Atomic Occupation Probabilities Research Articles

Nonlinear optical effects on the atom–field interaction based on the nonlinear coherent states approach

In this paper, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformed su ( 2 ) algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.

Stability of phase boundary between L12-Ni3Al phases: A phase field study

The evolution and stability of phase boundaries (PBs) between L12-Ni3Al phases in Ni75Al11V14 alloy aged at 1050k was studied using the microscopic equation phase-field method (MPFM). Four types of L12 PBs were found through atomic configuration, migration and occupation probability (OP). The evolution of metastable PBs and formation of stable PBs were tracked and explored, the effect of coherent elastic strain energy on the evolution and stability of PBs is also investigated by coupling the micro elastic theory with MPFM. In addition, the formation enthalpy, interface energy and electron distribution function of PBs are calculated by FP method, and the stability of PBs is further quantitatively predicted from the perspective of thermodynamic energy and gaining or losing electrons. FP calculation results are consistent with MPFM prediction, and the essence of the transition and stability of PBs is revealed based on the atomic migration dynamics, interface evolution morphology and thermodynamic energy. This is an effective method to further explore the formation and structure of PBs and design high stability PBs.

Microscopic phase-field study on L12 interface properties of Ni75Al18Cr7 superalloy

In this study, the solidification and precipitation process of Ni75Al18Cr7 superalloy was investigated based on the microscopic phase-field method. The simulation results were validated by using the experimental results. There were three types of ordered interfaces between L12 phase, namely (200)L//(200)L·½[001]L, (200)L//(200)L and (100)L//(200)L·½[001]L, which were studied by plotting the microstructural characteristics of Ni75Al18Cr7 superalloy and the distribution of atomic occupation probability and evolution of atomic occupation probability on both sides of the interface between L12 phases. The simulation results show that the former two interfaces could migrate with the precipitation evolution process, while the latter ordered interface (100)L//(200)L·½[001]L could not migrate. The interface migration was caused by the migration and exchange of Ni/Al atoms at the ordered interface. The atomic concentration in the ordered interface before and after migration was almost constant, i.e., the segregation and dilution of each atom was almost constant. The experimental results show that the L12 phase structure grew gradually with the increase in heat treatment time, which is consistent with the simulation results of microscopic phase-field method. Moreover, the volume fraction of L12 phase calculated by the phase-field method was almost the same as that obtained by X-ray diffraction (XRD) experiments, which indicates the feasibility of using microscopic phase-field method to guide the optimization design of alloy.

Long-lived quantum coherence and nonlinear properties of a two-dimensional semiconductor quantum well

In this paper, we present an analytical solution to the Maxwell–Bloch equations of the two-level semiconductor quantum well, G a A s / A l G a A s . In addition, we discuss the effects of coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) on atomic occupation probabilities, ρ 11 ( t ) and ρ 22 ( t ) , population inversion, ρ z ( t ) , and information entropies, H ( σ x ) , H ( σ y ) , and H ( σ z ) . We observe clearly the emergence of long-lived quantum coherence and the decay in curves for some special cases of Ω ( t ) and ν ( t ) . Also, we show that the dynamic nonlinear properties of the system can be controlled by changing the values of the coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) . Due to the lack of mathematical treatment of such systems, our study promises significant advantages for a large number of nonlinear dynamic systems, opening up a wide range of applications for semiconductor quantum wells.

Information entropy and population inversion of a three-level semiconductor quantum dot

In this paper, an analytical solution for a three-level semiconductor quantum dot has been presented. From this solution, we have discussed the effects of the phenomenological damping parameters, the electromagnetic field amplitude $$E_{0}$$ of the excitation pulse $$E(\omega )$$ , and the detuning parameters on the atomic occupation probabilities, the atomic population inversion, the purity, and the information entropy $$H(\sigma _\mathrm{{z}}). $$ A long-lived quantum coherence obviously has emerged in all figures. Besides, a decay has appeared in all curves of the atomic occupation probability $$\rho _{gg}(t),$$ the atomic population inversion, and the purity. Since there are not sufficient mathematical solutions for such systems, our study may add further insight into many dynamic systems, and this in turn should open up a wide range of applications for semiconductor quantum dot.

Atomic-scale characterization of the site occupancies in the B2 FeAl phase: Effects of Ni addition, temperature and lattice misfit

A microscopic phase-field model is constructed to study the influences of Ni addition, temperature and lattice misfit on the site occupancies in complex B2 FeAl–Ni intermetallic phase. The tendencies of six site occupancies are explored through tracing the atomic site occupation probability. The results reveal that six site occupancies are monotone functions of Ni concentration, temperature and the lattice misfit, respectively. For the antisite behavior of Fe (AlFe), Al (FeAl) and the substitution behavior of Ni (AlNi, FeNi), the ranks of four defect occupancies are identical under three factors. The transformation rate and ordering degree of the complex FeAl–Ni are dependent of three factors. The mechanism of configuration of six site occupancies is revealed from the energy analysis. The results are in accordance with experimental and theoretical data and provide theoretical support to the questioned validity of the lattice misfit effect on the ordering behavior in intermetallics.

Microscopic Phase-field Simulation for the Influence of Aging Process on the Precipitation Process of Ni75Al15Ti10 Alloy

The precipitation process of Ni75Al15Ti10 alloy was simulated by a microscopic phase-field kinetics model. The microscopic morphology evolution was studied, which indicates that the precipitation process can be divided into two stages: the first is the transformation from L10 phase to L12 phase, and the second is the formation of the stoichiometric L12 phase. The effect of single aging temperature on the microstructure, atomic occupation probability and atomic diffusion was investigated. The result shows that the shape of γ′ precipitates transforms from irregular shape to regular cuboid and the degree of orientation growth increases with increasing aging temperature. But the higher the aging temperature, the lower the occupation probability and the order degree. Meanwhile, the path of diffusion of Al atom is from the interface of the γ′ phase to the internal, and the diffusion of Ti atom is the opposite. Furthermore, we studied the dual aging to improve occupation probability of γ′ precipitates and to discuss their influence on the γ′ phase. Dual aging can not only obtain a stable γ′ phase with regular shape, but also increase the occupation probability of Al and Ti and inhibit the formation of anti-site defects.

Entanglement of a nonlinear two two-level atoms interacting with deformed fields in Kerr medium

In this paper we investigate the entanglement dynamics between two two-level atoms interacting with two coherent fields in two spatially separated cavities which are filled with a Kerr-like medium. We examine the effect of nonlinear medium on the dynamical properties of entanglement and atomic occupation probabilities in the case of even and odd deformed coherent states. The results show that the deformed fields play important roles in the evolution of entanglement. Also, the results demonstrate that entanglement sudden death, sudden birth and long-distance can be controlled by the deformation and nonlinear parameters.

Microscopic Phase-Field Simulation for the Influence of Interatomic Potential on the Precipitation Process of Ni75Al14Mo11 Alloy

The process of γ′ phase precipitating from Ni75Al14Mo11 is studied by a computational simulation technique based on microscopic phase-field kinetics model. We studied the phase transformation with the purpose of clarifying the influence of the nearest interatomic potential V Ni–Al (the nearest interatomic potential) on the precipitation process of γ′ phase. The result demonstrates that there are two kinds of ordered phases, respective L10 and L12 in the early stage, and L10 phase transforms into L12 phase subsequently. For L12 phase, Ni atoms mainly occupy α site (face center positions), while Al and Mo atoms occupy β sites (the vertex positions). When V Ni–Al is increased by 10 MeV, the occupation probability of Ni atoms on α sites and Al atoms on β sites are enhanced. Enhanced V Ni–Al facilitates clustering and ordering of Al atom, which promotes the formation of the γ′ phase. At last, the simulation result was discussed by employing the thermodynamic stability.

Quantitative calculation on atomic site occupation during precipitation of Ni3(Al1–xFex) by microscopic phase-field study

Microscopic phase-field method was used to simulate the site occupation of a series of alloys with a stoichiometric composition of Ni75Al25–xFex (x=0, 5–10) aged at 1273 K. With the change of Fe content, quantitative calculations were made on each atomic site occupation probability (SOP) in L12-Ni3 (Al1–xFex), so as to find out the dynamic response law. The result of the study shows that, with the increase of Fe content, the Fe atom preferentially occupies the B sites (corner sites of FCC) with its SOP value being increased gradually, and the SOP of the Al atom on the B sites is greatly decreased. Meanwhile, AlNi and FeNi anti-sites form in the precipitation of L12 phase. Moreover, with the increase of Fe content, the formation of AlNi and FeNi anti-sites becomes much easier. In addition, it has been found that the instantaneous dynamic evolution of the atomic SOP is completed at the early stage of the growth of L12 phases.

Curvature effects on the interaction of nonlinear sphere coherent states with a three-level atom

In this paper, we consider the interaction of the nonlinear coherent states (CSs) on a sphere with a three-level atom. Since these generalized CSs depend on the curvature of the sphere, this model enables us to investigate the curvature effects of the physical space. By using the time-dependent state of the atom-field system, we first study the curvature effects on the occupation probabilities of the atomic levels. We especially study the relation between the revival time of the atomic occupation probabilities and the curvature. Then, to study the curvature effects on the dynamical properties of the cavity field, we consider photon distributions, correlation functions, and Mandel parameters of the field. The cavity field in this atom-field system exhibits nonclassical features which depend on the curvature of the physical space.

Dynamics of a tri-beam laser interacting with a three-level atom

We investigate the dynamics of a tri-beam laser interacting with a closed three-level atomic system. The Bloch equations are obtained using Hesinberg’s equation of motion. The impact of the resulting parameters on the atomic occupation probabilities and information entropy is discussed. It is shown that the populations are affected by the detuning in different ways which are then compared in order to simulate realizations entanglement through the information entropy.

Atomic Anti-Site Evolution during L1<sub>2</sub> Precipitation Using Microscopic Phase-Field Simulation

The influence of temperature on atomic site occupation probability (SOP) in L12--Ni3(Al1-xFex) has been studied using microscopic phase-field simulation for Ni3Al-Fe alloy with the lower Fe content. Microscopic phase-field kinetics model was further extended to study the temporal evolution of atomic site occupation and atomic anti-sites behavior, which was revealed in detail at the different temperatures. The results show that the size, number and the precipitation mechanism of L12phases also present obvious changes with the increase of temperature. The SOP of each atom on its right-sites decreases slowly; while the SOP of Fe atoms are far lower than those of Al atoms. On the other hand, the SOP of each atom on its anti-sites increases gradually. The formation of NiAl(Ni atoms form anti-sites on Al sites) is more easily and the formation of NiAlis more sensitive to temperature than that of FeNi(Fe atoms form anti-sites on Ni sites). Atomic site occupation will not evolve during the early stage of precipitation, which becomes more and more obvious.

Atomic structure and composition of the2×Nreconstruction of the Ge wetting layer on Si(001) investigated by surface x-ray diffraction

The 2 \ifmmode\times\else\texttimes\fi{} $N$ reconstruction of the Ge/Si(001) wetting layer has been investigated by surface x-ray diffraction. At a substrate temperature of $670 {}^{ˆ}\mathrm{C}$, the average $N$ periodicity decreases from $N$ $=$ 11.5 to 8 with an increasing Ge coverage from one to three monolayers (ML). The top layer consists of asymmetric dimers with a bond length in the range of 2.50--2.60 \AA{} and a buckling angle in the range of 9.4\ifmmode^\circ\else\textdegree\fi{}--15.6\ifmmode^\circ\else\textdegree\fi{}, depending on the Ge coverage. The obtained dimer bond lengths are similar to those calculated for alternating asymmetric mixed dimers. Intermixing of Ge with Si is found down to the sixth (eighth) layer for 2 (from 3 to 5) ML coverage. For 2 ML coverage, a quantitative surface x-ray diffraction data set has been measured. It is analyzed using a model describing the atomic structure and Ge occupation probability with a limited set of parameters to bypass the intrinsic lack of appreciable reflections of the 2 \ifmmode\times\else\texttimes\fi{} $N$ ($N$ $=$ 9) reconstruction. The Ge occupation probability varies periodically along the $N$ direction, having its minimum value below the dimer vacancy lines. In addition, a more direct calculation of the Lorentz and detector acceptance corrections is given for rocking and radial scans.

ENTANGLEMENT CONTROLLING OF A THREE-LEVEL CASCADE ATOM INTERACTING WITH A TIME-DEPENDENT COHERENT FIELD

The interaction between a three-level cascade atom and an initial coherent field with a time-varying frequency has been investigated, including the dynamic behavior of the atomic level occupation probabilities and the entanglement between the atom and the field. The frequency of the field is modulated in the forms of sine and rectangle. It is found that the field-frequency variation has a great influence on the properties of the generalized Jaynes-Cummings model. Appropriate frequency modulation can enhance and stabilize the degree of entanglement between the atom and the field.

Microscopic phase-field study on atomic site occupation probability in L1 2–Ni 3(Al 1 − xFe x) structure

The effect of Fe content on atomic site occupation in L1 2–Ni 3(Al 1 − x Fe x ) structure at 1073 K was studied by using microscopic phase-field model. The results show that with increasing Fe, Fe atoms prefer to occupy the Al sites (β sites), and the site occupation probability (SOP) gradually increases, while the SOP of Al atoms on β sites decreases accordingly. Meanwhile, a small amount of Ni atoms also occupy β sites which is the so-called anti-site behavior; reversely, such behavior happens as a trace amount of Al and Fe atoms occupies α sites. Unlike Ni atoms, the anti-site behavior of Al and Fe atoms is strengthened with the increase of Fe content. Further, the precipitation mechanism, the size and the ordering degree of L1 2 structure also present obvious changes with the addition of Fe.

Microscopic phase-field simulation of atomic site occupation in ordering process of NiAl 9Fe 6 alloy

The process of γ(fcc)→γ(fcc)+γ′(L1 2) phase transformation was simulated by using microscopic phase-field method for the low supersaturation NiAl 9Fe 6 alloy. It is found that in the γ′ phase, the ordering degree of Al atoms is obviously higher than that of Fe atoms, and the ordering of Al atoms precedes their clustering, while the case of Fe atoms is opposite. The α site is mainly occupied by Ni atoms, while the β site is occupied in common by Al, Fe and Ni atoms. At order-disorder interphase boundary, the ordering degree of Al atoms is higher than that of Fe atoms, and at the β site, the Fe atomic site occupation probabilities vary from high to low during ordering; the Al atomic site occupation probabilities are similar to those of Fe atoms, but their values are much higher than those of Fe atoms; Ni atoms are opposite to both of them. Meanwhile, during the ordering transformation, γ′ phase is always a complex Ni 3(AlFeNi) single-phase, and it is precipitated by the non-classical nucleation and growth style. Finally, in the alloy system, the volume of γ′ ordered phase is less than that of γ phase, and the volume ratio of order to disorder is about 77%.

Simulation of interphase boundary of Ni 75Al xV 25- x alloys using microscopic phase-field method

Abstract The evolution of ordered interphase boundary (IPB) of Ni 75Al x V 25- x alloys was simulated using the microscopic phase-field method. Based on the atomic occupation probability figure on 2D and order parameters, it was found that the IPB formed by different directions of θ phase has great effect on the precipitation of γ′ phase. The γ′ phase precipitated at the IPB that is formed by [100] θ direction where the (001) θ plane is opposite, and then grows up and the shape is strap at final. The IPB structure between γ′ phase and θ phase is the same. There is no γ′ phase precipitate at the IPB where the (002) θ and (001) θ planes are opposite, the ordered IPB is dissolved into disordered area. There is γ′ phase precipitation at the IPB formed by the [001] θ and [100] θ directions, and the IPB structure is different between γ′ phase and the different directions of θ phase. The IPB where (001) γ′ and (100) θ plane opposite does not migrate during the γ′ phase growth, and γ′ phase grows along [100] θ direction.

Microscopic phase-field simulation for nucleation incubation time of Ni75AlxV25−x alloy

With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25−x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms, such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25−x alloy, the incubation time of L12 phases shortens continuously and that of D022 phases is prolonged. The effects of temperature on the incubation time of L12 and D022 phases are accordant, i.e. the incubation time is greatly prolonged with the temperature rising.

Electron channeling X-ray microanalysis for partially filled skutterudite structure

Occupancy of Ce atoms on voids and coordinates of Sb atoms in a partially filled skutterudite CeFe 6Ni 2Sb 24 were determined by the method for atomic location by channeling enhanced microanalysis (ALCHEMI), where characteristic X-ray intensities were measured and calculated at various electron incidence directions in a transmission electron microscope. The calculation was based on dynamical electron diffraction and inelastic scattering theories. The calculated intensities were significantly dependent on the occupation probability of Ce atoms on voids, the coordinates of Sb atoms and the sample thickness. Using the Levenberg–Marquardt least squares method, the occupation probability of Ce atoms and the coordinates of Sb atoms were 0.33 and 0 0.336 0.147, respectively.