBSCs. Furthermore, this research indicates that applying a magnetic field positively influences conversion efficiency. Through the optimization of IBSC parameters, an efficiency of approximately 50% is achievable, surpassing the conventional Shockley–Queisser limit. This theoretical study demonstrates the potential for next-generation photovoltaic technology advancements. Full article