Quantized Energy States Research Articles

In situ laser microprocessing of single self-assembled quantum dots and optical microcavities

The authors employ a focused laser beam both as a probe and as a local heat source to tune in situ, over a broad range and with resolution-limited accuracy, the quantized energy states of single optical microcavities and self-assembled quantum dots (QDs). The approach is demonstrated by bringing an optical mode of a microdisk into resonance with the emission of a single QD and by tuning spatially separated QDs in mutual resonance. This processing method may be used, e.g., to fabricate arrays of perfectly resonant QDs.

Artificial Atom in Carbon Nanotubes and its Teraherz Response

Single quantum dots (QDs) have been fabricated in an individual single-wall carbon nanotube (SWCNT) simply by depositing source-drain metal on it. The SWCNT between the contacts behaved as a single QD. The single electron transport measurements have been carried out in a dilution refrigerator, which revealed unique artificial atom behavior. Those include clear observation of quantized energy states and their Zeeman splitting in magnetic fields, two or four electron shell structures, and quantum states of an interacting two-electron system. The above characteristics are well modeled by electrons confined in a one-dimensional hard wall potential. The unique features in the SWCNT artificial atom, as compared with semiconductor artificial atoms, are, first, that the single electron charging energy and the quantized level spacing are larger by more than an order, and, second that the simple shell structures are observable even with many electrons in the dot. To demonstrate the larger energy scales for the artificial atom, the teraherz (THz) photon assisted tunneling is presented.

Theoretical Study on Controllability of Quantum State Energy in an InGaAs/GaAs Quantum Dot Buried in InGaAs

We theoretically studied the relationship between quantum energy states and structural parameters of an InGaAs/GaAs quantum dot (QD) buried in strained InGaAs, emitting at 1.1 to 1.4 em. The crystal distortion of the buried QD structure in three dimensions was computed based on the three-dimensional finite element method. Under the computed strain fields, the Schrödinger equation was solved to obtain wavefunctions and eigenenergies. By calculating the dependence on structural parameters, we investigated the controllable range of the ground state energy and the energy separation between the ground state and the first excited state. We found that the energy separation exhibited a maximum value as a function of QD composition, enabling us to identify the composition of the QD structure. The effects of the burying layer composition and QD diameter were also investigated to expand the controllable range of the state energy. We also showed that the wavefunction symmetry was improved by burying the QD in the InGaAs layer. Our results will be useful in developing advanced devices for optical telecommunications and quantum information technology.

Resonant transmission through a double domain wall in magnetic nanowires

As experimentally verified, a large magnetoresistance arises due to domain walls creation (or destruction) in Ni nanowires and in some nanostructures based on GaMnAs magnetic semiconductors. Hence the presence and structuring of magnetic domain walls have important potential applications in magnetoelectronics devices. Here, we uncover a way of controlling the conductance via resonant transmission through a double domain wall structure. This phenomenon is due to quantum interference of charge carrier wave functions in spin quantum wells, which leads to the formation of quantized energy states in the potential well created by a double domain wall. When the energy of a state in the spin quantum well is resonant with the Fermi energy in the wire, the spin–flip transmission through the domain walls becomes most effective. This gives rise to a resonance-type dependence of the conductance on the distance between the domain walls or on the Fermi energy.

Continuous-wave operation of 1.5μm InGaAs∕InGaAsP∕InP quantum dot lasers at room temperature

Continuous-wave operation at room temperature from InGaAs∕InGaAsP∕InP quantum dot (QD) laser diodes (LD) has been achieved. A ridge waveguide QD LD with 7 QD-stacks in the active region lases at 1.503μm at 20°C and that with 5 QD-stacks lases at 1.445μm at room temperature. The shift in lasing wavelength is believed to be due to the difference in the quantized energy states involved in producing gain for lasing. With smaller number of QD stacks and shorter cavity length, the lasing wavelength shifts to shorter wavelength indicating that more of higher excited states are involved in producing gain. By increasing the number of QD stacks to 15, lasing at 1.56μm has been achieved under pulsed mode.

Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

This paper studies the elastic fields in InAs∕GaAs quantum wire (QWR) structures arising from the lattice mismatch between InAs and GaAs. The present treatment is different from recent analyses based on the Eshelby inclusion approach where the QWR material, for simplicity, is assumed to be the same as the matrix/substrate. Here, a more complete treatment is developed taking into account the structural inhomogeneity using the boundary integral equation method. We implement our model using discrete boundary elements at the interface between the QWR and its surrounding matrix. The coefficients of the algebraic equations are derived exactly for constant elements using our recent Green’s-function solutions in the Stroh formalism. For both (001) and (111) growth directions, our results show that while the elastic fields far from the QWR are approximated well by the homogeneous inclusion approach, for points within or close to the QWR, the differences between the fields computed with the simplified inclusion and complete inhomogeneity models can be as large as 10% for the test system. These differences in the strain fields will have strong implications for the modeling of the quantized energy states of the quantum wire nanostructures. Since the strain fields inside and close to the wire are more important than the exterior strain fields from the standpoint of the confined electronic states, we suggest that in the vicinity of the QWR, the inhomogeneity model be used with proper elastic constants, while the simple exact inclusion model be used in the bulk of surrounding medium.

Spectroscopic and NMR identification of novel hydride ions in fractional quantum energy states formed by an exothermic reaction of atomic hydrogen with certain catalysts

2K+ to K + K2+ and K to K3+ provide a reaction with a net enthalpy equal to one and three times the potential energy of atomic hydrogen, respectively. The presence of these gaseous ions or atoms with thermally dissociated hydrogen formed a so-called resonance transfer (rt)-plasma having strong VUV emission with a stationary inverted Lyman population. Significant line broadening of the Balmer , , and lines of 18 eV was observed, compared to 3–4 eV from a hydrogen microwave plasma. Emission from rt-plasmas occurred even when the electric field applied to the plasma was zero. The reaction was exothermic since excess power of 20 mW cm−3 was measured by Calvet calorimetry. An energetic catalytic reaction was proposed involving a resonant energy transfer between hydrogen atoms and 2K+ or K to form very stable novel hydride ions H−(1/p) called hydrino hydrides having a fractional principal quantum numbers p = 2 and p = 4, respectively. Characteristic emission was observed from K2+ and K3+ that confirmed the resonant nonradiative energy transfer of 27.2 eV and 3 × 27.2 eV from atomic hydrogen to 2K+ and K, respectively. The product hydride ion H−(1/4) was observed spectroscopically at 110 nm corresponding to its predicted binding energy of 11.2 eV. The 1H MAS NMR spectrum of novel compound KH*Cl relative to external tetramethylsilane (TMS) showed a large distinct upfield resonance at −4.4 corresponding to an absolute resonance shift of −35.9 ppm that matched the theoretical prediction of p = 4. A novel peak of KH*I at −1.5 ppm relative to TMS corresponding to an absolute resonance shift of –33.0 ppm matched the theoretical prediction of p = 2. The predicted catalyst reactions, position of the upfield-shifted NMR peaks for H−(1/4) and H−(1/2), and spectroscopic data for H−(1/4) were found to be in agreement with the experimental observations as well as previously reported spectroscopic data for H−(1/2) and analysis of KH*Cl and KH*I containing these hydride ions.

A closed-form expression to analyze electronic properties in delta-doped heterostructures

We develop a closed-form model to describe the electronic properties for delta modulation doped heterostructures, particularly the 2DEG sheet charge density and the electric field distribution in the direction of growth. The model includes the effects of real-space charge transfer and carrier degeneracy. The electron transfer and quasi-equilibrium condition in growth direction have been used in order to express the 2DEG sheet charge density that is only a function of material parameters and constants. An empirical constant, corresponding to quantized energy states, has been employed to further simplify this description and to arrive at a closed-form expression. Results from the analytical expressions are shown to agree well with numerical simulations based on a self-consistent solution of a modified Schrödinger and Poisson equations. In addition to their use in modeling of current conduction in modulation doped field effect transistors (MODFETs), we expect that these expressions would serve as versatile tools in the modeling of optical and spectral effects that occur in the AlGaAs/GaAs heterostructures.

The nature of free electrons in superfluid helium—a test of quantum mechanics and a basis to review its foundations and make a comparison to classical theory

The Schrödinger equation was originally postulated in 1926 as having a solution of the one electron atom. It gives the principal energy levels of the hydrogen atom as eigenvalues of eigenfunction solutions of the Laguerre differential equation. But, as the principal quantum number n⪢1, the eigenfunctions become nonsensical. Despite its wide acceptance, on deeper inspection, the Schrödinger solution is plagued with many failings as well as difficulties in terms of a physical interpretation that have caused it to remain controversial since its inception. Only the one electron atom may be solved without approximations, but it fails to predict electron spin and leads to models with nonsensical consequences such as negative energy states of the vacuum, infinities, and negative kinetic energy. In addition to many predictions which simply do not agree with observations, the Schrödinger equation predicts noncausality, nonlocality, spooky actions at a distance or quantum telepathy, perpetual motion, and many internal inconsistencies where contradicting statements have to be taken true simultaneously. Recently, the behavior of free electrons in superfluid helium has again forced the issue of the meaning of the wave function. Electrons form bubbles in superfluid helium which reveal that the electron is real and that a physical interpretation of the wave function is necessary. Furthermore, when irradiated with light of energy of about a 0.5 to several electron volts (H.J. Marris, J. Low Temp. Phys. 120 (2000) 173), the electrons carry current at different rates as if they exist with different sizes. It has been proposed that the behavior of free electrons in superfluid helium can be explained in terms of the electron breaking into pieces at superfluid helium temperatures (H.J. Marris, J. Low Temp. Phys. 120 (2000) 173). Yet, the electron has proven to be indivisible even under particle accelerator collisions at 90 GeV (LEPII). The nature of the wave function must now be addressed. It is time for the physical rather than the mathematical nature of the wave function to be determined. A theory of classical quantum mechanics (CQM) was derived from first principles by Mills (The grand unified theory of classical quantum mechanics. January 2000 ed; Cranbury, NJ, 2000, Blacklight Power, Inc., (Distributed by Amazon.com; Posted at www.blacklightpower.com)) that successfully applies physical laws on all scales. Using the classical wave equation with the constraint of nonradiation based on Maxwell's equations, CQM gives closed form physical solutions for the electron in atoms, the free electron, and the free electron in superfluid helium. The prediction of fractional principal quantum energy states of the electron in liquid helium match the photoconductivity and mobility observations without requiring that the electron is divisible.

Organic single-quantum-well electroluminescent device

A new kind of single-quantum-well electroluminescent (EL) device consists of a hole transport N,N-Bis(3-methyphenyl)-N,N-diphenylbenzidine(TPD) layer, and electron transport 8-(quinolinolate)-aluminum(Alq) layer and a light emitting layer of Alq doped with 5,6,11,12-tetraphenylnaphthacene (rubrene) has been fabricated by the multisource-type high-vaccum organic molecular deposition. The dopant rubrene is as a potential well, and the undoped Alq layer is as a barrier layer. The EL spectra shows the spectral narrowing and the emission peak energy blue-shift, and the efficiency and luminance of the device have been significantly improved. The experimental phenomena is explained as the result of recombination of carriers from the quantized energy state.

Characteristics of the Organic Single-Quantum-Well Devices Fabricated by the Doping Method

A doping technique to fabricate an organic quantum-well electroluminescent device is demonstrated. The fabricated single-quantum-well device consists of the following structure: an N,N'-Bis(3-methyphenyl)-N,N'-diphenylbenzidine layer for hole transportation, an 8-(quinolinolate)-aluminum(Alq) layer for electron transportation and a light emitting layer of Alq doped with 5,6,11,12-tetraphenylnaphthacene(rubrene). The dopant rubrene serves as a potential well, whereas the undoped Alq layer serves as a barrier layer. The efficiency and luminance of the device have been significantly improved. The observed phenomena of the spectral narrowing and the emission peak energy blue-shift are a result of the recombination of carriers from the quantized energy states.

Mass quantization of the Schwarzschild black hole

We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild black hole in Kucha\v r-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are non-vanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner (ADM) mass of the black hole according to a relation conjectured long ago by Bekenstein, $M \sim \sqrt{n}M_p$. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.

Study on GaAs/GaAlAs MQW structure for photovoltaic applications

GaAs/GaAlAs MQW structures with varying well widths having narrowest wells on the top layers and gradually wider wells for the inner layers were studied and confirmed by Auger spectroscopy and photoluminescence measurements. Multiplication of quantum wells gives stronger photoluminescence due to higher density of quantized states in the structure. This MQW structure was experimented in the photoconductivity and photocurrent measurements at room temperature. It is found that at low multiplication of quantum wells in MQW structure, the photoconductivity effect was mainly controlled by bulk material as shown in the spectral response. Photocurrent at low bias voltage shows relatively better spectral sensitivity at shorter wavelength. The photoconductivity and photocurrent measurements indicate that appropriate MQW structures acting as broader absorbers due to graded characters of quantized energy states are needed for photovoltaic application. Integration of MQW structure to solar cell structure was also investigated.

Optical properties of ZnS and [formula omitted] MQW grown by molecular beam epitaxy on GaAs and CaF2 substrates

ZnS-based II–VI materials were successfully grown by molecular beam epitaxy (MBE). Epitaxial growth was confirmed on GaAs(100) and CaF2(100) substrates by observing reflection high-energy electron diffraction (RHEED) patterns. The low-temperature photoluminescence (PL) spectrum of undoped ZnS grown on both substrates exhibits dominant excitonic emission without any deep emission. Nitrogen (N) doping of ZnS was performed using an RF plasma cell. A new excitonic emission related to N-acceptors was observed around 3.765 eV. A ZnCdSZnS multiple quantum well (MQW) exhibits a dominant excitonic PL band, and its quantized energy states up to n = 3 were observed in the photoluminescence excitation (PLE) spectrum by monitoring the lower energy side of the PL emission. Oscillatory structures at equidistant energies (about 42 meV) were also observed in the PLE spectrum by monitoring the higher energy side of the PL emission. These peaks are attributed to a multiple-LO-phonon relaxation process of hot excitons.

The interpretation of experimentally measured magnetic susceptibilities of a SQUID ring in terms of the quantum mechanics of a double Josephson junction

For some years, experimental measurements of magnetic susceptibilities of SQUIDs have been reported and interpreted in terms of a quantum mechanical model that depends on the system having a very small capacitance ( F) and occupying different quantum energy states for macroscopically long times. This interpretation is criticized on the grounds that the relevant capacitance is very much larger and that the very long lifetimes are difficult to understand. An alternative model, consisting of a grain or island connected to the SQUID ring by two Josephson junctions, is proposed. The capacitance relevant to symmetric motion of charge on and off the island through the two junctions is then of the right order and the other degrees of freedom of the system are treated classically. The resulting susceptibilities are in reasonably good agreement with experiment. The question of the long lifetimes of the states is considered in some detail, and their implications for the conventional and normal-electron tunnelling resistance are analysed.

Photon-assisted transport through quantized energy states in a lateral dual-gate device.

Photon-assisted transport through quantized energy states in a lateral dual-gate device.

Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e2/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.

Nanometer-scale columns in GaAs fabricated by angled chlorine ion-beam-assisted etching

Angled chlorine ion-beam-assisted etching has been used in combination with masked ion beam lithography to produce columns in GaAs with widths of less than 10 nm and height-to-width ratios greater than 25. This technique allows the highly controllable fabrication of structures with dimensions smaller than initially defined by the lithography. It can be applied to the fabrication of ultrasmall GaAs/AlGaAs quantum well structures having quantized energy states in two or three dimensions while at the same time being compatible with full-wafer processing.

On the correspondence between classical and quantum energy states in stationary geometries

On the correspondence between classical and quantum energy states in stationary geometries

Quantum and classical relativistic energy states in stationary geometries

The positive and negative root states ( E +, E −) for a particle moving along a geodesic in a stationary background, introduced by Christodoulou and Ruffini, are here interpreted in the framework of a relativistic quantum field theory. It is shown how E + and E − have to be considered as the classical correspondent of the positive and negative energy states of a quantized field. It is explicitly shown that crossing between the states E + and E − can occur and consequently the necessary condition for particle creation as given by Klein, Sauter, Heisenberg and Euler can be encountered.