Smearing of Observables and Spectral Measures on Quantum Structures

An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure.     

Tunneling time in space fractional quantum mechanics

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.     

Quantum Discord for a Central Two-Qubit System Coupled to an XY Spin Chain with Energy Current

We investigate the quantum discord dynamics of a two-qubit system coupled to an XY spin-chain environment with energy current. We compared dynamical behaviors of quantum discord under different system-environment couplings, the size of the degrees of freedom of the environment, the anisotropy parameter, and the energy current. The results indicate that the energy current can strongly suppress the quantum discord in the weak-coupling region, while it has no obvious effect on the quantum discord in the strong-coupling regime.     

Superconducting proximity effect in interacting quantum dots revealed by shot noise

We study the full counting statistics of charge transport through a quantum dot tunnel coupled to one normal and one superconducting lead with a large superconducting gap. As a function of the level detuning, there is a crossover from a regime with strong superconducting correlations in the quantum dot to a regime in which the proximity effect on the quantum dot is suppressed. We analyze the current fluctuations of this crossover in the shot-noise regime. In particular, we predict that the full counting statistics changes from Poissonian with charge 2e, typical for Cooper pairs, to Poissonian with charge e, when the superconducting proximity effect is present. Thus, the onset of the superconducting proximity effect is revealed by the reduction of the Fano factor from 2 to 1.     

Substitutional impurity in the graphene quantum dots

The process of formation of the localized defect states due to substitutional impurity in sp²-bonded graphene quantum dot is considered using a simple tight-binding-type calculation. We took into account the interaction of the quantum dot atoms surrounding the substitutional impurity from the second row of elements. To saturate the external dangling sp² orbitals of the carbon additionally 18 hydrogen atoms were introduced. The chemical formula of the quantum dot is H₁₈C₅₁X, where X is the symbol of substitutional atom. The position of the localized levels is determined relative to the host-atoms (C) ε_p energies. We focused on the effect of substitutional doping by the B, N and O on the eigenstate energies and on the total energy change of the graphene dots including for O the effect of lattice distorsion. We conclude that B, N, and O can form stable substitutional defects in graphene quantum dot.     

Quantum Coherence and Correlation in Spin Models with Dzyaloshinskii-Moriya Interaction

We study quantum coherence and quantum correlation for detecting quantum phase transition (QPT) by means of quantum renormalization group (QRG) in various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including XXZ model with DM interaction, Ising model with DM interaction and XY model with DM interaction. It is found that through enough QRG iterations, l ₁ norm quantum coherence and one-norm geometric quantum discord can effectively characterize QPT. We also discuss the effect of DM interaction and anisotropy on quantum coherence and quantum correlation.     

Quantum size effects of CO reactivity on metallic quantum dots

We study the reactivity of a metallic quantum dot when exposed to a gas phase CO molecule. First, we perform a Newns-Anderson model calculation in which the valence electrons of the quantum dot are confined by a finite potential well and the molecule is characterized by its lowest unoccupied molecular orbital in the gas phase. A pronounced quantum size effect regarding the charge transfer between the quantum dot and molecule is observed. We then perform a first-principles calculation for a selected size interval. The quantum dot is described within the jellium model and the molecule by pseudopotentials. Our results show that the charge transfer between the quantum dot and the molecule depends critically on the size of the quantum dot, and that this dependence is intimately connected with the electronic structure. The key factor for charge transfer is the presence of states with the symmetry of the chemically active molecular orbital at the Fermi level.     

Effect of interface roughness on the density of states of finite barrier height quantum wells

We calculate the density of states of a 2D electron gas in finite barrier height quantum wells with the explicit inclusion of the interface roughness effect. By using Feynman path-integral method, the analytic expression is derived. The results show that the 2D density of states is dependent on the RMS of the fluctuation potential. The interface roughness causes localized states below the subband edge. We also apply the theory to model the finite barrier height quantum wells in Al_xGa_1?xAs/GaAs.     

Fractional Quantum Hall Effect in SiGe/Si/SiGe Quantum Wells in Weak Quantizing Magnetic Fields

We have experimentally studied the fractional quantum Hall effect in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few XX. Minima of the longitudinal resistance have been observed corresponding to the quantum Hall effect of composite fermions with quantum numbers p = 1, 2, 3, and 4. Minima with p = 3 disappear in magnetic fields below 7 T, which may be a consequence of the intersection or even merging of the quantum levels of the composite fermions with different orientations of the pseudo-spin, i.e., those belonging to different valleys. We have also observed minima of the longitudinal resistance at filling factors ν = 4/5 and 4/11, which may be due to the formation of the second generation of the composite fermions.     

Dielectric mismatch effect on the photoionization cross section and intersublevel transitions in GaAs nanodots

A theoretical study of the electronic states in a spherical quantum dot with and without a hydrogenic impurity is performed within the effective mass approximation taking into account the dielectric mismatch effect. By considering the joint action of the quantum confinement and polarization charges, the photoionization cross section for an on-center donor and intersublevel optical absorption are investigated. We found that: i) the subband energies increase while the 1s and 2p impurity levels decrease when the dielectric mismatch between the dot and its environment enhances; ii) the dielectric mismatch has a significant effect on the peak position and magnitude of the photoionization cross section so that the behavior of this quantity can indicate the material in contact with the nanostructure; iii) the absorption spectrum is less sensitive to the environment dielectric properties but it significantly depends on the dot radius as well as on the impurity presence. The possibility of tuning the resonant energies by using the combined effect of the quantum confinement and dielectric mismatch between the dot and the surrounding medium can be useful in designing new optoelectronic devices.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

InAs quantum dot field effect transistors

We have studied single electron and hole storage in self-assembled InAs quantum dots (QDs) embedded in GaAs/n-AlGaAs field effect transistors (QD-FETs). We prepared two types of QD-FETs. A single electron and a photo-generated single hole can be stored in each QD in Type 1. In the new Type II, single-electron discharge processes can be controlled by a surface gate voltage (V_g) as well as single-electron storage processes. We demonstrate possible application to novel photo devices and quantum dot memory devices.     

Quantum to classical transition in the ground state of a spin-S quantum antiferromagnet

We study a frustrated spin-S staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the emergence of classical magnetic order from the quantum mechanical (staggered-dimer singlet) ground state for increasing S. Using triplon analysis, we find the critical couplings for this quantum phase transition to scale as 1 /S(S + 1). We extend the triplon analysis to include the effect of quintet dimer-states, which proves to be essential for establishing the classical order (Néel or collinear in the present study) for large S, both in the purely Heisenberg case and also in the model with single-ion anisotropy.     

Observing quantum trajectories: From Mott’s problem to quantum Zeno effect and back

The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct “trajectories” in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a “quantum trajectory” first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories differ from those produced in a typical particle tracker and the key to this difference lies in the active suppression of the quantum potential necessary to produce Mott-type trajectories. We show, using a rigorous mathematical argument, how the active suppression of this potential arises. Finally we discuss in detail how this suppression also accounts for the quantum Zeno effect.     

Probing spin physics in the quantum Hall regime by heat capacity and magnetotransport measurements

We review recent heat capacity and magnetotransport experiments on GaAs/AlGaAs heterostructures containing multilayer two-dimensional electron systems (2DESs) in the quantum Hall regime. Emphasis in this article is on the study of the heat capacity near Landau level filling factor ν=1. We also present a detailed survey of the development of the quantum Hall effect in tilted-magnetic fields for ν≲2. Among the novel phenomena we address is the strong coupling between the nuclear spins and the electrons associated with the spin phase transitions of the 2DES at ν=4/3 and near ν=1. To cite this article: S. Melinte et al., C. R. Physique 3 (2002) 667–676.     

Transition to sub-Planck structures through the superposition of q-oscillator stationary states

We investigate the superposition of four different quantum states based on the q-oscillator. These quantum states are expressed by means of Rogers-Szegö polynomials. We show that such a superposition has the properties of the quantum harmonic oscillator when q→1, and those of a compass state with the appearance of chessboard-type interference patterns when q→0.     

Optical properties of a hydrogenic impurity in a confined Zn1−xCdxSe/ZnSe spherical quantum dot

The effect of longitudinal optical phonon field on the ground state and low lying-excited state energies of a hydrogenic impurity in a Zn_1−xCd_xSe/ZnSe strained quantum dot is investigated for various Cd content using the Aldrich-Bajaj effective potential. We consider the strain effect considering the internal electric field induced by the spontaneous and piezoelectric polarizations. Calculations have been performed using Bessel function as an orthonormal basis for different confinement potentials of barrier height. Polaron induced photoionization cross section of the hydrogenic impurity in the quantum dot is investigated. We study the oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of incident photon energy for 1s-1p and 1p-1d transitions with and without the polaronic effect. It is observed that the potential taking into account the effects of phonon makes the binding energies more than the obtained results using a Coulomb potential screened by a static dielectric constant and the optical properties of hydrogenic impurity in a quantum dot are strongly affected by the confining potential and the radii. It is also observed that the magnitude of the absorption coefficients increases for the transitions between higher levels with the inclusion of phonon effect.     

Analysis of wetting layer effect on electronic structures of truncated-pyramid quantum dots

We carry out a theoretical analysis of wetting layer effect on band-edge profiles and electronic structures of InAs/GaAs truncated-pyramid quantum dots, including the strain effect. A combination of an analytical strain model and an eight-band Fourier transform-based k · p method is adopted in the calculation. Strain modified band-edge profiles indicates that wetting layer widens the potential well inside the dot region. Wetting layer changes ground-state energy significantly whereas modifies probability density function only a little. The main acting region of wetting layer is just underneath the base of the dot. Wetting layer redistributes probability density functions of the lowest electron state and probability density functions of highest hole state differently because of the different action of quantum confinement on electrons and holes.     

Skyrmion burst and multiple quantum walk in thin ferromagnetic films

We propose a new type of quantum walk in thin ferromagnetic films. A giant Skyrmion collapses to a singular point in a thin ferromagnetic film, emitting spin waves, when external magnetic field is increased beyond the critical one. After the collapse the remnant is a quantum walker carrying spin S. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two quantum walkers after two Skyrmion bursts. The system presents a new type of quantum walk for S>1/2, where a quantum walker breaks into 2S quantum walkers.