Quantum Box Research Articles

Bounds on quantum confinement effects in metal nanoparticles

Quantum size effects on the permittivity of metal nanoparticles are investigated using the quantum box model. Explicit upper and lower bounds are derived for the permittivity and relaxation rates due to quantum confinement effects. These bounds are verified numerically, and the size-dependence and frequency-dependence of the empirical Drude size parameter is extracted from the model. Results suggest that the common practice of empirically modifying the dielectric function can lead to inaccurate predictions for highly uniform distributions of finite-sized particles.

5a-J-4 量子細線、量子箱の電子状態における界面の不規則性の効果

5a-J-4 量子細線、量子箱の電子状態における界面の不規則性の効果

Adsorbate-Induced Modification of the Confining Barriers in a Quantum Box Array.

Quantum devices depend on addressable elements, which can be modified separately and in their mutual interaction. Self-assembly at surfaces, for example, formation of a porous (metal-) organic network, provides an ideal way to manufacture arrays of identical quantum boxes, arising in this case from the confinement of the electronic (Shockley) surface state within the pores. We show that the electronic quantum box state as well as the interbox coupling can be modified locally to a varying extent by a selective choice of adsorbates, here C60, interacting with the barrier. In view of the wealth of differently acting adsorbates, this approach allows for engineering quantum states in on-surface network architectures.

Removal of accidental degeneracy in semiconductor quantum dots

We present a quantitative analysis of the energy levels and wave functions of carriers in a cubic quantum dot of GaAs embedded in ${\mathrm{Ga}}_{(1\ensuremath{-}x)}{\mathrm{Al}}_{x}\mathrm{As}$ with finite confining potential barriers at their interfaces. The energy spectrum has substantially reduced degeneracies compared to the analytically determined energy levels of the infinite-barrier quantum box of the same dimensions. The level degeneracy of states has been explained by group representations of the point group ${O}_{h}$. Projection operators for the irreducible representations provide a way to obtain the linear combinations of the degenerate wave functions which form a basis set for the representations. Energy-level splittings in the presence of externally applied electric and magnetic fields are also studied.

Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory

A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.

Configuring Electronic States in an Atomically Precise Array of Quantum Boxes.

A 2D array of electronically coupled quantum boxes is fabricated by means of on-surface self-assembly assuring ultimate precision of each box. The quantum states embedded in the boxes are configured by adsorbates, whose occupancy is controlled with atomic precision. The electronic interbox coupling can be maintained or significantly reduced by proper arrangement of empty and filled boxes.

Optical properties of a semispherical quantum dot placed at the center of a cubic quantum box: Optical rectification, second and third-harmonic generations

In the present paper, we first apply finite element method (FEM) and Arnoldi algorithm to obtain energy eigenvalues and eigenfuctions of a semispherical quantum dot located at the center of a cubic box. Then, the compact-density matrix approach and an iterative method are used to find the optical rectification (OR) coefficient, second harmonic generation (SHG) and third harmonic generation (THG). Numerical calculations are performed for the typical GaAs/Ga1−xAlxAs system. It is found that OR coefficient has a red-shift when the semispherical radius R becomes larger. Raising R and potential height V0, the magnitude of OR coefficient, SHG and THG are increased. Moreover, the position of resonant peaks of OR coefficient, SHG and THG are affected by the semispherical radius and potential height.

Gain optimization of the optical waveguide based on the quantum box core/shell structure

In order to implement an integrated optical quantum circuit, designing waveguides based on the quantum box is of prime importance. To do this we have investigated optical waveguide both with and without optical pumping. The rate of absorption and emission using an array of AlGaAs/GaAs quantum box core/shell structure in the optical waveguide with various pumping intensities has computed. By considering an external pumping with maximum emission, the gain of the optical waveguide based on the AlGaAs/GaAs quantum box core/shell structure, for two different sizes 3×3×3 nm and 6×6×6 nm has been optimized. We have shown that in the absence of any external excitation with different pumping power, the amount of absorption energy in the array of quantum box is greater than the amount of emission energy, and resulting in the positive gain. Finally, we noticed that by increasing the dimension of the quantum box, the optimum gain is achieved for the smaller wavelength.

Effect of quantum dot size and size distribution on the intersublevel transitions and absorption coefficients of III-V semiconductor quantum dot

The intersublevel absorption peak energy and absorption coefficient of non-uniform quantum dot (QD) ensembles are calculated analytically. The effect of size variations and size distribution of QDs on their energy states is analyzed. The dots are considered as a quantum box with finite potential at the barriers and the size distribution described by a Gaussian function. The influence of the aspect ratio (base to height ratio) of the QDs on the optical transitions is studied. Our model predicts the dot size (height and base) accurately to determine the absorption peaks and corresponding absorption coefficient. We also compute the absorption coefficient of the QD with different size distributions to verify the results calculated using this model with the reported experimental and other theoretical results.

Directional luminescence control of InGaN/GaN heterostructures using quantum structure lattice arrays

The spontaneous surface luminescence properties of InGaN/GaN quantum structure lattice (QSL) are reported. The QSL consists of a two-dimensional array of InGaN/GaN quantum boxes (QBs) arranged in a rectangular pattern of 200 nm periodicity. The measured angular dependent photoluminescence (PL) spectra show a strong dependence on the in-plane Bragg diffractions between QBs. The maximum PL intensity of the InGaN/GaN QSL array that fulfill the Bragg condition points in the normal direction of the sample surface with a narrow radiation angle of ∼ ±12°. In addition, a small side lobe is also shown at ±40°. For the QSL sample that does not fulfill the Bragg diffraction condition, the radiation pattern shows a conventional cosine distribution. The finite-difference time-domain numerical analysis confirms that the lowest order and higher order Bragg diffractions between QBs determine the main and the small side lobe of the radiation pattern measured in QSLs, respectively.

Coupling polariton quantum boxes in sub-wavelength grating microcavities

We report the construction of decoupled, coupled, and quasi-one dimensional polariton systems from zero dimensional polariton quantum boxes using microcavities with sub-wavelength gratings as the top mirror. By designing the tethering patterns around the suspended sub-wavelength gratings, we control the coupling between individual quantum boxes through different optical potentials. Energy levels and real-space or momentum space distributions of the confined modes were measured, which agreed well with simulations.

Interplay of weak interactions in the atom-by-atom condensation of xenon within quantum boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined ‘quantum boxes’. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on—but is not limited to—the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

Electroluminescence of copper-nitride nanocrystals

Nanocrystals can behave as quantum boxes with confined electronic states governing their optoelectronic properties. The formation of nanometer-size crystals of copper nitride $({\mathrm{Cu}}_{3}\mathrm{N})$ grown by nitrogen sputtering of a Cu(110) surface is reported. Scanning tunneling spectroscopy shows that the nanocrystals exhibit a series of well-defined sharp electronic resonances, which correspond to confined free-electron-like states. We observe that electrons from a scanning tunneling microscope tip induce the emission of light with a larger efficiency than on the bare metal surface. The spectral analysis of the emitted photons reveals various radiative inelastic pathways enabled by the confined states, which explain the enhanced light emission. Thus, the ${\mathrm{Cu}}_{3}\mathrm{N}$ nanocrystals can be employed as nanometer-size light sources.

A Delocalized Proton-Binding Site within a Membrane Protein

The role of protein-bound water molecules in protein function and catalysis is an emerging topic. Here, we studied the solvation of an excess proton by protein-bound water molecules and the contribution of the surrounding amino acid residues at the proton release site of the membrane protein bacteriorhodopsin. It hosts an excess proton within a protein-bound water cluster, which is hydrogen bonded to several surrounding amino acids. Indicative of delocalization is a broad continuum absorbance experimentally observed by time-resolved Fourier transform infrared spectroscopy. In combination with site-directed mutagenesis, the involvement of several amino acids (especially Glu-194 and Glu-204) in the delocalization was elaborated. Details regarding the contributions of the glutamates and water molecules to the delocalization mode in biomolecular simulations are controversial. We carried out quantum mechanics/molecular mechanics (QM/MM) self-consistent charge density functional tight-binding simulations for all amino acids that have been experimentally shown to be involved in solvation of the excess proton, and systematically investigated the influence of the quantum box size. We compared calculated theoretical infrared spectra with experimental ones as a measure for the correct description of excess proton delocalization. A continuum absorbance can only be observed for small quantum boxes containing few amino acids and/or water molecules. Larger quantum boxes, including all experimentally shown involved amino acids, resulted in narrow absorbance bands, indicating protonation of a single binding site in contradiction to experimental results. We conclude that small quantum boxes seem to reproduce representative extreme cases of proton delocalization modes: proton delocalization only on water molecules or only between Glu-194 and Glu-204. Extending the experimental spectral region to lower wave numbers, a water-delocalized proton reproduces the observed continuum absorbance better than a glutamate-shared delocalized proton. However, a full agreement between QM simulations and experimental results on the delocalized excess proton will require a larger quantum box as well as more sophisticated QM/MM methods.

Conceptual integration of covalent bond models by Algerian students

The concept of covalent bonding is characterized by an interconnected knowledge framework based on Lewis and quantum models of atoms and molecules. Several research studies have shown that students at all levels of chemistry learning find the quantum model to be one of the most difficult subjects to understand. We have tried in this paper to analyze the extent to which Algerian students, at the end of their training, have integrated the covalent bonding theories based on the quantum model of atom theory and are able to interpret Lewis structures using the quantum model. The analysis of the responses to a written questionnaire showed that this integration was not achieved by our students and that they are not able to correctly describe covalent bonds in a Lewis structure using the concepts of the quantum model. They have a “quantum box” conception of atomic or hybrid orbitals. This conception acts as a “pedagogical learning impediment” to the integration of the geometrical representations of atomic and hybrid orbitals, the conditions of their overlapping to give bonds and consequently the description of covalent bonds using the quantum model. So, the students use an alternative conceptual framework based on the use of Lewis model paired valence electrons to form covalent bonds that we have named the: “electrons pair framework”. Furthermore, the students restricted the denomination of a covalent bond to the sharing of one electron (either s or p but not spn) from each atom to give one “electron pair σ”, and thought that σ bonds are only formed in single bonds.

Fano–Kondo and the Kondo box regimes crossover in a quantum dot coupled to a quantum box

In this work, we study the Kondo effect of a quantum dot (QD) connected to leads and to a discrete set of one-particle states provided by a quantum box represented by a quantum ring (QR) pierced by a magnetic flux side attached to the QD. The interplay between the bulk Kondo effect and the so-called Kondo box regime is studied. In this system the QR energies can be continuously modified by the application of the magnetic field. The crossover between these two regimes is analyzed by changing the connection of the QD to the QR from the weak to the strong coupling regime. In the weak coupling regime, the differential conductance develops a sequence of Fano–Kondo anti-resonances due to destructive interference between the discrete quantum ring levels and the conducting Kondo channel provided by the leads. In the strong coupling regime the differential conductance has very sharp resonances when one of the Kondo discrete sub-levels characterizing the Kondo box is tuned by the applied potential. The conductance, the current fluctuations and the Fano coefficient result as being the relevant physical magnitudes to be analyzed to reveal the physical properties of these two Kondo regimes and the crossover region between them. The results were obtained by using the slave boson mean field theory (SBMFT).

Effective Josephson dynamics in resonantly driven Bose–Einstein condensates

We show that the orbital Josephson effect appears in a wide range of driven atomic Bose–Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: the Gross–Pitaevskii equation, exact diagonalization of the few-mode problem and the multi-configurational time-dependent Hartree for bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that the few-mode approximation represents the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the (t,t′)-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.

On the existence of localized states in quantum pillars

We have investigated the localization of electrons in quantum pillars, i.e. in nanometric structures in which electrons are confined by 5 sides, but are free to communicate with a bulk substrate of the same material through the 6th side and hence can be considered as open from this side. All nanopillars produced by an etching top-down process conform to this physical model. At first sight, electrons in such structures should have an equal probability of being everywhere, so confinement effects and consequently band-gap changes should not be present. However, experimentally, confinement effects are observed. We show, by a proper effective mass equation analysis of the combined pillars and substrate system, that eigenstates with a high degree of localization exist in the pillars – irrespective of the height of the pillar. Moreover, the eigenenergies of these states are extremely close to the energies of the quantum boxes that would be produced if the pillars were closed by all six sides. This analysis provides the justification for the previous application of effective mass calculations on the pillars alone.

Opening up three quantum boxes causes classically undetectable wavefunction collapse.

One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the "three-box" quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315-2328] by using state-of-the-art control and measurement of the nitrogen vacancy center in diamond. In this protocol, the back-action of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurement-induced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59-87] that successfully addresses the measurement detectability loophole.

Evaluating dot–lead coupling in a non-parabolic quantum dot connected to two conducting leads

A manifestly novel approach is developed by considering excitons in a semiconductor non-parabolic quantum dot as hydrogen-atom-like quasi-particles confined in a spherical quantum box, the dot being connected to two conducting leads. In fact, the maximal dot–lead coupling energy is calculated in terms of maximum Fermi velocity within a new perspective.