Electronic states of quantum dots: beyond the 2D parabolic model

The quantum states of interacting electrons in a quantum dot in a magnetic field are calculated and the effects of corrections to the 2D parabolic model are examined. The quantum states are obtained by a new method which involves three steps: first the electrostatic potential of the device is obtained from a solution of the Poisson equation, next this potential is used together with a combination of variational and Hartree–Fock calculations to obtain an orthogonal basis whose low-lying states are localised in the region of the dot and finally this basis is used to perform an exact diagonalization. Special attention is paid to the effect of motion perpendicular to the ideal 2D plane and the effect of screening of the Coulomb interaction by metallic electrodes close to the dot. Both effects result in a weakened effective interaction and increase the magnetic fields at which ground-state transitions occur.     

Spin-magnetoplasma waves in a 2D electron system

Oscillations of a 2D electron plasma in a transverse magnetic field have been theoretically studied taking into account spin-orbit interaction. Four branches of spin-plasmon oscillations associated with different selection rules for spin and orbital quantum numbers have been shown to appear at a small plasmon momentum in a semiclassical limit (the Fermi energy is much higher than the Landau quantum). In the quantum case (the filling factor ν is about unity), the number of branches changes from three to six depending on ν value.     

Hopping conductivity and Coulomb correlations in 2D arrays of Ge/Si quantum dots

The temperature and magnetic-field dependences of the conductivity associated with hopping transport of holes over a 2D array of Ge/Si(001) quantum dots with various filling factors are studied experimentally. A transition from the Éfros-Shklovski? law for the temperature dependence of hopping conductivity to the Arrhenius law with an activation energy equal to 1.0–1.2 meV is observed upon a decrease in temperature. The activation energy for the low-temperature conductivity increases with the magnetic field and attains saturation in fields exceeding 4 T. It is found that the magnetoresistance in layers of quantum dots is essentially anisotropic: the conductivity decreases in an increasing magnetic field oriented perpendicularly to a quantum dot layer and increases in a magnetic field whose vector lies in the plane of the sample. The absolute values of magnetoresistance for transverse and longitudinal field orientations differ by two orders of magnitude. The experimental results are interpreted using the model of many-particle correlations of holes localized in quantum dots, which lead to the formation of electron polarons in a 2D disordered system.     

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al _x Ga_1−x As heterojunction. The results are in good agreement with the existing experimental data.     

Spin interaction and magnetic field strength effects on the system of two interacting electrons in a 2D quartic confinement potential

In this study we review concepts of double quantum dot, quantum chaos with shifted 1/N expansion method associated with semiquantum nonlinear system. We present a numerical study of two interacting particle motions in a time dependent magnetic field in quartic geometry. It is evident that, the area where the interaction particle motions are stochastic decreases as the spin interaction strength decreases, as well as, the magnetic field strength decreases. Moreover, we describe their possible connections with other aspects of quantum information. Furthermore, we pay attention to a system of two interacting electrons in a two-dimensional quartic confinement potential and hypothesis leading to analytical energy expression. The dynamics of double quantum dot gallium arsenide are of great importance and are also emphasized.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.     

Simulating cyclotron-Bloch dynamics of a charged particle in a 2D lattice by means of cold atoms in driven quasi-1D optical lattices

Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.     

Generation of squeezed vacuum on cesium D2 line down to kilohertz range

We report the experimental generation of a squeezed vacuum at frequencies ranging from 2.5 kHz to 200 kHz that is resonant on the cesium D2 line by using a below-threshold optical parametric oscillator(OPO). The OPO is based on a periodically-poled KTiOPO_4(PPKTP) crystal that is pumped using a bow-tie four-mirror ring frequency doubler. The phase of the squeezed light is controlled using a quantum noise locking technique. At a pump power of 115 mW, maximum quadrature phase squeezing of 3.5 d B and anti-squeezing of 7.5 d B are detected using a home-made balanced homodyne detector. This squeezed vacuum at an atomic transition in the kilohertz range is an ideal quantum source for quantum metrology of enhancing measurement precision, especially for ultra-sensitive measurement of weak magnetic fields when using a Cs atomic magnetometer in the audio frequency range.     

Anisotropic positive magnetoresistance of a nonplanar 2D electron gas in a parallel pagnetic field

Magnetotransport properties of a 2D electron gas in narrow GaAs quantum wells with AlAs/GaAs superlattice barriers were studied. It is shown that the anisotropic positive magnetoresistance observed in selectively doped semiconductor structures in a parallel magnetic field is caused by the spatial modulation of the 2D electron gas.     

Pinning mode resonances of new phases of 2D electron systems in high magnetic fields

A striking rf or microwave resonance is a generic feature of electron solid phases of two-dimensional electron systems. These resonances have served to identify and characterize such solids, in the insulator that terminates the series of fractional quantum Hall effects at high magnetic field, in the range of the integer quantum Hall effect, and in bubble phases in the first excited and higher Landau levels.     

Susceptibility of the 2D spin-1 / 2 Heisenberg antiferromagnet with an impurity

We use a quantum Monte Carlo method (stochastic series expansion) to study the effects of a magnetic or nonmagnetic impurity on the magnetic susceptibility of the two-dimensional Heisenberg antiferromagnet. At low temperatures, we find a log-divergent contribution to the transverse susceptibility. We also introduce an effective few-spin model that can quantitatively capture the differences between magnetic and nonmagnetic impurities at high and intermediate temperatures.     

Magnetoplasma oscillations in a 2D electron system with spin-orbit interaction

The magnetoplasmon spectrum in a 2D electron plasma is investigated theoretically taking into account the spin—orbit interaction in the Rashba model. The expression is derived for the polarization operator in the semiclassical range of magnetic fields (in which the Fermi energy eF is much larger than the Landau quantum). Approximate analytic formulas are obtained for spin—plasmon branches. The dependences of plasma wave frequencies on the wavevector and magnetic field are calculated from a numerical solution of the dispersion equation. In addition, the magnetic field and frequency dependences of the plasmon absorption intensity are constructed. The absorption intensity at the peak is found to be sensitive to the spin—orbit interaction constant.     

Ab initio study of electronic and magnetic properties in TM-doped 2D silicon carbide

The magnetic properties of SiC monolayer with different TM atoms and substitutional sites are investigated using first-principles method. Magnetism is observed for all the TM dopants. The magnetic moments and binding energies are quite different between Si (TM_Si) and C (TM_C) sites. Dependent to the larger magnetic moments and binding energy, we also investigate the interaction between two Mn atoms in the TM_Si system. The results show that the ferromagnetic states are originated by the p–d hybridization mechanism between Mn and its neighboring C atoms. Moreover, the antiferromagnetic coupling is observed with increasing Mn-Mn distance, which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method.     

2D chaotic quantum states in superlattices

The semiclassical motion of an electron along the axis of a superlattice may be calculated from the miniband dispersion curve. Under a weak electric field the electron executes Bloch oscillations which confines the motion along the superlattice axis. When a magnetic field, tilted with respect to the superlattice axis, is applied the electron orbits become chaotic. The onset of chaos is characterised by a complex mixed stable-chaotic phase space and an extension of the orbital trajectories along the superlattice axis. This delocalisation of the orbits is also reflected in the quantum eigenstates of the system some of which show well-defined patterns of high probability density whose shapes resemble certain semiclassical orbits. This suggests that the onset of chaos will be manifest in electron transport through a finite superlattice. We also propose that these phenomena may be observable in the motion of trapped ultra-cold atoms in an optically induced superlattice potential and magnetic quadrupole potential whose axis is tilted relative to the superlattice axis.     

Measurement-induced disturbance and thermal negativity in 1D optical lattice chain

We study the measurement-induced disturbance (MID) in a 1D optical lattice chain with nonlinear coupling. Special attention is paid to the difference between the thermal entanglement and MID when considering the influences of the linear coupling constant, nonlinear coupling constant and external magnetic field. It is shown that MID is more robust than thermal entanglement against temperature T$T$ and external magnetic field B$B$, and MID may reveal more properties about quantum correlations of the system, which can be seen from the point of view that MID can be nonzero when there is no thermal entanglement and MID can detect the critical point of quantum phase transition at finite temperature.     

Ground state phase diagram of the 1D XXZ model in a transverse magnetic field

The Ground state phase diagram of the 1D spin-1/2 XXZ model in a transverse magnetic field is studied by the numerical Lanczos method. Also by computing the energy gap and different spin-spin structure factors, quantum phase transitions in whole range of the anisotropy parameter are determined.     

Quantum Bocce: Magnon–magnon collisions between propagating and bound states in 1D spin chains

The dynamics of two magnons in a Heisenberg spin chain under the influence of a non-uniform magnetic field is investigated by means of a numerical wave-function-based approach using a Holstein–Primakoff transformation. The magnetic field is localized in space such that it supports exactly one single-particle bound state. We study the interaction of this bound mode with an incoming spin wave and the interplay between transmittance, energy and momentum matching. We find analytic criteria for maximizing the interconversion between propagating single-magnon modes and true propagating two-magnon states. The manipulation of bound and propagating magnons is an essential step towards quantum magnonics.     

Magnetic anticrossing of 1D subbands in ballistic double quantum wires

We study the low-temperature in-plane magnetoconductance of vertically coupled double quantum wires. Using a novel flip-chip technique, the wires are defined by two pairs of mutually aligned split gates on opposite sides of a  ≤ 1 micron thick AlGaAs/GaAs double quantum well heterostructure. We observe quantized conductance steps due to each quantum well and demonstrate independent control of each 1D wire. A broad dip in the magnetoconductance at  ∼ 6 T is observed when a magnetic field is applied perpendicular to both the current and growth directions. This conductance dip is observed only when 1D subbands are populated in both the top and bottom constrictions. This data is consistent with a counting model whereby the number of subbands crossing the Fermi level changes with field due to the formation of an anticrossing in each pair of 1D subbands.     

NMR determination of 2D electron spin polarization at nu = 1/2

Using a "standard" NMR spin-echo technique we determined the spin polarization P of two-dimensional electrons, confined to GaAs quantum wells, from the hyperfine shift of Ga nuclei located in the wells. Concentrating on the temperature ( 0.05 less, similarT less, similar10 K) and magnetic field ( 7 less, similarB less, similar17 T) dependencies of P at Landau level filling factor nu = 1/2, we find that the results are described well by a simple model of noninteracting composite fermions, although some inconsistencies remain when the two-dimensional electron system is tilted in the magnetic field.     

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.