N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Exact results for the spectra of bosons and fermions with contact interaction

An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.     

Cardinality enhancement of spectral/spatial modified double weight code optical code division multi-access system by PIIN suppression

A new two-dimensional (2-D) optical code division multiple access (OCDMA) scheme to increase the achievable system capacity is proposed. The code exhibits good cross-correlation property time and wavelength shift. Performances are analyzed on code size and correlation properties affecting two important system parameters, bit error rate (BER) as a function of cardinality generated and optical power transmission requirement. The proposed system can effectively suppress phase-induced intensity noise (PIIN) and has multi-access interference (MAI) cancellation property. Results in a good agreement indicate that 2-D modified double weight (MDW) offers 163.7% and 336.2% larger cardinality compare to 2-D perfect difference code (PDC) and 2-D modified quadratic congruence (MQC) code. By increasing spatial code (N) and keeps similar code length system performance can be further optimized. 2-D MDW (M = 45, N = 18) accommodates 252.2% and 18.3% cardinality increment and low effective transmitted power (P_sr) at −17.9 dBm, compare to 2-D MDW (M = 247, N = 3) and (M = 84, N = 9) at 10⁻⁹ BER error floor. The architecture of the spectral/spatial MDW OCDMA system with property of MAI cancellation is presented.     

43 W picosecond laser and second-harmonic generation experiment

Combining the advantages of diode-end-pumped Nd: YVO₄ and diode-side-pumped Nd: YAG amplifiers, a high average power and high beam quality picosecond laser is designed. The system delivers a picosecond laser with average power of 43.4 W and good beam quality of M² < 1.7. By focusing the high power picosecond laser in LBO crystal, 532 nm green laser with maximal power of 20.8 W is generated and the conversion efficiency of second-harmonic generation reaches 56.4% when 17.7 W green laser obtained from the fundamental frequency laser with power of 31.4 W and beam quality of M² < 1.25.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

Observation of fast sound in metal-nonmetal transition in liquid Hg

Liquid Hg undergoes the metal-nonmetal (M-NM) transition when it is expanded from 13.6 g cm⁻³ at ambient conditions to 9 g cm⁻³ at high temperature and high pressure. To investigate collective and single particle motions in expanded fluid Hg, we have made inelastic X-ray scattering experiments and obtained the dynamic structure factor, S(Q,ω), of fluid Hg. We analyzed S(Q,ω) within the framework of generalized hydrodynamics and found that the excitation energies of collective modes disperse three times as fast as the hydrodynamic sound velocity in the M-NM transition region at 9 g cm⁻³. The results indicate the existence of fast sound in expanded fluid Hg accompanying the metal-non-metal transition and strongly hint that fluctuations intrinsic to the M-NM transition are induced on atomic length scale and sub-picosecond time scale.     

High-efficiency continuous-wave and Q-switched diode-end-pumped multi-wavelength Nd:YAG lasers

We demonstrate high-efficiency diode-end-pumped multi-wavelength Nd:YAG lasers for continuous-wave and Q-switched operation. For the continuous-wave case, the Nd:YAG laser oscillates at 1.06 and 1.3 μm simultaneously; the maximum output power of 2.0 W (M² = 1.3) and 3.6 W (M² = 1.8) have been achieved at the incident pump power of 20.3 W, with the respective average slope efficiencies of 12.0% and 21.4%, for the lines of 1.06 and 1.3 μm, respectively. For the Q-switched operation, we achieve the average output power of 1.3 W (M² = 2.7) at 1.06 μm and 2.0 W (M² = 3.0) at 1.3 μm with the corresponding peak power of 10.2 and 4.2 kW under an incident pump power of 20.3 W.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Effect of the spiral phase element on the radial-polarization (0, 1) LG beam

Radially-polarized beams can be strongly amplified without significant birefringent-induced aberrations. However, radially-polarized beam is a high-order beam, and therefore has to be transformed into a fundamental Gaussian beam for reduction the beam-propagation factor M². In effort to transform the radially-polarized beam to a nearly-Gaussian beam, we consider effect of a spiral phase element (SPE) on the Laguerre-Gaussian (LG) (0, 1)^∗ beam with radial polarization, and compare this with the case when the input beam is a LG (0, 1)^∗ beam with spiral phase and uniform or random polarization. The LG (0, 1)^∗ beam with radial polarization, despite its identity in intensity profile to the beam with spiral phase, has distinctly different properties when interacting with the SPE. With the SPE and spatial filter, we transformed the radially-polarized (0, 1)^∗ mode with M² = 2.8 to a nearly-Gaussian beam with M² = 1.7. Measured transformation efficiency was 50%, and the beam brightness P/(M²)² was practically unchanged. The SPE affects polarization state of the radially-polarized beam, leading to appearance of spin angular momentum in the beam center at the far-field.     

High-beam-quality, 5.1 J, 108 Hz diode-pumped Nd:YAG rod oscillator-amplifier laser system

A high efficiency, high beam quality diode-pumped Nd:YAG master oscillator power-amplifier (MOPA) laser with six amplifier stages is demonstrated. The oscillator with two-rod birefringence compensation was designed as a thermally determined near hemispherical resonator, which presents a pulse energy of 223 mJ with a beam quality value of M² = 1.29 at a repetition rate of 108 Hz. The MOPA system delivers a pulse energy of 5.1 J with a pulse width of 230 μs, a M² factor of 3.6 and an optical-to-optical efficiency of 38.5%. To the best of our knowledge, this is the highest pulse energy for a diode-pumped Nd:YAG rod laser operation with a high beam quality and a pulse width of hundreds of microseconds at a repetition rate of over 100 Hz.     

The simulation of nanoscale sputter depth profiles using molecular dynamics

The feasibility of using molecular dynamics (MD) for simulation of a nanoscale sputter depth profile experiment is examined for the idealised case of depth profiles of individual atomic layers in a Cu(1 0 0) target. Issues relating to the extraction of depth profile information from MD simulations are discussed in detail. The simulations examine the sputter erosion of static and azimuthally-rotated Cu(1 0 0) targets produced by 3 keV Ar projectiles incident at 25° from the surface. The simulated projectile fluence extends to 5 × 10¹⁵ cm⁻², and the mean value of the sputter depth, z, amounts to 8 Cu(1 0 0) monolayers (ML) or 15 Å. The simulations directly supply progressive layer erosion profiles (curves that depict the extent of sputter erosion of each atomic layer vs. total sputter depth). A fitting method is then used to extract smooth depth profiles for each atomic layer from these predicted erosion profiles. The depth profile characteristics (height, width, shift) for the first 10 layers of the target show a pronounced dependence on layer depth.     

Collective dynamics of supercritical water

Inelastic X-ray scattering experiments on sub- and supercritical water were performed to investigate collective dynamics of this unique solvent. Analysis within a generalized Langevin formalism shows that the positive dispersion of the sound velocity, as compared to the hydrodynamic value, first decreases (1.0<ρ<0.8 g cm⁻³) at all measured momentum transfers (1.3-10.7 nm⁻¹), and then increases (0.7<ρ<0.26 g cm⁻³) again only at higher momentum transfers. We suggest the initial decrease is due to approaching the percolation limit in the number of hydrogen bonds, and the subsequent increase is due to the formation of rigid dimers in sub- and supercritical water.     

Femtosecond laser-induced damage of gold films

Single- and multi-shot ablation thresholds of gold films in the thickness range of 31-1400 nm were determined employing a Ti:sapphire laser delivering pulses of 28 fs duration, 793 nm center wavelength at 1 kHz repetition rate. The gold layers were deposited on BK7 glass by an electron beam evaporation process and characterized by atomic force microscopy and ellipsometry. A linear dependence of the ablation threshold fluence F_th on the layer thickness d was found for d ≤ 180 nm. If a film thickness of about 180 nm was reached, the damage threshold remained constant at its bulk value. For different numbers of pulses per spot (N-on-1), bulk damage thresholds of ∼0.7 J cm⁻² (1-on-1), 0.5 J cm⁻² (10-on-1), 0.4 J cm⁻² (100-on-1), 0.25 J cm⁻² (1000-on-1), and 0.2 J cm⁻² (10000-on-1) were obtained experimentally indicating an incubation behavior. A characteristic layer thickness of L_c ≈ 180 nm can be defined which is a measure for the heat penetration depth within the electron gas before electron-phonon relaxation occurs. L_c is by more than an order of magnitude larger than the optical absorption length of α⁻¹ ≈ 12 nm at 793 nm wavelength.     

Comparison and semiconductor properties of nitrogen doped carbon thin films grown by different techniques

Amorphous carbon nitride (a-CN_x) thin films have been synthesised by three different deposition techniques in an Ar/N₂ gas mixture and have been deposited by varying the percentage of nitrogen gas in the mixture (i.e. the N₂/Ar + N₂ ratio) from 0 to 10%. The variation of the electrical conductivity and the gap values of the deposited films versus the N₂/Ar + N₂ ratio were investigated in relation with their local microstructure. Film composition was analysed using Raman spectroscopy and optical transmission experiments. The observed variation of electrical conductivity and optical properties are attributed to the changes in the atomic bonding structures, which were induced by N incorporation, increasing both the sp² carbon content and their relative disorder. The low N content samples seem to be an interesting material to produce films with interesting properties for optoelectronic applications considering the facility to control the gas composition as a key parameter.     

Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

In this paper, we develop two new upwind difference schemes for solving a coupled system of convection–diffusion equations arising from the steady incompressible MHD duct flow problem with a transverse magnetic field at high Hartmann numbers. Such an MHD duct flow is convection-dominated and its solution may exhibit localized phenomena such as boundary layers, namely, narrow boundary regions where the solution changes rapidly. Most conventional numerical schemes cannot efficiently solve the layer problems because they are lacking in either stability or accuracy. In contrast, the newly proposed upwind difference schemes can achieve a reasonable accuracy with a high stability, and they are capable of resolving high gradients near the layer regions without refining the grid. The accuracy of the first new upwind scheme is O(h + k) and the second one improves the accuracy to O(ε²(h + k) + ε(h² + k²) + (h³ + k³)), where 0 < ε ? 1/M ? 1 and M is the high Hartmann number. Numerical examples are provided to illustrate the performance of the newly proposed upwind difference schemes.     

Fabrication of Al nanoparticles and their electrical properties studied by capacitance-voltage measurements

Nanometer-scale Al particles are fabricated and are embedded in a GaAs matrix using molecular beam epitaxial technique. The Al particle is self-assembled on GaAs by supplying an Al molecular beam. The average particle size is found to be 25 nm. The density is 7 × 10¹⁰ cm⁻² when Al of 6.2 × 10¹⁵ atoms/cm² is supplied on (1 0 0)GaAs at a substrate temperature of 300 °C. Clear hysteresis and plateaus in capacitance-voltage (C-V) curves are found in an Al-embedded sample, whereas monotonic increase of capacitance is obtained in a reference sample having an AlAs layer instead of Al. This difference results from trapping of electrons by the Al particles, suggesting that the particles have metallic character.     

Complete state counting for Gentile's generalization of the Pauli exclusion principle

In the present work, we perform the complete state counting for Gentile's approach to the generalized Pauli exclusion principle (GPEP), which has been lacking in the literature. We count the total number of ways to allocate n identical particles occupying a group of g states with up to q particles in each state, in order to derive an exact expression for the statistical weight. Our obtained expression for the statistical weight gives the fermionic one for q=1; and for q>1, it tends fast to a bosonic weight. Moreover, we perform a numerical comparison between our state counting and Wu's (corresponding to the Haldane-Wu's formulation of the GPEP), which implies that Gentile's formulation gives rise to more boson-like behavior while Haldane-Wu's approach to more fermion-like behavior; this difference lies on the fact that each formulation has its own state-occupation rules on which correlation plays a key role.     

Effect of film morphology on the magnetic properties for Nd-Fe-B thin films

The microstructure and magnetic properties of Nd-Fe-B thin films with a particulate structure were investigated. The nominal thickness of the Nd-Fe-B layer (t_N) was varied from 2 to 50 nm on a (0 0 1) Mo buffer layer. The films were grown with their c-axis perpendicular to the plane, and the morphology of the film with t_N=2 nm was shown to be particulate from an atomic force microscope image. The slope of the initial magnetization curve became steeper by increasing the t_N value in the initial magnetization curve, indicating that the film morphology composed of single domain particles changed to that of multi-domain particles with growth. The film with t_N=8 nm, which had a structure consisting of a mixture of single and multiple domain particles, showed the maximum value of the coercivity measured in the direction perpendicular to the film plane (H_c) as 19.5 kOe.     

Phase control in a coherent superposition of degenerate quantum states through frequency control

We demonstrate a controlled phase change of π in a degenerate superposition by altering a laser frequency by only 10 MHz. The method relies on the preparation of an adiabatic state involving the M = ±2 and M = 0 states of the ³P₂ (J = 2) level of metastable neon. Dependent on the frequency, the preparation proceeds either by stimulated Raman adiabatic passage (STIRAP) or by coherent population trapping (CPT). In the former case the superposition is prepared by adiabatic transfer induced in an extended tripod linkage scheme. In the latter case population is optically pumped into the Zeeman manifold of the level ³P₂. The population which does not reach a dark state decays to the ground state of neon. The amplitudes and relative phases of the dark states differ for the two cases. The phase change is monitored using the method of phase-to-population mapping.