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## GENERAL

2020, 69 (14): 140201. doi: 10.7498/aps.69.20200154
Abstract +
${\gamma }'$ phase with L12 structure and of $\theta$ phase with DO22 structure.The two ordered phases constitute a pseudo binary system. The L10 phase precipitates at the same time as DO22, and the L10 phase gradually transforms into the L12-γ′ phase, while the traditional Ni75Al7.5V17.5 alloy first precipitates L10 phase, and then the DO22 phase precipitates at the boundary of anti-phase domain of L12 phase. In the transition from L10 to L12, α position of fcc lattice is occupied by Ni atom, and the β position is occupied by Al atom and V atom. The congruent ordering of atoms results in the formation of θ single-phase ordered domain of DO22 structure, followed by spinodal decomposition; the non-classical nucleation of L10 structure gradually transforms into L12-γ′ phase and spinodal decomposition. The interaction potential between the first-nearest-neighbor atoms of Ni-Al increases linearly with temperature, and increases gradually with the increase of long range order parameters. The incubation period of Ni60Al20V20 medium entropy alloy lengthens with temperature increasing. This study can be applied to the design of Ni-Al-V medium entropy alloy.">Medium entropy alloys have attracted much attention because of their excellent physical and chemical properties. Nano-scaled L12 structure ordered phase plays an important role in strengthening the mechanical properties of medium entropy alloys, and its local atomic arrangement plays a decisive role in yield strength of medium entropy alloys. In this paper, the microscopic mechanism of the precipitation process of Ni60Al20V20 medium entropy alloy is studied by using the micro diffusion phase field dynamics model, in which the probability of atoms to occupy the lattice position is taken as a field variable to describe the configuration of atoms and the morphology of precipitates. In this model, the shape and concentration of precipitate phase, the position and appearance of new phase cannot be set in advance. Combined with the inversion algorithm, the precipitation mechanism of ordered phases of γ' (L12-Ni3Al) and θ (DO22-Ni3V) is discussed by analyzing the evolution of atomic images, the change of order parameters and volume fraction. The result shows that two kinds of ordered phases are precipitated in the kinetical process of disordered phase ordering into Ni60Al20V20 medium entropy alloys, which are of ${\gamma }'$ phase with L12 structure and of $\theta$ phase with DO22 structure.The two ordered phases constitute a pseudo binary system. The L10 phase precipitates at the same time as DO22, and the L10 phase gradually transforms into the L12-γ′ phase, while the traditional Ni75Al7.5V17.5 alloy first precipitates L10 phase, and then the DO22 phase precipitates at the boundary of anti-phase domain of L12 phase. In the transition from L10 to L12, α position of fcc lattice is occupied by Ni atom, and the β position is occupied by Al atom and V atom. The congruent ordering of atoms results in the formation of θ single-phase ordered domain of DO22 structure, followed by spinodal decomposition; the non-classical nucleation of L10 structure gradually transforms into L12-γ′ phase and spinodal decomposition. The interaction potential between the first-nearest-neighbor atoms of Ni-Al increases linearly with temperature, and increases gradually with the increase of long range order parameters. The incubation period of Ni60Al20V20 medium entropy alloy lengthens with temperature increasing. This study can be applied to the design of Ni-Al-V medium entropy alloy.

## GENERAL

2020, 69 (14): 140301. doi: 10.7498/aps.69.20200372
Abstract +
Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.

## GENERAL

2020, 69 (14): 140501. doi: 10.7498/aps.69.20191657
Abstract +
In classic statistical physics, an isolated system corresponds to a constant energy shell in the phase space, which can be described by the microcanonical ensemble. While, for an isolated quantum system, the conventional treatment is to subject the system to a narrow energy window in the Hilbert space instead of the energy shell in classical phase space, and then confine the participating eigen states of system wave function in the narrow window, so that the microcanonical ensemble can be recovered in the framework of quantum mechanics. Apart from the traditional theory, there is a more self-consistent description for the isolated quantum system, that is, the quantum microcanonical (QMC) ensemble. The QMC ensemble abandons the narrow energy window assumption, and allows all the eigen states to contribute to the system wave function on condition that the system average energy is fixed at a given value. At the same time, the total occupation probability of these eigen states is conserved to unity. The most probable probability distribution obtained in the Hilbert space for an isolated quantum system according to the constraints specified above is called the QMC statistics. There is a clear difference between the QMC distribution and the traditional Gibbs distribution having an exponential form. Through the external periodic drives, an isolated quantum system may produce the QMC distribution, which is a consequence of the interplay between internal origins and external drives. In this paper, we investigate the conditions for the formation and suppression of QMC distribution by using the exact diagonalization method based on the one-dimensional Ising model. We start with the one-dimensional Ising model and focus on three different cases of periodic drives: systems under vertical (along the z axis), horizontal (along the x axis), horizontal magnetic field together with random internal (along the y axis) magnetic field. For all these three cases, the external magnetic fields are set to be ordinary rectangular pulses and the Gibbs distributions are taken as the initial states. We then study the evolutions and their asymptotic tendencies to the QMC distributions of the eigen state occupation probability under the effect of external periodic magnetic field. The results show that under the vertical magnetic field, the eigen state occupation probability does not change, and the system cannot produce the QMC distribution; under the horizontal magnetic field, the system tends to display a QMC distribution, but only partly; under horizontal and random internal magnetic fields at the same time, the transition to QMC distribution can be fully realized, and finally the system is almost completely thermalized. In order to clarify the different behaviors of the Ising model in the three cases, we also calculate the information entropy of the eigen state of Floquet operator in the eigen representation of the unperturbed Hamiltonian. We find that as the information entropy of the Floquet eigen state increases, the convergence to the QMC distribution in the Hilbert space is improved. We also notice that the mechanism for the emergence of QMC distribution is closely related to the thermalization effect of the isolated quantum system. Our analyses show that when the magnetic field is vertical, it cannot trigger the thermalization of the system. When the magnetic field is horizontal, the system becomes partly, but not completely, thermalized. When we add a horizontal periodic magnetic field and a random internal magnetic field at the same time, the system can be completely thermalized to infinite temperature. Thus, the asymptotic behavior towards the QMC statistics is a reflection of the fact that the isolated quantum system is thermalizable under periodic drives.

## GENERAL

2020, 69 (14): 140502. doi: 10.7498/aps.69.20191981
Abstract +
Multi-stable structures are deformable structures that can have large deformations under external excitation. Generally, multi-stable structures have at least two stable points and can jump from one to another. Because multi-stable structures have excellent nonlinear characteristics, they are widely used in many fields. In the field of energy harvesting, multi-stable structures are often obtained by means of cantilever beams. This is because the cantilever beam is simple to make, low in stiffness, and high in sensitivity, and can undergo large deformations under small excitation forces. Besides, by simply sticking magnets on its free end and its outside, various kinds of multi-stable characteristics can be constructed, such as bi-stable characteristics, tri-stable characteristics, quad-stable characteristics, etc. Furthermore, the cantilever beam and the magnet at its end can generally be simplified into an equivalent mass-spring-damping mechanical model, which is convenient for the analysis of system potential function and dynamics.In recent years, many vibration energy harvesters proposed by researchers have adopted the conventional multi-stable cantilever beams, which involve many bi-stable cantilever beams and tri-stable cantilever beams. However, if the cantilever beams need to introduce more stable points, the number of magnets required will also increase accordingly. As a result, the adjustable parameters are continuously increasing, which increases the complexity of structural optimization and the tediousness of dynamic analysis. In order to make up for the shortcomings of conventional multi-stable cantilever beams, in this paper we present a multi-stable cantilever beam with only two magnets, a ring magnet and a rectangular magnet. By changing the size of the rectangular magnet and the distance between the two magnets, this cantilever beam can have mono-stable, bi-stable, tri-stable or quad-stable characteristics. This multi-stable cantilever beam greatly simplifies the complexity of the system design, dynamic analysis, debugging and installation, and provides new ideas and technical methods for the design and application of the vibration energy harvester realized by the multi-stable cantilever beam.In this paper, firstly, the magnetizing current method is used to analyze the magnetic induction intensity of the ring magnet at any point in the three-dimensional coordinate system, and the simulation and experimental results prove its correctness. Secondly, two methods of calculating the position of the rectangular magnet at the free end of the cantilever beam are compared. Thirdly, the magnetic force between the ring magnet and the rectangular magnet is calculated and verified in experiment. Fourthly, the system potential functions under different structural parameters are analyzed and it is found that the change of the number of the stable points of the system is caused by the change of the magnetic force between the two magnets. Finally, the correctness of the number of stable points of the system under different parameters is verified in experiment and by dynamic simulations.

## INVITED REVIEW

2020, 69 (14): 140503. doi: 10.7498/aps.69.20200161
Abstract +
Self-organization represents a ubiquitous transition from disorder to order. It plays a critical role in forming crystalline materials and functional structures in biology. Functional structures are generally hybrid on a multiple scale in which nano-structures are often organized in a specific way such that they can perform functions. There are two typical functional structures: static equilibrium structures and dynamic non-equilibrium structures. In this review, recent advances in understanding and mimicking functional structures are summarized. Although great advances have been achieved, it is still a big challenge to realize dynamic non-equilibrium structures. In this case, we suggest that the controlling of self-organization in active systems may be a route toward interactive and adaptive structures.

## GENERAL

2020, 69 (14): 140504. doi: 10.7498/aps.69.20200133
Abstract +
Grain boundary affects the microstructure of metal material, and thus further its macroscopic properties. As is well known, under the action of applied stress, the grain boundary migrates. The structures and arrangements of grain boundary dislocations at different misorientation angles are very different, which affects the macrophysical and chemical properties of metal crystal. Therefore, it is of great theoretical and practical significance to study the dislocation structure and reaction mechanism of grain boundary under different misorientations for further studying the material properties.The phase field crystal method is used to simulate the low-angle asymmetric tilt grain boundary structure and dislocation motion on a nanoscale. From the perspective of the change of the position of the grain boundary dislocation motion under the applied stress and the change of the free energy of the crystal system, the influences of the misorientation angle on the low-angle asymmetric tilt grain boundary structure and the motion of the grain boundary dislocation are analyzed. The results show that the types of dislocation pairs of low-angle asymmetric tilt grain boundaries at different misorientation angles are the same. With the increase of misorientation angle, the grain boundary dislocation pairs increase, and n1n2 and n4n5 type dislocation pairs are more easily formed at the grain boundaries. Under the action of applied stress, the initial movement states of the grain boundary dislocation pairs at different misorientation angles are all climbing along the grain boundaries. As the system energy accumulates, the larger the misorientation angle is, the more the number of decomposed grain boundary dislocation pairs decomposed will be, and only in the dislocation pairs of n1n2 and n4n5 type there occurs decomposition reaction. There are four stages in the free energy curve of the low-angle asymmetric tilt grain boundary system at different misorientation angles, which correspond to the dislocation pairs climbing, dislocation pairs sliding and decomposition, dislocation pairs reaction to form single crystal, and the free energy rising process of the system. Further research shows that as the misorientation angle increases, the time for the single crystal system formed by the dislocation of grain boundary pairs to annihilate is required to be long.

## GENERAL

2020, 69 (14): 140601. doi: 10.7498/aps.69.20191800
Abstract +
Cold collision frequency shift is one of the major systematic effects which limit the frequency uncertainty of the cesium fountain atomic clock. It is proportional to the effective atomic density, which is defined as the average density over the initial spacial and velocity distribution. The measurement of the frequency shift is based on a differential method, in which the fountain clock is operated with two different atomic densities, i.e. high density and low density, in turn. The clock frequency without collision shift can be achieved by linear extrapolation with the frequencies and density ratios of two states. For the density ratio is estimated with the atom number, it plays a crucial role in generating atoms with same density distribution for reducing systematic uncertainty in cold collision frequency shift estimation. The rapid adiabatic passage method is used in Cesium fountain clock to realize homogeneous transition probability, which modulates the amplitude and frequency of microwave continuously to prepare atom sample. To investigate the precision of this method, theoretical analysis and experimental measurement are both used here. An equation of deviation is derived from the time evolution of Bloch vector. The vector rotates at angular speed Ω with the rotation axis processing at lower angular speed. The deviations in the two directions on the surface of Bloch sphere are determined by the equations which are similar to wave equations, and can be simplified into wave equations when the deviations are sufficiently small. It is shown in the equations that the deviations are stimulated by angular velocity and angular acceleration of the precession, and is inversely proportional to the square of Ω. Further calculation shows that the deviation becomes smaller when the amplitude of microwave frequency and Rabi frequency are close to each other. It is then confirmed experimentally. The effects of some other parameters, such as the pulse length and time delay, on transition probability are also measured, showing that the RAP method is insensitive to these parameters up to a large scope. The precision of RAP method is dominated by three factors. The first factor is the product of rotating angular speed Ω and pulse length T, i.e. ΩT: The increase of ΩT can reduce the uncertainty to a satisfactory degree. The second factor is the uncertainty of resonant frequency, so the measurement is required to be precise. The third factor is the unexpected atoms which are not selected by the microwave, and may be attributed to pulling light. After optimizing the parameters, the ratio of low density to high density can approach to 0.5 with 3 × 10–3 uncertainty, which leads to a systematic relative uncertainty of cold collision shift up to 1.6 × 10–16.

## ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2020, 69 (14): 144201. doi: 10.7498/aps.69.20200125
Abstract +
In this paper, a near-infrared laser heterodyne spectrometer developed by the laboratory is used to investigate the inversion of greenhouse gas column concentration and approximately evaluate the system measurement errors based on the optimal estimation algorithm. Firstly, the spectral database and the calculation results from the reference forward model are compared with the ground-based FTIR results, thereby selecting the detection window, the corresponding laser and detector. Secondly, the optimal estimation concentration inversion algorithm based on the reference forward model is established, and the Levenberg-Marquardt (LM) iterative method is adopted to realize the inversion of the concentration and vertical distribution profile of atmospheric CO2 column in the whole layer, and the long-term observation comparative experiment is carried out to verify the feasibility of this algorithm. Finally, by simulating the selected detection window spectrum in different white noise, the approximate corresponding relationship between the system signal-noise-ratio (SNR) and CO2 column concentration measuring error is eventually obtained. This research is an indispensable theoretical calculation part of the detection system and will conduce to improving the application of laser heterodyne technology in atmospheric observations.

## ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2020, 69 (14): 144202. doi: 10.7498/aps.69.20200496
Abstract +
Recent years, with the rapid development of information technology, the information security has received more and more attention. A variety of encryption methods to protect the information have been reported. Visual cryptography is one of the encryption methods, which has highly security because of its threshold feature. And the cryptographic information can be explained by a naked eye in the decryption process. In the application of visual cryptography, however, each shared image is limited to transparency films and overlapping on computer. In our previous work, we proposed the scheme of invisible visual cryptography and developed the visual-cryptography-based optical hiding system (VCOH), which transformed the conventional visual cryptography shares into diffraction optical elements (DOEs). It not only increases the application range of visual cryptography, but also enhances security. In this paper, we propose an optical information hiding system based on the extended visual cryptography, which inherits the concept of invisible visual cryptography. In contrast to our previous work, the method proposed in this work can hide a meaningful image instead of text messages. Meanwhile, the capacity and imperceptibility of the method are greatly increased. The hiding process of the system contains two steps. Firstly, the secret image is converted into meaningful shares through the extended visual cryptography algorithm. Secondly, the meaningful shares are able to hide in phase-keys through an iterative phase retrieval algorithm, such as Gerchberg-Saxton algorithm and Yang-Gu iterative algorithm. Then the phase-keys can be made into diffraction optical elements (DOEs) to store and transport in a physical way. In the decryption process, DOEs are illuminated with the laser beam to reconstruct the meaningful shares. The secret image can be explained by the direct overlapping of the reconstructed shares without any optical or cryptographic knowledge. The simulation and optical experimental results show that the proposed method has good performance of security and validate the feasibility of the proposed method. Besides, in this paper the robustness and security issues are also analyzed. This system has a high security because of its indistinguishability under adaptive chosen ciphertext attack (IND-CCA2) security. Additionally, this system is relatively less robust than the VCOH because it shares meaningful images with highly complex and detailed structures.

## ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2020, 69 (14): 144203. doi: 10.7498/aps.69.20200243
Abstract +
Vortex beams with orbital angular momenta with different mode numbers are mutually orthogonal to each other, which makes it possible to improve the information transmission efficiency in space optical communication system. Nevertheless, the implementation of this strategy is limited by the orbital angular momentum crosstalk caused by atmospheric turbulence. Focused Laguerre-Gaussian vortex beams are less affected by atmospheric turbulence due to their lager intensity density. Consequently, focused Laguerre-Gaussian vortex beams can be used as the carriers to reduce the orbit angular momentum crosstalk and increase the channel capacity of information transmission. In this paper, based on the spiral spectrum analysis theory, the analytical expression of spiral spectrum of focused Laguerre Gaussian beam propagating in anisotropic atmospheric turbulence is derived. The influences of turbulence and beam parameters on the received power of focused and unfocused Laguerre Gaussian beam are investigated via numerical calculations. Finally, the multi-phase screen method is used for verificating the simulation. The research findings are as follows. First, with the increase of transmission distance, turbulence intensity and topological charge, the receiving power of orbital angular momentum decreases, that is, the orbital angular momentum crosstalk turns more serious. Second, the larger the turbulence inner-scale, anisotropy index and beam wavelength are, the smaller the orbital angular momentum crosstalk is. Third, when the receiving aperture reaches a certain value, its influence on the orbit angular momentum crosstalk is very small. Fourth, different parameters have different effects on crosstalk, and the orbit angular momentum crosstalk of the focused vortex beam is less than that of the unfocused vortex beam. Therefore, in the vortex optical communication, the focused vortex beams can be used as the signal light to reduce the crosstalk between the orbit angular momentum modes, and thus improving the communication quality. These results have some theoretical reference values for reducing crosstalk in free-space optical communication.
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