Effects of relative phase on transient evolution in an open resonant ladder-type atomic system

In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion （GWI） always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion （refractive index） without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.

Relative phase-dependent two-electron emission dynamics with two-color circularly polarized laser fields

With the semiclassical ensemble model, we explore the relative phase-dependent nonsequential double ionization (NSDI) of Mg by counter-rotating two-color circularly polarized (TCCP) laser pulses. The yield of Mg2+ sensitively depends on the relative phase Δφ and the intensity of TCCP laser fields. At Δφ=1.5π, the yield of Mg2+ exhibits a pronounced peak in the 0.05 PW/cm2 laser field. This behavior results from the increase of the initial transverse velocity compensating for the drift velocity with the decreasing angle by analyzing the angular distributions of the electron pairs in four relative phases. By changing the relative phases, we find that the recollision excitation with subsequent ionization and the recollision-impact ionization mechanisms can be controlled with TCCP laser fields.

Influence of relative phase on the nonsequential double ionization process of CO_(2) molecules by counter-rotating two-color circularly polarized laser fields

We investigate the nonsequential double ionization(NSDI) of linear triatomic molecules by the counter-rotating two-color circularly polarized(CRTC) laser fields with a classical ensemble method. The results of the simulation reveal that NSDI yield strongly connected with the relative phase. The trajectory tracking method shows that the return time of the electron is controlled by the relative phase. In addition, when we change the CRTC laser wavelengths, the relative phase of the maximum and minimum yield of NSDI also changes. This shows that the influence of the Coulomb potential in the triatomic molecules on the electron return process cannot be ignored. This work will effectively promote the electronic dynamics study of NSDI for the triatomic molecule.

Relative carrier-envelope phase dependence of resonant propagation of two-colour femtosecond pulses in V-type atomic medium

Using numerical solution of the full Maxwell-Bloch equations, which is obtained by the finite-difference time-domain method and the iterative predictor-orrector method, we investigate the modulation effect of relative carrierenvelope phase （hereinafter referred to as the relative phase） on resonant propagation of two-colour femtosecond ultrashort laser pulses in a V-type three-level atomic medium. It is found that the pulse splitting occurs for a smaller value of relative phase; when the value of relative phase increases to a certain value, only the variation of pulse shape is present and the pulse splitting does not occur any more; moreover, when the value of relative phase is smaller, the pulse group velocity is larger. The relative phase also has an obvious effect on population and spectral property. Different population transfers can be realized by adjusting the value of relative phase. Generally speaking, for the pulses with smaller areas their spectral strengths and frequency ranges decrease obviously with the value of relative phase increasing; for the pulses with larger areas, with value of the relative phase increasing, their spectral strengths decrease remarkably but the relative strengths of the higher frequency components increase significantly, while the spectral frequency range is not varied evidently.

Phase control of light amplification in steady and transient processes in an inverted-Y atomic system with spontaneously generated coherence

We investigate the effects of spontaneously generated coherence （SGC） on both the steady and transient gain properties in a four-level inverted-Y-type atomic system in the presence of a weak probe, two strong coherent fields, and an incoherent pump. For the steady process, we find that the inversionless gain mainly origins from SGC. In particular, we can modulate the inversionless gain by changing the relative phase between the two fields. Moreover, the amplitude of the gain peak can be enhanced and the additional gain peak can appear by changing the detuning of the coupling field. As for the transient process, the transient gain properties can also be dramatically affected by the SGC. Compared to the case without SGC, the transient gain can be greatly enhanced with completely eliminated transient absorption by choosing the proper relative phase between the two fields. And the inverted-Y-type system with SGC can be simulated in both atomic and semiconductor quantum well systems avoiding the conditions of SGC.

the phase-dependent gain without inversion in a Doppler broadened open four-level system

It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence （SGC）, the gain without inversion （GWI） is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate （R0） and the ratio （S） of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with R0 increasing; in a certain value range of S, GWI increases monotonically with S increasing; by adjusting the values of R0 and S, in an open system a much larger GWI can be obtained than in the corresponding closed system [2011 Phys. Rev. A 83 043805]. The modulation effects of R0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.

Phase control of group-velocity-based biexciton coherence in a multiple quantum well nanostructure

A double cascade-type four-level multiple-quantum-well-based exciton-biexciton transitions are proposed. The study is carried out on a 4.8-rim ZnSe single-quantum well which is embedded into ZnMgSSe cladding layers and pseudomor- phically grown by molecular beam epitaxy on a （0 0 1） GaAs substrate. It is displayed that the exciton spin relaxation and relative phases between applied fields can influence the transient and steady-state behaviors of absorption, dispersion, and group velocity of two weak probe and signal fields. Also, transient behaviors of electron population of different levels are discussed. It is found that the probe or signal amplification occurs in the absence of population inversion.

The statistical laws of strong seismic motion phase characteristics

Under the assumption of an effective point source model,this paper introduces a conception of equivalent phase velocity to describle the average propagation processes and dispersion properties of seismic waves from seismic source to the site,then illuminates the relation between the phase properties of seismic motion and equivalent phase velocity and obtains a simple formula of estimating the equivalent phase velocity through the use of the phase difference spectrum of seismic motion.After the parts of strong seismic records in the western American and the SMART-1 array are used to identify the method presented by this paper in reason,the statistical relations of equivalent phase velocity are given in the above two regions.The results of the paper have demonstrated that the phase spectrum of seismic motion has its inner law as same as the amplitude spectrum does.

Modulation of atomic exit and injection rates on the phase-dependent gain without inversion in a Doppler broadened open four-level system

It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence (SGC), the gain without inversion (GWI) is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate (R0) and the ratio (S) of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with R0 increasing; in a certain value range of S, GWI increases monotonically with S increasing; by adjusting the values of R0 and S, in an open system a much larger GWI can be obtained than in the corresponding closed system [2011 Phys. Rev. A 83 043805]. The modulation effects of R0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.

Phase Relations in TiAl+Nb System

The microstructures and phases of ternary TiAl+Nb alloys containing 50-60 at.-%Al, 0-21 at.-%Nb have been studied using transmission electron microscopy (TEM) and X-ray powder diffraction. The phases present in the alloys and their distribution were found to be a sensitive function of composition. The phase relations between γ-TiAl and γ1 (a new ordered ternary intermetallic compound based on γ-TiAl) were determined. Essentially single γ phase was determined for alloys with relativety low Nb content (≤10 at.-%Nb). the γ1 phase was determined to exist in the composition range containing higher Nb contents (15-21 at.-%Nb). Between γ and γ1 phases, with intermediate Nb contents there is a transitional phase γ1 (a superstructure of γ-TiAl). As for the influence of Al concentration on the phase relations. the γ1 phase was inclined to form in the alloys with relatively high Al contents. The ordering transformation of γ, to γ1 is a continuous ordering process and the transition may be second order.

Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.

Phase and Structure in the System Gd_(2-x)Eu_xZr_2O_7 (0.0≤x≤2.0)

Pyrochlore Gd2Zr2O7 are considered as an excellent candidate for treatment of radioactive waste forms, because of its superior physical, chemical and anti-irradiation properties. To investigate the phase and structure of pyrochlore Gd2Zr2O7 used for immobilizing Pu （Ⅲ）, trivalent europium was used as the simulacrum for plutonium with trivalence. The compounds of stoichiometry Gd2-xEuxZr2O7（0.0≤x≤ 2.0） synthesized by high temperature solid state reaction method, were analyzed with the help of XRD and Rietveld structural refinement method. The results indicated that the phases of compounds continuously kept the phase of pyrochlore under our experimental condition. The linear relation between a and x was discovered in the system of Gd2-xEuxZr2O7（0.0≤x≤ 2.0） at 1 773 K, which accorded with a = 10.538 41 ＋ 0.008 95 x, V = 1 170.373 32 ＋ 2.985 97 x.

Phase Behavior of BaLn_2Mn_2O_7 (Ln=Rare Earth) with a Layered Perovskite Structure

Many phases appear in BaLn 2Mn 2O 7 family (Ln=rare earth) belonging to one of the Ruddlesden-Popper type compounds, depending upon the experimental conditions such as heating conditions when prepared and composition. Some of these phases were characterized by powder X-ray diffraction method using Rietveld analysis. These phases have only a little difference in crystal structure which has fundamentally K 2NiF 4 type structure, although the X-ray diffraction patterns are clearly different: a little deformation or tilting of the oxygen octahedron surrounding a central manganese ion composing the main frame of this structure induce these different diffraction patterns. Phase behavior of these compounds, mainly the detailed relation between various phases in BaTb 2Mn 2O 7, was refined including the data of high temperature X-ray diffractometry.

A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

Generation of quasi-chirp-free isolated attosecond pulses from atoms under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields

The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.

Sideband manipulation of population inversion in a three-level Λ atomic system

Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to π, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion ρ00 〉 ρ11 also becomes wider evidently.

Enhanced baseline determination for formation flying LEOs by relative corrections of phase center and code residual variations

Formation flying Low Earth Orbiters(LEOs)are important for implementing new and advanced concepts in Earth observation missions.Precise Baseline Determination(PBD)is a prerequisite for LEOs to complete specified mission targets.PBD is usually performed based on space-borne GNSS data,the relative corrections of phase center and code residual variations play crucial roles in achieving the best relative orbit accuracy.Herein,the influences of antenna Relative Phase Centre Variations(RPCVs)and Single-Difference(SD)Melbourne-Wu¨bbena(MW)Combination Residuals Variations(SD MWVs)on PBD are studied.The methods were tested using flight data from Gravity Recovery And Climate Experiment(GRACE)and GRACE Follow-On(GRACE-FO).Results showed that the maximum values for RPCVs and SD MWVs were 14 mm and 0.32 cycles,respectively.Then,the RPCVs correction significantly enhanced the baseline accuracy;the K-Band Ranging(KBR)measurement consistency improved by 30.1%and 37.5%for GRACE and GRACE-FO,respectively.The application of SD MWVs further improved the accuracy and reliability of PBD results.For GRACE,the ambiguities fixing success rate increased from 85.1%to 97.9%and a baseline consistency of 0.57 mm was achieved for the KBR measurements.It was found that the correction of both RPCVs and SD MWVs reduced the carrier phase observation minus computation residuals from double-difference ionosphere-free combination.In addition,in-flight data processing demonstrated that RPCVs and SD MWVs estimations for the current period could be used for the previous and subsequent periods.

Dynamic control of retrieval contrast in a Λ-type atomic system

We propose an efficient scheme for optimizing the optical memory of a sequence of signal light pulses in a system of ultracold atoms in ∧ configuration.The memory procedure consists of write-in,storage,and retrieval phases.By applying a weak microwave field in the storage stage,additional phase-dependent terms are included,and the contrast of the output signal pulses can be dynamically controlled（enhanced or suppressed） through manipulating the relative phase φ between optical and microwave fields.Our numerical analysis shows that the contrast is enhanced to the most extent when φ = 1.5π.In addition,the contrast is in proportion to the Rabi frequency of the microwave field with a certain relative phase.

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.