Two-electron Spectrum Research Articles

Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots.

We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8 meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5 meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.

Binding of two-electron metastable states in semiconductor quantum dots under a magnetic field

Applying a strong enough magnetic field results in the binding of few-electron resonant states. The mechanism was proposed many years ago but its verification in laboratory conditions is far more recent. In this work we study the binding of two-electron resonant states. The electrons are confined in a cylindrical quantum dot which is embedded in a semiconductor wire. The geometry considered is similar to the one used in actual experimental setups. The low-energy two-electron spectrum is calculated numerically from an effective-mass approximation Hamiltonian modelling the system. Methods for binding threshold calculations in systems with one and two electrons are thoroughly studied; in particular, we use quantum information quantities to assess when the strong lateral confinement approximation can be used to obtain reliable low-energy spectra. For simplicity, only cases without bound states in the absence of an external field are considered. Under these conditions, the binding threshold for the one-electron case is given by the lowest Landau energy level. Moreover, the energy of the one-electron bounded resonance can be used to obtain the two-electron binding threshold. It is shown that for realistic values of the two-electron model parameters it is feasible to bind resonances with field strengths of a few tens of tesla.

Highly tunable exchange in donor qubits in silicon

AbstractIn this article we have investigated the electrical control of the exchange coupling (J) between donor-bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We found that the asymmetric 2P–1P system provides a highly tunable exchange curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange coupling can be achieved using a modest range of electric field (3 MV/m) for ~15-nm qubit separation. Compared with the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the gate density by a factor of ~2. By combining large-scale atomistic tight-binding method with a full configuration interaction technique, we captured the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P–1P and 2P–1P qubits.

Attosecond pulse generation from two-electron harmonic emission spectrum**Project supported by the Scientific Research Fund of Liaoning Provincial Education Department, China (No. L2014242) and the Scientific Research Fund of Liaoning University of Technology, China (Grant Nos. X201319 and X201312).

In this paper, we theoretically investigate the high-order harmonic generation and attosecond pulse generation when a two-electron He atom is exposed to the intense laser pulse. It shows that due to the two-electron double recombination mechanism, an extended plateau beyond the classical single-electron harmonic has been obtained on the two-electron harmonic spectrum. Further by using this two-electron harmonic extension scheme combined with the two-color field, two supercontinuum bandwidths with 200 eV have been obtained. As a result, a series of sub-60 as extreme ultraviolet (XUV) pulses have been directly generated.

Correlated few-electron dynamics in intense laser fields

The time-dependent multi-configuration Hartree method is applied to nonsequential double ionization and to high harmonic generation and molecular tomography in a two-electron diatomic model molecule with two-dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semi-classical model. A mechanism for the ionization dynamics is suggested. In HHG, all relevant multi-electron effects are identified and quantified and their implications on molecular tomography are discussed.

Must Kohn–Sham oscillator strengths be accurate at threshold?

The exact ground-state Kohn-Sham (KS) potential for the helium atom is known from accurate wave function calculations of the ground-state density. The threshold for photoabsorption from this potential matches the physical system exactly. By carefully studying its absorption spectrum, we show the answer to the title question is no. To address this problem in detail, we generate a highly accurate simple fit of a two-electron spectrum near the threshold, and apply the method to both the experimental spectrum and that of the exact ground-state Kohn-Sham potential.

Signatures of bound-state-assisted nonsequential double ionization

The time-dependent multiconfiguration Hartree method is optimized for intense laser dynamics and applied to nonsequential double ionization in a two-electron diatomic model molecule with two dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semiclassical model. A mechanism for the ionization dynamics is suggested.

Shape variation of the two-electron photoionization spectrum with photon energy growth

We trace the evolution of the shape of the two-electron photoionization spectrum with photon energy growth using quite a precise two-electron wave function, obtained by the correlation function hyperspherical harmonic method. We obtain the values of {omega}{sub 1} and {omega}{sub 2} at which the spectrum curve changes its shape. At {omega}={omega}{sub 1} the U shape changes to a W shape. At {omega}={omega}{sub 2} the central W peak splits into two. We consider ground states of the helium atom and of heliumlike ions with the nuclear charge Z, the negative ion of hydrogen H{sup -}, and the excited n{sup 1}S state of helium. The limiting laws for Z>>1 and n>>1 are obtained. The analysis is carried out without calculations of the particular energy distributions themselves.

Recent progress in chirality studies of non-relativistic, few interacting particle systems

This work reviews recent achievements in the understanding of highly excited, interacting few-particle systems with a well defined internal helicity. To contrast theory with experiments we consider specifically the spectrum of two interacting continuum electrons with a positive (or a negative) chirality that move in the field of a positive ion. This doubly excited state is achieved upon the absorption of a circular photon with the appropriate helicity by an isotropic target. The dependence of the two-electron spectrum on the sign of the helicity of the exciting photon is utilized to study internal phase relations and mirror-reflection symmetries of the two-electron wave function.

Interaction-induced chaos in a two-electron quantum dot system

A quasi-one-dimensional quantum dot containing two interacting electrons is analyzed in search of signatures of chaos. The two-electron energy spectrum is obtained by diagonalization of the Hamiltonian including the exact Coulomb interaction. We find that the level-spacing fluctuations follow closely a Wigner-Dyson distribution, which indicates the emergence of quantum signatures of chaos due to the Coulomb interaction in an otherwise non-chaotic system. In general, the Poincar\'e maps of a classical analog of this quantum mechanical problem can exhibit a mixed classical dynamics. However, for the range of energies involved in the present system, the dynamics is strongly chaotic, aside from small regular regions. The system we study models a realistic semiconductor nanostructure, with electronic parameters typical of gallium arsenide.

Two electrons in a quantum dot: a semiclassical approach

The spectra of two electrons in a parabolic quantum dot in a magnetic field are obtained using the WKB approximation. No restrictions are imposed on the value of the electron-electron interaction. A simple approximation allowing an exact solution to be obtained for the interaction between two electrons in a quantum dot is proposed. It reproduces all of the qualitative features of the two-electron spectrum. Quantitatively, it is in good agreement with the WKB solution for the range of parameters of experimental interest.

Interaction of He+ and Ne+ ions with Ni(100)-K and Cu(100)-K surfaces having variable potassium coverage.

This paper presents an electron-spectroscopic study employing slow ${\mathrm{He}}^{+}$ and ${\mathrm{Ne}}^{+}$ ions incident on Ni(100) and Cu(100) surfaces with varying amounts of adsorbed potassium. Investigation of the changes in electron-energy spectra as the work function of the surface is varied probes the pattern of resonance tunneling, excitation conversion, and Auger electron-ejection processes. When the surface is clean the work function \ensuremath{\varphi} is high and the mode of electron ejection is the two-electron process of Auger neutralization of the incident ions yielding a folded two-electron spectrum. As the macroscopic \ensuremath{\varphi} is reduced by K adsorption the surface develops more and more regions near K atoms where the local \ensuremath{\varphi} is small, permitting resonance neutralization of the incident ion to form a metastable atom which on Auger deexcitation ejects electrons in a one-electron spectrum.This paper reports an investigation of this transition from the two-electron, kinetic energy spectrum to the one-electron spectrum and of the specific characteristics of each of these spectral types. Results are compared in detail with a published study by other investigators of the interaction of thermal He metastable atoms with a Cu(110)-K surface having variable K coverage. This comparative study has illuminated the differences observed in the spectra produced by incident 12-eV ions which turn to metastables in the high-K-coverage regime and thermal metastables which turn to ions at low K coverage. We have demonstrated that the local work function of ``clean'' sites decreases as K coverage increases in the low-coverage regime by interpreting small observed changes in the kinetic energy spectra of ejected electrons. This, in turn, leads to an estimate of the variation of the mean separation of K atoms with increasing K adsorption. We present new data for ion neutralization at the clean Cu(100) surface. From these we obtain the deconvolution of the kinetic energy spectrum that is the initial-state transition density for comparison with photoemission spectra. These results are also compared in detail, particularly with respect to energy broadening, with the results of an investigation by others employing ions descendent from incident thermal metastables.

On the hyperfine structure and isotope shift of radium

The hyperfine structure and isotope shift of the heaviest known alkaline earth element radium (Z=88) have been studied in both the atomic Ra I and ionic Ra II spectra. The measurements, carried out by on-line collinear fast-beam laser spectroscopy, yield the hyperfine constantsA andB of the 7s and 7p1/2 states in Ra II, of all states of the excited 7s 7p configuration and the 7s 7d3D3 state in Ra I. The data allow a consistent evaluation of the nuclear moments for eight odd-A radium isotopes. In particular, a complete analysis of the hyperfine structure of thesp configuration in the two-electron system provides a stringent test of the validity of the semi-empirical modified Breit-Wills theory. It is shown that the effective operator formalism is equivalent, if relativistic correction functions are used to reduce the number of parameters. The semi-empirical hyperfine fields are evaluated and found to agree generally with those from ab-initio calculations. The isotope shifts in thes−p,s2−sp,sp−sd transitions are analysed semi-empirically and compared with ab-initio calculations. The consistency of the different analyses proves their validity and classifies the spectrum of Ra I as a model case for a simple and clean two-electron spectrum.

Laser-microwave spectroscopy of lithium ions: 23 S 1 hyperfine structure of7Li+

The hyperfine structure (hfs) splittings of the metastable 1s2s3S1 state of7Li+ have been measured with combined laser optical pumping and microwave resonance. A lowenergy Li+ ion beam, optically excited by an intersecting laser beam, passed a waveguide where radio frequency transitions were induced. The resulting population transfer among the hfs levels of the3S1 was detected via the change in intensity of the fluorescence light from a second crossing region of laser light and ion beam located past the waveguide. The magnetic hfs constantA(7Li+, 1s2s3S1) was measured and compared with theory. A deviation of the two transition frequenciesν(F=3/2−F=5/2) andν(F=1/2−F=3/2) from the interval rule is due to a depression of theF=3/2 hfs sublevel, caused by mixing of the 23S1 and 21S0 states via hyperfine interaction. This shift was never observed so far in a two-electron spectrum, because of absence ofI>1/2 isotopes in He, the only two-electron atom investigated spectroscopically with high precision. The size of the shift is in fair agreement with a theoretical estimate.

Ab-initio interpretation of 〈r−3〉 electronic quantities in the hfs of Mg I 3s 3p 3 P and1 P

It has been known for a long time that, in a two-electron arc spectrum, the properties of the3P and1P terms of the lowests p configuration cannot be interpreted correctly in a pure-configuration model. Following the experimental determination of the hyperfine constantA(3s 3p1P1) in Mg I by Kluge and Otten, this paper presents the ab-initio interpretation of the 〈r−3〉3p hyperfine electronic quantities in 3s 3p through the use of the multiconfigurational Hartree-Fock method. It appears that taking into account the effects of the monoelectronic excitations 3s→nd, 2p→np and 3p→np leads to ab-initio evaluations in very good agreement with experiment. The case of the 3p→np excitation, to which Brillouin's theorem should apply in principle, is discussed. Using the same method, a refined evaluation is proposed for the nuclear electric-quadrupole moment of Mg25 (Q=0.200 ± 0.01 barn).

Study of Two-Electron Transitions of a Donor in CdSe

Two-electron transitions, in which an exciton bound to a neutral donor decays leaving the donor in an excited state, were measured in CdSe. The donor was not identified. The transition energies from the 1s ground state to the $2s$, $2p$, $n=3$, and $n=4$ levels were measured. The transitions were identified by their Zeeman splittings. The spectrum was complicated because a number of the transitions originated from excited states of the three-particle bound-exciton complex. There was a one-to-one correspondence between this spectrum and the two-electron spectrum previously observed in CdS. From these measurements, we deduce that ${E}_{D}=19.5\ifmmode\pm\else\textpm\fi{}0.3$ meV and $m=(0.13\ifmmode\pm\else\textpm\fi{}0.005){m}_{e}$, where ${E}_{D}$ is the donor binding energy, $m$ is the measured electron mass, and ${m}_{e}$ is the free-electron mass.