Parabolic Confinement Research Articles

Active matter in lateral parabolic confinement: From subdiffusion to superdiffusion

In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement intensity. We argued that the subdiffusion regimes appear as consequence of the restricted space available for diffusion (achieved either through large confinement and/or large noise); we saw that when there are large confinement and noise intensity, a similar configuration to single file diffusion appears; on the other hand, normal and superdiffusive regimes may occur due to low noise (longer persistent motion), either through exploring a wider region around the potential minimum in the transverse direction (low confinement), or by forming independent clusters (high confinement).

Quantum wire and magnetic control of a spin qubit in the Landau–Zener–Stückelberg interferometry transition

Landau–Zener–Stückelberg interferometry is extensively investigated in a 3D heterostructure magnetic quantum wire. Local magnetic fields are used to coherently manipulate and control a qubit’s quantum state. For our numerical calculations, a parabolic confinement is assumed. Energy eigenvalues, non-adiabatic and adiabatic transition probabilities are calculated from the diabatic and adiabatic bases for two-level systems. Here, we show that the spatial crossing between interspin levels becomes a spatial anticrossing if the two spin states are coupled by external fields, and that consequently, due to the spin dependence of the harmonic confinement, it will undergo Landau–Zener–Stückelberg interference. It is shown that the system undergoes nonadiabatic Landau–Zener dynamics for a strong confinement in a strong external field, whereas a weak external field induces adiabatic Landau–Zener transition dynamics. Our system allows the coupling strength between the level states at the anti(crossing) point to be modulated. This system allows one to tune the wire’s parabolic confinement potential using experimentally accessible parameters.

Thermoelectric ionization of, D(-)-centers in a semiconductor quantum wire with a parabolic confinement potential in a strong longitudinal electric field

Conductivity of a semiconductor quantum wire with a parabolic confinement potential was studied within the framework of the zero-range potential model, containing donor impurities, in the longitudinal with respect to its axis electric field at low temperatures. A dispersion equation determining the dependence of the binding energy of the impurity on the electric field strength was obtained. It has been shown that the bound state of an electron on an impurity is destroyed by a strong electric field, i.e. the thermoelectric phenomenon of ionization occurs. It was found that under conditions of low temperatures the dependence of the current density in a quantum wire in the longitudinal electric field has a superlinear character.

Magnetoplasmon modes of a terahertz-laser-driven quantum well wire

A quantum well wire system with lateral parabolic confinement, under an intense terahertz radiation and a uniform quantizing magnetic field is considered. The exact electronic states of the system are determined by constructing unitary transformations. Then, by obtaining the response of the system to a weak probing potential, the dielectric function and the magnetoplasma modes of the system are calculated in the framework of RPA theory. Results indicate roton-like behaviour for the plasmon modes of the system.

Massive Goldstone (Higgs) mode in two-dimensional ultracold atomic lattice systems

We discuss how to reveal the massive Goldstone mode, often referred to as the Higgs amplitude mode, near the Superfluid-to-Insulator quantum critical point (QCP) in a system of two-dimensional ultracold bosonic atoms in optical lattices. The spectral function of the amplitude response is obtained by analytic continuation of the kinetic energy correlation function calculated by Monte Carlo methods. Our results enable a direct comparison with the recent experiment [M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schau{\ss}, C. Gross, E. Demler, S. Kuhr, and I. Bloch, Nature 487, 454-458 (2012)], and demonstrate a good agreement for temperature shifts induced by lattice modulation. Based on our numerical analysis, we formulate the necessary conditions in terms of homogeneity, detuning from the QCP and temperature in order to reveal the massive Goldstone resonance peak in spectral functions experimentally. We also propose to apply a local modulation at the trap center to overcome the inhomogeneous broadening caused by the parabolic trap confinement.

Implementation of Kohn's theorem for the ellipsoidal quantum dot in the presence of external magnetic field

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls in the presence of external magnetic field is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the gas in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. The parabolic confinement potential depends on the geometry of the ellipsoid, which allows, together with the magnetic field to control resonance frequencies of transitions by changing the geometric dimensions of the QD.

Excitonic spectra of wide parabolic quantum wells

The optical properties of wide Quantum Wells are considered, taking into account the screened electron-hole interaction potential and parabolic confinement potentials, different for the electrons and for the holes. The role of the interaction potential which mixes the energy states according to different quantum numbers is stressed. The results obtained by our method are in agreement with the observed spectra and give the possibility to the assessment of the resonances.

Decay of the Kohn mode in hydrodynamic regime

We develop a hydrodynamic description of the collective modes of interacting liquids in a quasi-one-dimensional confining potential. By solving Navier-Stokes equations we determine analytically excitation spectrum of sloshing oscillations. For parabolic confinement, the lowest frequency eigenmode is not renormalized by interactions and is protected from decay by the Kohn theorem, which states that center of mass motion decouples from internal dynamics. We find that the combined effect of potential anharmonicity and interactions results in the depolarization shift and final lifetime of the Kohn mode. All other excited modes of sloshing oscillations thermalize with the parametrically faster rates. Our results are significant for the interpretation of recent experiments with trapped Fermi gases that observed weak violation of the Kohn theorem.

Density-functional-theory approach to the thermodynamics of the harmonically confined one-dimensional Hubbard model

The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic Hubbard model with parabolic confinement is studied by a density-functional theory approach, based on Mermin's generalization to finite temperatures. A local-density approximation (LDA), based on exact results for the homogeneous model, is used to approximate the correlation part in the Helmholtz free-energy, comprising the thermodynamic Bethe ansatz LDA (TBALDA). The general presentation of the method is given and some properties of the homogeneous model that are relevant to the DFT approach are analyzed. Extensive comparison between TBALDA and numerical exact diagonalization results for thermodynamic properties of small inhomogeneous chains is discussed. In the remaining, a classical thermodynamic treatment of the confined system is developed with the focus on global properties of large systems. A unusual behavior under isentropic expansion is found and discussed.

Dimensionality effect on two-electron energy spectrum: A fractional-dimension-based formulation

We analyze the spectrum of two-electron quantum dot with anisotropic parabolic confinement by using the fractional-dimension formulation which allows us to reduce the two-particle problem to two equations for independent particles in an effective space with variable dimension, ranging between two and three for ellipsoidal-shaped quantum dots and between one and two for elliptical-shaped quantum disks. The dependencies of energy levels on the heterostructure sizes for quantum dots, disks and wires are presented.

Molecule-induced quantum confinement in single-walled carbon nanotube

A method of fabricating quantum-confined structures with single-walled carbon nanotubes (SWNTs) has been developed. Scanning tunneling spectroscopy revealed that a parabolic confinement potential appeared when collagen model peptides were attached to both ends of an individual SWNT via the formation of carboxylic anhydrides. On the other hand, the confinement potential was markedly changed by yielding the peptide bonds between the SWNT and the collagen model peptides. Photoluminescence spectroscopy measurements showed that a type-II quantum dot was produced in the obtained heterostructure.

Two-electron impurity in the parabolic quantum dot: Uncertainty relation and perturbation approach

Two-electron impurity states in parabolic confinement have been investigated. We have estimated the ground-state energy value, using the Heisenberg uncertainty relation. Using variational methods the ground state energy and wave function of the single-electron impurity problem have been achieved. The dependence of ground-state energy and Coulomb electron–electron interaction energy correction on the QD size is studied. The dependence of the state exchange time on the QD radius has been calculated. It has been shown that the presence of the impurity leads to the appearance of negative values of the energy of the system on the one hand, and to the saturating character of the state exchange time.

Nonlinear optical rectification of hydrogenic impurity in a disk-like parabolic quantum dot: The role of applied magnetic field

We report a detailed theoretical study of the effect of combined electric and magnetic field on the nonlinear optical rectification of a hydrogenic impurity, confined in a two dimensional disk-like quantum dot, with parabolic confinement potential. We use the compact density matrix formalism and iterative method to obtain nonlinear optical rectification and absorption coefficients. To find energy levels and wave functions, we employ exact diagonalization method in the effective mass approximation. As main result, we found that the transition energy from ground to first excited state redshifts with increasing the magnetic field while blueshifts for transition from ground to second excited state, moreover, for former transition, nonlinear optical rectification coefficient decreases with increasing magnetic field in contrast to that occurs for latter one.

The low-lying states and optical absorption properties of a hydrogenic impurity in a parabolic quantum dot modulation by applied electric field

Using the configuration-integration method, we investigated theoretically the low-lying states and optical absorption properties of a hydrogenic impurity in a parabolic quantum dot modulation by applied electric field. The low-lying states and optical absorption properties depend sensitively on the electric field F and the strength of the parabolic confinement ℏω0. We discuss the linear and third-order nonlinear optical absorption coefficients of the dot (i) with the impurity ion and (ii) without the impurity ion. In the first case, the increase of the parabolic confinement ℏω0 (or the electric field F) can induce the blueshift (or redshift) of the peak of the absorption coefficient. Also the optical intensity can induce the increase of the third-order nonlinear optical absorption coefficients to weaken and even bleach the total optical absorption coefficients. Similar behavior has also been observed in the second case, but there is no redshift of the peak positions of the absorption coefficient with the increase of the electric field F. Compared with the second case, it is easily seen that there are the blueshifts of the peak of the absorption coefficients, which can be used as a technical means for detecting impurities.

Impurity Binding Energyin Quantum Dots with Parabolic Confinement in the Presence of Electric Field

We present an efficient method for calculation of the impurity binding energy in a quantum dot with parabolic confinement in the presence of the electric field. The unknown wave function is expanded into a basis of one-dimensional harmonic oscillator states describing the electron's movement perpendicular to the plane of quantum well. Green's function technique used to calculate the coefficients of the expansion. Binding energy of impurity states is defined as poles of the wave function. Developed method applied to calculation of impurity binding energy for different position of impurity and the intensity of electric field.

Effect of geometry and composition on the intraband transitions of holes in quantum dots

The effect of shape and size anisotropy on unipolar intraband transitions of holes in quantum dots (QDs) is studied. The optical matrix elements are calculated for transitions of holes in valence band. To get the optical matrix elements, energy eigenvalues and eigenvectors are calculated using 4 × 4 Luttinger Hamiltonian in the effective mass approximation. The formulation is applied to InGaAs/GaAs QD with parabolic confinement potential in xy-plane. The optical matrix elements for intraband hole transitions are calculated for x and y polarised light. The transitions are considered from ground state to other excited states. The effect of In concentration on optical matrix elements is also investigated. It is important to note that the transitions of holes are governed by the character of initial and final states for different light polarisations that give specific transition selection rules. It is found that the polarisation is strongly dependent on the in-plane anisotropy of the QDs.

Impurity binding energies in quantum dots with parabolic confinement

We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.

Exciton related optical absorption in a spherical quantum dot

An exciton in a spherical quantum dot is studied analytically within the effective mass approximation. A parabolic confinement under an electric field is considered. The linear and nonlinear optical absorption coefficients are calculated within the density matrix formalism. No assumptions are made about the strength of the confinement. It is shown how the competing mechanisms of the Coulomb interaction, the confinement and the applied static electric field affect the optical absorption.

Optical rectification and third harmonic generation of spherical quantum dots: Controlling via external factors

In this paper simultaneous effects of pressure, temperature, external electric field and laser radiation on the optical rectification and third harmonic generation of a spherical quantum dot with parabolic confinement and dressed impurity are studied. By means of matrix diagonalization technique, energy eigenvalues and functions are evaluated and used to find the optical rectification coefficient and third harmonic generation of the system via density operator method. It is shown that these nonlinear optical quantities strongly depend on pressure, temperature, electric field, confinement frequency and dressing laser intensity. Obvious effects of these external factors propose new facilities with different effects to control nonlinear optical properties of such systems.

Optical properties of parabolic quantum dots with dressed impurity: Combined effects of pressure, temperature and laser intensity

In this paper simultaneous effects of pressure, temperature and laser radiation on the optical absorption coefficient and refractive index of a spherical quantum dot with parabolic confinement and dressed impurity are studied. By means of matrix diagonalization technique, energy eigenvalues and functions are evaluated and used to find the optical properties of the system via density operator method. It is shown that linear and nonlinear optical properties strongly depend on pressure, temperature and dressing laser intensity. The interesting point is that the influence of laser radiation depends on pressure and temperature.