Two Interacting Electrons in a Vertically Coupled Quantum Dot

We study a two-electron system in a double-layer quantum dot under a magnetic field by means of the exact diagonalization of the Hamiltonian matrix.We find that discontinuous ground-state energy transitions are induced by an external magnetic field in the case of strong coupling.However,in the case of weak coupling,the angular momentum L of the true ground state does not change in accordance with the change of the magnetic field B and remains L=0.     

Ground State Transitions in Vertically Coupled Four-Layer Single Electron Quantum Dots

We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.     

Ground State Transitions in Vertically Coupled Four-Layer Single Electron Quantum Dots

We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.     

CORRELATION EFFECTS ON THE GROUNDSTATES OF THREE-ELECTRON QUANTUM DOTS IN A STRONG MAGNETIC FIELD

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Off—Center D—Centers in a Quantum Dot in the Presence of a Perpendicular Magnetic Fields

We investigate the effect of the position of the donor in quantum dots on the energy spectrum in the presence of a perpendicular magnetic field by using the method of few-body physics,As a function of the magnetic field,we find,when D^- centers are placed sufficiently off-center,discontinuous ground-state transitions which are similar to those found in many-electron parabolic quantum dots.Series of magic numbers of angular momentum which minimize the ground-state electron-electron interaction energy have been discovered.The dependence of the binding energy of the gound-state of the D^- center on the dot radius for a few values of the magnetic field strength is obtained and compared with other results.     

Biexcitons in artificial molecules with in-plane magnetic field

We theoretically investigate the effect of a magnetic field perpendicular to the tunneling direction on the ground-state properties of biexcitons in coupled quantum dots. The single-particle states are computed by numerically solving the 3D Scrödinger equation. The biexciton states are obtained by means of a configuration-interaction approach, which fully accounts for the intra- and inter-dot Coulomb correlations. We show that the biexciton ground state undergoes non-trivial transitions as a function of the applied magnetic field, which can be traced back to unexpected carrier localizations.     

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state. Received 17 February 1999 and Received in final form 1 June 1999     

Magic numbers in vertically coupled quantum dots

A coupled quantum dot system has been studied by numerical diagonalization of the Hamiltonian. Discontinuous ground-state transitions induced by an external magnetic field have been predicted. Series of magic numbers of angular momentum which minimize the ground-state electron-electron interaction energy have been discovered. Theoretical explanations derived from the first principles have been formulated. Received: 13 July 1997 / Accepted: 7 October 1997     

Emission of polarization-entangled microwave photons from a pair of quantum dots

We describe a mechanism for the production of polarization-entangled microwaves using intraband transitions in a pair of quantum dots. This proposal relies neither on spin-orbit coupling nor on control over electron-electron interactions. The quantum correlation of microwave polarizations is obtained from orbital degrees of freedom in an external magnetic field. We calculate the concurrence of emitted microwave photon pairs and show that a maximally entangled Bell pair is obtained in the limit of weak interdot coupling.     

Quantum cascade transitions in nanostructures

In this article we review the physical characteristics of quantum cascade transitions (QCTs) in various nanoscopic systems. The quantum cascade laser which utilizes such transitions in quantum wells is a brilliant outcome of quantum engineering that has already demonstrated its usefulness in various real-world applications. After a brief introduction to the background of this transition process, we discuss the physics behind these transitions in an externally applied magnetic field. This has unravelled many intricate phenomena related to intersubband resonance and electron relaxation modes in these systems. We then discuss QCTs in a situation where the quantum wells in the active regions of a quantum cascade structure are replaced by quantum dots. The physics of quantum dots is a rapidly developing field with its roots in fundamental quantum mechanics, but at the same time, quantum dots have tremendous potential applications. We first present a brief review of those aspects of quantum dots that are likely to be reflected in a quantum-dot cascade structure. We then go on to demonstrate how the calculated emission peaks of a quantum-dot cascade structure with or without an external magnetic field are correlated with the properties of quantum dots, such as the choice of confinement potentials, shape, size and the low-lying energy spectra of the dots. Contents PAGE 1 Introduction 456 2 Intersubband transitions in quantum wells 458 3 Quantum cascade transitions 462 3.1. Basic principles 462 3.1.1. Minibands and minigaps 464 3.1.2. Vertical transitions 464 3.1.3. GaAs/AlGaAs quantum cascade lasers 464 3.1.4. QCLs based on superlattice structures 465 3.1.5. Type-II quantum cascade lasers 466 3.1.6. Recent developments 466 3.2. Applications: sense-ability and other qualities 466 4 Quantum cascade transitions in novel situations 467 4.1. External magnetic field 467 4.1.1. Parallel magnetic field 468 4.1.2. Many-body effects: depolarization shift 470 4.1.3. The role of disorder 471 4.1.4. Tilted magnetic field 475 4.2. Magneto-transport experiments and phonon relaxation 479 4.3. Magneto-optics experiment and phonon relaxation 484 5 A brief review of quantum dots 485 5.1. From three- to zero-dimensional systems 485 5.2. Making the dots 487 5.2.1. Lithographic patterning 487 5.2.2. Self-assembled quantum dots 488 5.3. Shell filling in quantum dots 489 5.4. Electron correlations: spin states 490 5.5. Anisotropic dots 491 5.6. Influence of an external magnetic field 491 5.6.1. The Fock diagram 491 5.6.2. The no-correlation theorem 492 5.6.3. Correlation effects and magic numbers 492 5.6.4. Spin transitions 493 5.7. Quantum dots in novel systems 494 5.8. Potential applications of quantum dots 494 5.8.1. Single-electron transistors (SETs) 494 5.8.2. Single-photon detectors 494 5.8.3. Single-photon emitters 495 5.8.4. Quantum-dot lasers 495 6 Quantum cascade transitions in quantum-dot structures 496 6.1. Quantum dots versus quantum wells 496 6.2. QCT with rectangular dots 497 6.2.1. Vertical transitions 500 6.2.2. Diagonal transitions 501 6.3. QCT in a parabolic dot 504 6.4. Magnetic field effects on intersubband transitions 506 6.5. Mid-IR luminescence from a QD cascade device 512 7 Summary and open questions 513 Acknowledgements 515 References 515     

Polarization selective magneto-optical study on the coupled quantum dots using resonant excitation

We have studied a double-layer self-assembled quantum dot (QD) structures consisting of non-magnetic CdSe and magnetic CdMnSe. Transmission electron microscopy image shows that QDs are formed within the CdSe and CdMnSe layers, and they are vertically correlated in the system. The strong interband ground state transition was observed in magneto-photoluminescence (PL) experiments. In contrast to a typical behavior for many low-dimensional systems involving diluted magnetic semiconductors (DMSs), where PL signal dramatically increases when an external magnetic field is applied, we have observed a significant decrease of the PL intensity as a function of magnetic field in the double-layer structures where the alternating QD layers contain the DMS and non-DMS QDs. We attribute such effect to carrier transfer from non-magnetic CdSe dots to magnetic CdMnSe dots due to the large Zeeman shift of the band edges of DMS QDs in magnetic field. Since the band alignment of QD structure strongly depends on the spin states of system, we performed polarization-selective PL measurement to identify spin-dependent carrier tunneling in this coupled system.     

Entanglement and Zeeman interaction in diluted magnetic semiconductor quantum dot

We present theoretically the Zeeman coupling and exchange-induced swap action in spin-based quantum dot quantum computer models in the presence of magnetic field. We study the valence and conduction band states in a double quantum dots made in diluted magnetic semiconductor. The latter have been proven to be very useful in building an all-semiconductor platform for spintronics. Due to a strong p–d exchange interaction in diluted magnetic semiconductor (Cd_0.57Mn_0.43Te), the relative contribution of this component is strongly affected by an external magnetic field, a feature that is absent in nonmagnetic double quantum dots. We determine the energy spectrum as a function of magnetic field within the Hund–Mulliken molecular-orbit approach and by including the Coulomb interaction. Since we show that the ground state of the two carriers confined in a vertically coupled quantum dots provide a possible realization for a gate of a quantum computer, the crossing between the lowest states, caused by the giant spin splitting, can be observed as a pronounced jump in the magnetization of small magnetic field amplitude. Finally, we determine the swap time as a function of magnetic field and the inter dot distance. We estimate quantitatively swap errors caused by the field, establishing that error correction would, in principle, be possible in the presence of nonuniform magnetic field in realistic structures.     

Effects of Impurity on the Ground—State Transitions of a Quantum Dot in Strong Magnetic Field

The low-lying spectra of parabolic quantum dots with or without an impurity at the center are investigated.While it has been known that the electron-electron interaction leads to ground-state transitions on magic values of angular momentum in a magnetic field.We show,in this paper,that the implantation of an impurity ion at the center can either enhance or suppress such transitions,depending on whether it is an acceptor or a donor ion.     

Two interacting spins in external fields and application to quantum computation

We study the four-level-system given by two quantum dots immersed in a time-dependent magnetic field, which are coupled to each other by an effective Heisenberg-type interaction. We describe the construction of the corresponding evolution operator in a special case of different time-dependent parallel external magnetic fields. We find a relation between the external field and the effective interaction function. The obtained results are used to analyze the theoretical implementation of a universal quantum gate.     

One-dimensional δ-function attractive Fermi gas in an external magnetic field

We investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.     

Fixed-distance coupling and encapsulation of heterogeneous quantum dots using phonon-assisted photo-curing

We propose a novel method of coupling heterogeneous quantum dots at fixed distances and capsulating the coupled quantum dots by utilizing nanometric local curing of a photo-curable polymer caused by multistep electronic transitions based on a phonon-assisted optical near-field process between quantum dots. Because the coupling and the capsulating processes are triggered only when heterogeneous quantum dots floating in a solution closely approach each other to induce optical near-field interactions between them, the distances between the coupled quantum dots are physically guaranteed to be equal to the scale of the optical near fields. To experimentally verify our idea, we fabricated coupled quantum dots, consisting of CdSe and ZnO quantum dots and a UV-curable polymer. We also measured the photoluminescence properties due to the quantum-dot coupling and showed that the individual photoluminescences from the CdSe and ZnO quantum dots exhibited a trade-off relationship.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Interacting electrons in quantum dots

The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with the results of exact diagonalization. Analytic results for the lower bounds to the ground-state energies of the quantum dots in a strong magnetic field (known as electron molecule) agree very well with numerically calculated lower bounds.     

Few-electron molecular states and their transitions in a single InAs quantum dot molecule

We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.     

Excitons and magnetoexcitons in coupled quantum nanostructures: the role of a dirty environment

The effect of a random field caused by impurities, interface roughness and so on, on the optical properties and superfluidity of a quasi-two-dimensional system of excitons is studied. The influence of a random field on the density of the superfluid component of excitonic systems at low temperatures is investigated. For quasi-two-dimensional excitonic systems in a random field the Kosterlitz–Thouless temperature in the superfluid state is calculated. The superfluidity and Bose–Einstein condensation of indirect excitons in coupled quantum dots are studied. Magnetoexciton light absorption in the disordered quantum wells is considered. The two-particle problem of the magnetoexciton motion in the external field depending on the external magnetic field is reduced to the one-particle motion with effective magnetic mass in some effective field. The energy and optical absorption of the magnetoexciton in a single and coupled quantum dots are studied using the effective-magnetic-mass Hamiltonian. In the coherent potential approximation the coefficient of magnetoexciton optical absorption in single and coupled quantum wells is calculated. In the strong magnetic fields the exciton peak decreases with magnetic field increasing in accordance with the experimental data. The localization of direct and indirect magnetoexcitons is investigated. Received: 14 April 2000 / Accepted: 17 April 2000 / Published online: 6 September 2000