Energy Level Spacing Research Articles

Geometrical and spectral study of β-skeleton graphs.

We perform an extensive numerical analysis of β-skeleton graphs, a particular type of proximity graphs. In a β-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter β∈(0,∞), is satisfied. Moreover, for β>1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of β, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at β=1.

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of hw for neutrons and protons separately, as functions of the neutron number Ν and the proton number Ζ respectively, are derived. The dependence of hωn{hωp) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of hω show "discontinuities in the slope" at the closed shells throughout the periodic table. The difference hωn — hωΛ is also discussed

Determination of the Harmonic Oscillator Energy Level Spacing for Atomic Clusters

The harmonic oscillator energy level spacing Κω for atomic clusters as a function of the particle number Ν is expressed analytically in terms of the parameters of a Woods-Saxon (or Symmetrized Woods-Saxon) potential which approximates the effective spherical self-consistent jellium model potential. The expressions derived depend an the particular scheme adopted to approximate the potential by the harmonic oscillator one and on the assumed dependence of the potential radius R on N. It is also observed, considering the case of sodium clusters,that for large Ν the expressions of Ηω are in good agreement with the well known expression of Ηω in terms of the Wigner-Seitz radius.

Enhanced precision bound of low-temperature quantum thermometry via dynamical control

High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.

Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

We experimentally investigate spectral statistics in Anderson localization in two-dimensional amorphous disordered media. Intensity distributions captured over an ultrabroad wavelength range of $\sim 600$~nm and averaged over numerous configurations provided the Ioffe-Regel parameter to be $\sim2.5$ over the investigated wavelength range. The spectra of the disordered structures provided access to several quasimodes, whose widths and separations allowed to directly estimate the optical Thouless conductance $g_{Th}$, consistently observed to be below unity. The probability distribution of $g_{Th}$ was measured to be a log-normal. Despite being in the Anderson localization regime, the spacings of energy levels of the system was seen to follow a near Wigner-Dyson function. Theoretical calculations based on the tight-binding model, modified to include coupling to a bath, yielded results that were in excellent agreement with experiments. From the model, the level-spacing behavior was attributed to the degree of localization obtained in the optical disordered system.

Energy-level splitting for weakly interacting bosons in a harmonic trap

We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling parameter, these degenerate levels split, and we study the patterns of this splitting. It turns out that the problem is mathematically identical to diagonalizing the quantum resonant system of the two-dimensional Gross-Pitaevskii equation, whose classical counterpart has been studied previously in the mathematical literature on turbulence. Our purpose is to explore the implications of the symmetries and energy bounds of this resonant system, previously studied for the classical case, for the quantum level splitting. Simplifications in computing the splitting spectrum numerically result from exploiting the symmetries. The highest energy state emanating from each unperturbed level is explicitly described by our analytics. We furthermore discuss the energy-level spacing distributions in the spirit of quantum chaos theory. After separating the eigenvalues into blocks with respect to the known conservation laws, we observe the Wigner-Dyson statistics within specific large blocks, which leaves little room for further integrable structures in the problem beyond the symmetries that are already explicitly known.

Femtosecond time-resolved spectroscopic photoemission electron microscopy for probing ultrafast carrier dynamics in heterojunctions

The fast developing semiconductor industry is pushing to shrink and speed up transistors. This trend requires us to understand carrier dynamics in semiconductor heterojunctions with both high spatial and temporal resolutions. Recently, we have successfully set up a time-resolved photoemission electron microscopy (TR-PEEM), which integrates the spectroscopic technique to measure electron densities at specific energy levels in space. This instrument provides us an unprecedented access to the evolution of electrons in terms of spatial location, time resolution, and energy, representing a new type of 4D spectro-microscopy. Here in this work, we present measurements of semiconductor performance with a time resolution of 184 fs, electron kinetic energy resolution of 150 meV, and spatial resolution of about 150 nm or better. We obtained time-resolved micro-area photoelectron spectra and energy-resolved TR-PEEM images on the Pb island on Si(111). These experimental results suggest that this instrument has the potential to be a powerful tool for investigating the carrier dynamics in various heterojunctions, which will deepen our understanding of semiconductor properties in the submicron/nanometer spatial scales and ultrafast time scales.

Ladder climbing and autoresonant acceleration of the spherical plasma density wave

Ladder climbing (LC) and autoresonance (AR) of the spherical plasma density wave are studied for the first time. The governing equation of the perturbed spherical density wave in the energy level space based on a hydrodynamic model of the electron plasma is presented, and it is demonstrated that the quantum LC and classical AR transition can be achieved in the spherical plasma. The asymptotic thresholds of the LC and AR transition of the spherical plasma wave are obtained analytically and confirmed numerically. We find that the spherical wave energy is concentrated to the sphere center as the density wave climbs to the higher level, the spherical plasma behaves obvious compression character, and the perturbed density of the sphere center even can be amplified to 100 times larger of the initial perturbed density. Compared to the one-dimensional case, the energy spectrum of the spherical plasma wave shifts upward, and the energy level spacing of the spherical plasma wave is broadened. These result in the facts that the spherical plasma needs the larger driving strength to achieve the LC and AR, while the total perturbed density of the spherical plasma always is larger than that of the one-dimensional case.

Non-relativistic and relativistic investigation of the low lying electronic states of Sr2+Xe, Sr+Xe and SrXe systems

The potential energy curves and permanent and transition dipole moments of the neutral SrXe and the ionic Sr+Xe systems are calculated with an ab initio approach using pseudopotential techniques, core polarization potentials, large Gaussian basis sets and full configuration interaction for two electron calculations. The spectroscopic constants of the ground state and lower excited states are in good agreement with the available experimental and theoretical works. The spin–orbit coupling is also included for the ionic system Sr+Xe and the neutral one SrXe. Its effect is significant on the potential energy curves, dipole moments and energy level spacing. For SrXe, the spin–orbit splitting has been considered for the states (2)3Σ0,1, (1,2)3Π0,1,2 and (1)3Δ0,1,2,3.

Temperature dependence of the magnetization of La0.67Sr0.33MnO3 thin films on LaAlO3

The authors report on the interplay between magnetically ordered phases with temperature and magnetic field across compressively strained interfaces of thin La0.67Sr0.33MnO3 films on LaAlO3 substrates. From the temperature dependence of the magnetization and resistivity studies, they find two distinct temperature regimes, where this interplay is clearly exhibited. They ascribe this to the strain induced Jahn–Teller-like distortion that favors the stabilization of the d3z2−r2 orbitals and enhances superexchange between adjoining Mn atoms. The temperature and field sweep of the magnetization and electronic transport lead to a hybridization between the closely spaced energy levels of d3z2−r2 and dx2−y2 orbitals leading to the coexistence of ferromagnetic and antiferromagnetic phases. Such an observation, not reported earlier, offers new routes for the design and study of magnetic textures in variously strained interfaces between perovskite oxides.

Dopant‐Dependent Increase in Seebeck Coefficient and Electrical Conductivity in Blended Polymers with Offset Carrier Energies

AbstractThe strong and counterproductive interrelationship of thermoelectric parameters remains a bottleneck to improving thermoelectric performance, especially in polymer‐based materials. In this paper, a compositional range is investigated over which there is decoupling of the electrical conductivity and Seebeck coefficient, achieving increases in at least one of these two parameters while the other is maintained or slightly increased as well. This is done using an alkylthio‐substituted polythiophene (PQTS12) as additive in poly(bisdodecylquaterthiophene) (PQT12) with tetrafluorotetracyanoquinodimethane (F4TCNQ) and nitrosyl tetrafluoroborate (NOBF4) as dopants. The power factor increases two orders of magnitude with the PQTS12 additive at constant doping level. Using a second pair of polymers, poly(2,5‐bis(3‐dodecylthiophen‐2‐yl)thieno[3,2‐b]thiophene (PBTTTC12) and poly(2,5‐bis(3‐dodecylthiothiophen‐2‐yl)thieno[3,2‐b]thiophene, (PBTTTSC12), with higher mobilities, decoupling of the Seebeck coefficient and electrical conductivity is also observed and higher power factor is achieved. Distinguished from recently reported works, these two sets of polymers possess very closely offset carrier energy levels (0.05–0.07 eV), and the microstructure, assessed using grazing incidence X‐ray scattering, and mobility evaluated in field‐effect transistors, are not adversely affected by the blending. Experiments, calculations, and simulations are consistent with the idea that blending and doping polymers with closely spaced energy levels and compatible morphologies to promote carrier mobility favors increased power factors.

Precise estimation of doping-dependent Raman effect in inorganic solids

Here we solve the problem of estimating the Raman frequency shift and the changes to Raman peak intensity due to doping (or changing chemical composition) and temperature consistently. The formalism employed to derive the temperature and doping-dependent Raman intensity ratio [or the ionization energy theory (IET)-based Raman intensity ratio] formula is based on the IET and the energy-level spacing renormalization group method. Therefore, our formalism is entirely based on first principles that does not require any guessed wavefunction nor intrinsic adjustable parameter anywhere in our analysis. The IET-Raman theory is then applied to Si(111), CdS, CdSe, $$\text{Cd}_{1-x}\text{Ca}_x\text{TiO}_3$$ and 6H–SiC in order to expose the changes observed in the Raman spectra with respect to their peak intensity and frequency shift. We shall prove and highlight that the experimental Raman spectra obtained for the above-stated materials obey the physicochemical mechanism derived from the IET-Raman intensity formula unambiguously and without any exception. It is worth noting that the said formula can be implemented in all Raman spectroscopy machines as an additional feature to predict the Raman frequency shift and the Raman peak intensity with respect to temperature and changing chemical composition.

Resonance interaction between uniformly rotating two-level entangled atoms

We investigate the influence of acceleration and boundaries on the resonance interaction between two identical two-level entangled atoms in synchronous circular motions mediated by a fluctuating massless quantum scalar field. In the ultra-relativistic limit, we give the analytical results of the resonance interaction energy either in the absence or in the presence of a reflecting plane boundary. Our results indicate that the interatomic resonance interaction energy depends on the atomic intrinsic energy level spacing, the atomic acceleration, the interatomic separation, and the distance of the atoms from the boundary. By adjusting these parameters, the resonance interatomic force can be either enhanced or weakened and even its direction can be altered as compared with the case of two inertial entangled atoms in an unbounded Minkowski spacetime. Our work clearly suggests that the resonance interatomic interaction can be regulated and controlled significantly by changing the atomic motion state and the field’s boundary condition.

Spontaneous parametric four wave mixing and fluorescence lifetime manipulation in the diamond nitrogen vacancy center

We report the lifetime of spontaneous parametric four wave mixing (SP-FWM) and multiorder fluorescence in two-, three-, and four-level systems of negatively charged nitrogen vacancy (NV−) in diamond. The lifetime of SP-FWM is enhanced at high power by the induced dark state from coupling fields. The reduction and enhancement in fluorescence lifetime are attributed to destructive and constructive quantum interference, respectively. The quantum interference is induced by interaction among different decay pathways of spontaneous emission by closely spaced energy levels, which can be controlled by dipole–dipole interaction and the mutual orientations of dipole moments. The lifetime is observed to be longer in two-level as compared to three-level and four-level systems. The different measured lifetimes suggest the sensitivity of these NV systems to quantum interference and the dressing effect. These outcomes may provide new insights in development of all-optical communication devices and quantum storage on photonic chips.

Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles

We address the exact relations for the energy spectrum of massive Dirac fermions of graphene for a class of position-dependent magnetic field profiles, which could be created under inhomogeneous strain fields, with possibility of inducing a Dirac gap. We then show that in the linear regime our results correspond well to the earlier approaches for the massless case. We also prove that our approach for obtaining the relativistic Landau levels of Dirac fermions created by a constant magnetic field together with a spatially varying normal pseudo-magnetic profile, which varies as $ 1/x^2$ , recovers well the earlier results in this regard. It turns out that, in this case, the associated Landau energy levels are obtained by considering two shape-invariant potentials which belong to the family of isotonic oscillators with a set of equally spaced energy levels.

Development of Modulation p-Doped 1310 nm InAs/GaAs Quantum Dot Laser Materials and Ultrashort Cavity Fabry–Perot and Distributed-Feedback Laser Diodes

Multiple-layer InAs/GaAs quantum dot (QD) laser structures were etched to remove the p-side AlGaAs cladding layers to investigate the temperature-dependent photoluminescence (PL) characteristics. Four QD samples, including undoped as grown QDs, p-doped as grown QDs, undoped annealed QDs, and p-doped annealed QDs, were prepared by molecular beam epitaxy (MBE) and a postgrowth annealing process for comparison. Among them, modulation p-doped QD samples exhibit much less temperature-dependent characteristics of PL spectra and notable insensitivity to intermixing compared to undoped ones. This is attributed to the effects of modulation p-doping, which can inhibit holes’ thermal broadening in their closely spaced energy levels and significantly suppress In/Ga interdiffusion between QDs and their surrounding matrix. These results provide greater freedom in the choice of MBE growth for high-quality active regions and claddings of QD laser diodes. The superior features of the modulation p-doped QD materials have b...

The effect of defect emissions on enhancement photocatalytic performance of ZnSe QDs and ZnSe/rGO nanocomposites

A systematic study about the origin of defects emission of ZnSe structure was conducted by photoluminescence (PL) spectrometer at room temperature. It was observed that different intermediate energy levels in band-gap space of ZnSe structure were generated by different defects such as Se-, Zn-vacancies, Se-, Zn-interstitials, and surface states. Effects of these defects on the photocatalytic performance of ZnSe quantum dots (QDs) and ZnSe/graphene nanocomposites were investigated. The pristine ZnSe QDs and ZnSe/graphene nanocomposites were synthesized by a co-precipitation method. The PL spectra of the samples showed four emissions from four regions of the visible spectrum such as violet, green, orange, and red emissions. The violet emission was associated with the near-band-edge (NBE) of the ZnSe nanostructures, while, the other emissions were related to different defects of ZnSe structures. Annealing the samples in the H2 atmosphere caused to increase orange emission intensity and indicated that origin of orange emission was a donor-acceptor pair (DAPs) related to singly positively charged Se-vacancies (VSe) to singly negatively charged zinc vacancy (VZn−). Photocatalytic study of the samples to remove the methylene blue (MB) dye showed that the photocatalytic performance of the samples improved by graphene as an additive and increasing the orange emission intensity.

Observation of giant conductance fluctuations in a protein

Proteins are insulating molecular solids, yet even those containing easily reduced or oxidized centers can have single-molecule electronic conductances that are too large to account for with conventional transport theories. Here, we report the observation of remarkably high electronic conductance states in an electrochemically inactive protein, the ∼200 kD αVβ3 extracellular domain of human integrin. Large current pulses (up to nA) were observed for long durations (many ms, corresponding to many pC of charge transfer) at large gap (>5 nm) distances in an STM when the protein was bound specifically by a small peptide ligand attached to the electrodes. The effect is greatly reduced when a homologous, weakly binding protein (α4β1) is used as a control. In order to overcome the limitations of the STM, the time- and voltage-dependence of the conductance were further explored using a fixed-gap (5 nm) tunneling junction device that was small enough to trap a single protein molecule at any one time. Transitions to a high conductance (∼nS) state were observed, the protein being ‘on’ for times from ms to tenths of a second. The high-conductance states only occur above ∼100 mV applied bias, and thus are not an equilibrium property of the protein. Nanoamp two-level signals indicate the specific capture of a single molecule in an electrode gap functionalized with the ligand. This offers a new approach to label-free electronic detection of single protein molecules. Electronic structure calculations yield a distribution of energy level spacings that is consistent with a recently proposed quantum-critical state for proteins, in which small fluctuations can drive transitions between localized and band-like electronic states.

Resonances in a periodically driven bosonic system.

Periodically driven systems are a common topic in modern physics. In optical lattices specifically, driving is at the origin of many interesting phenomena. However, energy is not conserved in driven systems, and under periodic driving, heating of a system is a real concern. In an effort to better understand this phenomenon, the heating of single-band systems has been studied, with a focus on disorder- and interaction-induced effects, such as many-body localization. Nevertheless, driven systems occur in a much wider context than this, leaving room for further research. Here, we fill this gap by studying a noninteracting model, characterized by discrete, periodically spaced energy levels that are unbounded from above. We couple these energy levels resonantly through a periodic drive, and discuss the heating dynamics of this system as a function of the driving protocol. In this way, we show that a combination of stimulated emission and absorption causes the presence of resonant stable states. This will serve to elucidate the conditions under which resonant driving causes heating in quantum systems.

Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm.

Quantum algorithms use the principles of quantum mechanics, such as, for example, quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimization, simulation, and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3/2 spin carried by a Tb ion sitting in a single molecular magnet transistor. The coherent manipulation of this multilevel quantum system (qudit) is achieved by means of electric fields only. Grover's search algorithm is implemented by constructing a quantum database via a multilevel Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multilevel quantum system with nonequal spaced energy levels, opening the way to novel quantum search algorithms.