Two-dimensional Potential Well Research Articles

Escape of a particle from two-dimensional potential well

Escape of a particle from two-dimensional potential well

Optical Stark deceleration of neutral molecules from supersonic expansion with a rotating laser beam**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504112, 91536218, and 11604100).

Cold molecules have great scientific significance in high-resolution spectroscopy, precision measurement of physical constants, cold collision, and cold chemistry. Supersonic expansion is a conventional and versatile method to produce cold molecules with high kinetic energies. We theoretically show here that fast-moving molecules from supersonic expansion can be effectively decelerated to any desired velocity with a rotating laser beam. The orbiting focus spot of the red-detuned laser serves as a two-dimensional potential well for the molecules. We analyze the dynamics of the molecules inside the decelerating potential well and investigate the dependence of their phase acceptance by the potential well on the tilting angle of the laser beam. ND3 molecules are used in the test of the scheme and their trajectories under the impact of the decelerating potential well are numerically simulated using the Monte Carlo method. For instance, with a laser beam of 20 kW in power focused into a pot of in waist radius, ND3 molecules of 250 m/s can be brought to a standstill by the decelerating potential well within a time interval of about 0.73 ms. The total angle covered by the rotating laser beam is about 5.24° with the distance travelled by the potential well being about 9.13 cm. In fact, the molecules can be decelerated to any desired velocity depending on the parameters adopted. This scheme is simple in structure and easy to be realized in experiment. In addition, it is applicable to decelerating both molecules and atoms.

Imaging of Plasmonic Eigen Modes in Gold Triangular Mesoplates by Near-Field Optical Microscopy

We investigated the spectral and spatial characteristics of plasmons induced in chemically synthesized triangular gold nano- and microplates by aperture-type scanning near-field optical microscopy. Near-field transmission images taken at plasmon resonance wavelengths showed two-dimensional oscillating patterns inside the plates. These spatial features were well reproduced by the square moduli of calculated eigen functions confined in the two-dimensional triangular potential well. From the irreducible representations of the eigen functions, it was found that both the out-of-plane modes and in-plane modes were clearly visualized in the near-field images. We compared near-field transmission images of a triangular nanoplate to those of a truncated one with a similar dimension and revealed that the fine details of the geometrical shape of the apex on the plate strongly influence the experimentally observed eigen mode structures. We also performed near-field transmission measurements of micrometer-scale triangu...

Dynamical properties of the soft-wall elliptical billiard.

Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.

Room-temperature hydrogen storage via two-dimensional potential well in mesoporous graphene oxide

Hydrogen is an excellent energy carrier free of carbon dioxide emission, but safe and efficient storage of hydrogen has been a bottleneck for the commercial use of hydrogen as a fuel. Here, we present a strategy based on simple thermodynamic principles that the density of a gas residing in a potential well increases exponentially relative to the ambient gas by the corresponding Boltzmann factor. This mechanism allows for enormously enhanced H2 storage in the form of delocalized gas permeating throughout the void space of a material, in contrast to conventional storage localized to specific adsorption sites. We create mesoporous graphene oxide that provides a two-dimensional potential well and efficient hydrogen diffusion pathways. The gravimetric storage density measured with quartz-crystal microbalance reaches 4.65wt% reproducibly at a modest pressure of 40atm at room temperature. Our work demonstrates the attainability of the long-standing goal of room-temperature hydrogen storage.

Interference effects in silicon-germanium heterostructures with quantum wells of different widths

Weak localization effects and the interactions of charge carriers are studied in two Si0.7Ge0.3/Si0.2Ge0.8/Si0.7Ge0.3 p-type heterostructures, where one or two quantum levels are filled, respectively. A weak localization effect for two-dimensional charge carriers is found to occur in weak magnetic fields when the spin-orbital and inelastic scattering times are close, which is indicative of splitting of the spin states under the influence of a perturbing potential related to the formation of a two-dimensional potential well (Rashba mechanism). In higher magnetic fields when one quantum level is occupied, interaction effects appear that are caused by Coulomb interactions with a scatterer. When the two quantum levels are occupied, the dominant mechanism is scattering on Friedel oscillations of the charge carrier density induced by an impurity electric field. In all regions, the quantum corrections are in good agreement with modern theoretical predictions.

Self-organization into quantized eigenstates of a classical wave-driven particle

A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave particle duality at quantum scale where the wave is probabilistic by nature. Yet some dual characteristics were observed in a system where a macroscopic droplet is guided by a pilot wave it generates. Here we investigate the behaviour of these entities when confined in a two-dimensional harmonic potential well. A discrete set of stable orbits is observed, in the shape of successive generalized Cassinian-like curves (circles, ovals, lemniscates, trefoils and so on). Along these specific trajectories, the droplet motion is characterized by a double quantization of the orbit spatial extent and of the angular momentum. We show that these trajectories are intertwined with the dynamical build-up of central wave-field modes. These dual self-organized modes form a basis of eigenstates on which more complex motions are naturally decomposed.

Quasi-Ballistic Hole Transport in an AlGaN/GaN Nanowire

An AlGaN/GaN nanowire, with an isosceles-triangle cross-section, was designed to create a large negative polarization at the (000-1) facet. The resultant band bending at this interface formed a two-dimensional potential well that accumulated a hole gas. Transistor operation based on the two-dimensional hole gas showed characteristics of quasi-ballistic transport. A small number of elastic scattering sites were evident from quantum interference characteristics in the current-voltage data.

Dimensional phase transition in small Yukawa clusters

We investigate the one- to two-dimensional zigzag transition in clusters consisting of a small number of particles interacting through a Yukawa (Debye) potential and confined in a two-dimensional biharmonic potential well. Dusty (complex) plasma clusters with n<or=19 monodisperse particles are characterized experimentally for two different confining wells. The well anisotropy is accurately measured, and the Debye shielding parameter is determined from the longitudinal breathing frequency. Debye shielding is shown to be important. A model for this system is used to predict equilibrium particle configurations. The experiment and model exhibit excellent agreement. The critical value of n for the zigzag transition is found to be less than that predicted for an unshielded Coulomb interaction. The zigzag transition is shown to behave as a continuous phase transition from a one-dimensional to a two-dimensional state, where the state variables are the number of particles, the well anisotropy and the Debye shielding parameter. A universal critical exponent for the zigzag transition is identified for transitions caused by varying the Debye shielding parameter.

Dusty plasma ring model

A model of a dusty plasma (Yukawa) ring is presented. We consider n identical particles confined in a two-dimensional (2D) annular potential well and interacting through a Debye (i.e. Yukawa or screened Coulomb) potential. Equilibrium configurations are computed versus n, the Debye shielding parameter and the trap radius. When the particle separation exceeds a critical value the particles form a 1D chain with a ring topology. Below the critical separation the zigzag instability gives a 2D configuration. Computed critical separations are shown to agree well with a theoretical prediction for the zigzag threshold. Normal mode spectra for 1D rings are computed and found to be in excellent agreement with the longitudinal and transverse dispersion relations for unbounded straight chains. When the longitudinal and transverse dispersion relations intersect we observe a resonance due to the finite curvature of the ring.

Two-dimensional position-dependent massive particles in the presence of magnetic fields

In this work, we discuss the problem of a particle with a position-dependent mass interacting with a two-dimensional potential well with finite depth, as well as under the influence of a uniform magnetic field. The ordering ambiguity is taken in account, and we obtain the exact wavefunctions and energies for a complete set of eigenstates. It is shown that, even considering a finite-depth potential well, the system retains an infinite set of quantum states.

A Helium Atom Confined by a Spherical Gaussian Potential Well

The helium atom confined by a non-impenetrable spherical box, i.e., a spherical Gaussian potential well which possesses finite height and range, is studied employing the exact diagonalization method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other: in general, the energies of the states decrease and the energy intervals between states increase with the reduction of the space dimensions.

Effect of Trapping on Vortices in Plasma

Microscopic trapping of electrons is considered in one- and two-dimensional potential wells (shallow and deep) and its effect on vortex formation is investigated by deriving modified Hasegawa Mima (HM) equations. Inhomogenieties in the number density and magnetic field are taken into account. The modified HM equations are analysed by considering bounce frequencies of the trapped particles. Solitary vortices are obtained via Kortweg deVries (KdV) type of equations and both exact and Sagdeev potential solutions are obtained. In general it is observed that trapping produces stronger non-linearities and this leads to the modification of the original HM equation.

Low-energy thermal excitations in the V-O system

The thermal excitations of the atoms of the V-O solid solution have been investigated by the slow-neutron scattering method for low-energy transfers. The features of the low-frequency excitations of a light impurity in the metal lattice for energy transfers ɛ ≈ 1.3 and 2.4 meV have been revealed. It is assumed that the observed low-energy excitations appear in V-O due to strong local distortions around an impurity atom, which are responsible for the formation of the effective potential of a complex shape with the almost flat bottom. Analysis of the interaction of oxygen with the nearest matrix atoms shows that the low-energy excitations of oxygen atoms can be attributed to the splitting of the ground state in the complex potential. The level scheme of the split state can be obtained in the representation of decelerated circular quantum rotation about the axis passing through the two nearest metal atoms or the motion in a two-dimensional potential well. The results indicate that rotational low-energy excitations can exist in (metal-interstitial impurity) solid solutions.

Kinematics of bosons in a two-dimensional potential well

Analysis of the kinematics of bosons (photons, atoms) in two-dimensional potential channels with the transverse eigenvalues slowly varying along the longitudinal axis of the channel reveals the existence of Bose condensation without temperature lowering, the stratification of an atomic flux over phase states, and also processes which phenomenologically reproduce phenomena in nonlinear media (shock-like waves). These phenomena can form the basis for new experimental methods.

Multidimensional WKB approximation for particle tunneling

A method for obtaining the WKB wave function describing the particle tunneling outside of a two-dimensional potential well is suggested. The Cartesian coordinates $(x,y)$ are chosen in such a way that the $x$ axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by simultaneous expansion of the wave function in the coordinate $y$ and the parameter determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. It is shown that the method provides systematic approximation to the outgoing probability flux. Both the technical and conceptual advantages of this approach in comparison with the usual approach based on the solution of classical equations of motion are pointed out. The method is applied to the problem of the coupled anharmonic oscillators and verified through the dispersion relations.

Coherent rotations of a single spin-based qubit in a single quantum dot at fixed Zeeman energy

Coherent rotations of single spin-based qubits may be accomplished electrically at fixed Zeeman energy with a qubit defined solely within a single electrostatically-defined quantum dot; the $g$-factor and the external magnetic field are kept constant. All that is required to be varied are the voltages on metallic gates which effectively change the shape of the elliptic quantum dot. The pseudospin-1/2 qubit is constructed from the two-dimensional $S=1/2$, $S_z=-1/2$ subspace of three interacting electrons in a two-dimensional potential well. Rotations are created by altering the direction of the pseudomagnetic field through changes in the shape of the confinement potential. By deriving an exact analytic solution to the long-range Coulomb interaction matrix elements, we calculate explicitly the range of magnitudes and directions the pseudomagnetic field can take. Numerical estimates are given for {GaAs}.

Molecular aggregation and shape effects in the optical spectra of organic dye molecules in SiO 2 and SiO 2-PMMA matrices

The electronic spectra of four different types of organic colorants embedded into sol–gel SiO 2 xerogel or into a hybrid SiO 2-PMMA matrix were studied experimentally using optical absorption, photoluminescence excitation, emission techniques, atomic force microscopy and fluorescence microscopy. The results show a well defined set of energy levels for each type of dye. It turns out that the type of matrix and the degree of aggregation of the organic molecules have relatively small effects on the energy spectra, although they have a strong influence on the optical absorption of the material. A quantum mechanical description of the electronic spectra of these molecules was developed on the basis of free electron molecular orbitals approach. For that the molecule is considered as a two-dimensional potential well, using both periodic (Born-von Karman) boundary conditions to take into account aggregation effects, and the commonly used infinite wall conditions. The results obtained have a good agreement with experimental spectra without adjustable parameters. A new simple method to calculate the energy spectra of and electron in a two-dimensional potential well is proposed. For that, it has been considered the electron motion in a ‘box’ with reflecting walls, giving us a result identical to the classical model for rectangular-shaped molecules. This method also allows us to treat the triangular-shaped molecules, the results obtained being in a reasonable agreement with experiment, also without any adjustable parameters.

Quantum interferometry and spin–orbit effects in a heterostructure with a 2D hole gas in a Si0.2Ge0.8 quantum well

The magnetic-field dependence (up to 110 kOe) of the resistance of Si0.7Ge0.3/Si0.2Ge0.8/Si0.7Ge0.3 with a 2D hole gas in a Si0.2Ge0.8 quantum well is measured in the temperature range 0.335–10 K and in a range of variation of the currents from 100 nA to 50 μA. Shubnikov–de Haas oscillations are observed in the region of high magnetic fields, and in the low-field region H⩽1 kOe a positive magnetoresistance is observed which gives way to a negative magnetoresistance as the field is increased. This peculiarity is explained by effects of weak localization of the 2D charge carriers under conditions when the spin–orbit scattering time τso is close to the inelastic scattering time τφ, and it is evidence of a splitting of the spin states under the influence of a perturbing potential due to the formation of a two-dimensional potential well (the Rashba mechanism). Analysis of the weak localization effects gave the values of the characteristic relaxation times as τφ=7.2T−1×10−12 s and τso=1.36×10−12 s. From these characteristics of the heterostructure studied, a value of Δ=2.97 meV was obtained for the spin splitting.

Structure and Optical Properties of Nanocomposites Prepared by the Incorporation of Organic Dyes into a SiO 2 and SiO 2 -PMMA Glassy Matrix*

Electronic spectra of nine different types of organic colorants embedded in three different matrices (sol–gel SiO2 , PMMA, and SiO2–PMMA) were studied experimentally with the use of optical absorption, photoluminescence excitation, and emission techniques, as well as fluorescent microscopy and atomic force microscopy. We found a distinct set of energy levels for each type of dye. The type of matrix and the degree of aggregation of the organic molecules have relatively small effects on the spectra, although their influence on the optical density of the material is essential. The character of the energy spectra is mainly related with the shape of the dye molecule. A quantum mechanical description of the electronic spectra of these molecules was made on the basis of the free electron molecular orbitals approach. The molecules were considered as two-dimensional potential wells with different shapes. The effect of boundary conditions on the energy spectra was studied. The direct solution of the Schrodinger equation shows a good theory–experiment correlation.