## Vol. 66, No. 23 (2017)

##### 2017-12-05

###### GENERAL

2017, 66 (23): 230302.
doi: 10.7498/aps.66.230302

Abstract +

Quantum information theory can improve the performances of the classical information techniques by utilizing the entangled state of electromagnetic field. Path entangled microwave signal distributes its entangled states between spatially separated subsystems of an information system, which can be widely applied to quantum information technology in the future. Currently, there are only several reports on path entangled microwave signal generation. Therefore, the quality of path entangled microwave signal is far from satisfactory. In order to improve the quality of path entangled microwave signal further, we make a discussion about the factors that affect the quality of it and design a quality evaluation scheme for it. Based on the designed quality evaluation scheme, an optimal squeezed parameter selection method is suggested.Firstly, the generation principle of path entangled microwave signal is briefly introduced, and the generated signal is denoted as quantum mechanics operator in the Fock state representation. In the meantime, the qualitative relationship between generated signal and the squeezed parameter is determined. Secondly, a quality evaluation method for path entangled microwave signal is proposed:the quality of generated signal is evaluated by comparing with the expectation value of the entangled microwave photon number which reflects the degree of quantum entanglement. Finally, an approach to selecting the optimal squeezed parameter for generating the path entangled microwave signals is proposed based on the quality evaluation method. The process of it is as follows:an array of squeezed parameters which achieve the highest entanglement probability of different microwave photons is acquired under the premise that the maximal effective number of entangled microwave photons is set to be a certain value. Then an array of expectation values of number of entangled microwave photons corresponding to these squeeze parameters is acquired, and the squeezed parameter corresponding to the largest expectation value is what we are searching for. Through theoretical analysis, we draw a conclusion that the quality of path entangled microwave signal is determined by squeezed parameter. Accurately, it is related to the squeezed degree, but unrelated to the squeezed angle. From simulations, we find that the maximal expectation value of the total number of entangled microwave photons is 3.77 when the simulation proceeds on condition that the maximal number of effective entangled microwave photons is set to be 26. And its corresponding squeezed degree value is 1.77, which means that the optimal path entangled microwave signal can be generated when we set the value of squeezed degree to be 1.77. And our method is proved effective by the simulation results. We provide an original idea on generating high-quality path entangled microwave signals for its experiments and applications.

2017, 66 (23): 230303.
doi: 10.7498/aps.66.230303

Abstract +

Quantum communication protects information security by means of the basic laws of quantum mechanics and has aroused the wide public interest over the recent years.Quantum communication consists of quantum key distribution, quantum secure direct communication,quantum teleportation,quantum dense coding,and quantum secret sharing.The purpose of quantum key distribution,quantum secure direct communication and quantum secret sharing is to protect the security of information and thus they are called quantum cryptography.In quantum key distribution and secret sharing,data transmitted in the quantum channel are random keys rather than information,and the information is sent through another classical communication.The direct communication of information through quantum channel is realized in quantum secure direct communication.In this paper,we present a protocol for quantum communication by using quantum teleportation (QCUQT),and analyze it in detail.First,we answer the question whether QCUQT is a type of quantum secure direct communication.In QCUQT,only computational basis states are teleported,and both the Bell-basis measurement and the single particle operations can be simplified.It is found that the QCUQT is equivalent to the combined process of a quantum key distribution plus a classical communication rather than a type of quantum secure direct communication.In order to read out the information in the quantum channel,classical communication is required by QCUQT.Some misunderstandings about QCUQT are discussed and clarified in the paper.It was mistaken that the transmission of quantum state in QCUQT is irrelevant to the channel noise nor the distance between two parties,and QCUQT can even be used to realize superluminal communication.Our study shows that the QCUQT is affected by the medium and also the distance between two parties,and it does not have an advantage over quantum key distribution,and cannot realize quantum superluminal communication either.We also compare the QCUQT with quantum key distribution,quantum secure direct communication,and classical one-time-pad in several aspects such as the nature of the data in quantum channel,the way of reading out the key,the way of transmitting messages,and the amount of data carried in the process.We also point out the characteristics of each type of communication.It is concluded that single-photon quantum key distribution is easier to realize than QCUQT because single-photon detection and generation are easier to realize than the Bell-basis measurement and generation of EPR pairs.In particular,we discuss the use of these protocols in space communication and it is suggested that quantum secure direct communication be a better choice in outer-space quantum communication because of the low loss in quantum channels there.

2017, 66 (23): 230501.
doi: 10.7498/aps.66.230501

Abstract +

A traffic flow time series is a sequence of traffic detection parameters in chronological order. This differs from a general quantitative data sequence in that the time series includes a time attribute that contains not only the data with time characteristics, but also the distribution of the data itself. To date, studies of traffic time series have primarily adopted data mining methods consisting of data mining and machine learning methods–similar sequence search, dimension reduction, clustering, classification, pattern analysis, prediction, etc. In order to improve the visualization of traffic flow time series and feature analyses, a proposed method builds the association networks of traffic flow time series by using visibility graph theory. This approach differs from traditional traffic flow theory as it performs feature analysis of traffic flow time series from the perspective of complex networks, and then analyzes the relationship between the characteristics of the structure in the visual network and the state characteristics of the traffic flow. The proposed method also takes into account the different traffic flow time sequences that correspond to different traffic states.In the network building process using the proposed method, the traffic flow is classified by correlating the traffic flow parameters to the structure of the complex time series networks under different traffic conditions through considering the changes in traffic flow characteristics under various traffic conditions. Next, statistical analyses of the signs and attributes of the networks (e.g. degree distribution, clustering coefficient, network diameter, and modularization) are conducted. The analysis results show that the proposed visibility graph method can provide an effective approach to mapping traffic flow time series to the network. Moreover, the modularity, clustering coefficient, and degree distribution of the traffic flow time series networks in different traffic states show specifically varying patterns, providing a way to visually analyze the trends in traffic flow operation. When the traffic condition is at level 1, the distribution of the scattered points of the network conforms to a power law distribution. When the traffic condition is at any other level, the distribution of the scattered points of the network is consistent with a Gaussian distribution. The modularity of the time series network also shows some statistical characteristics, that is, the number of modules grows rapidly when the traffic state switches from smooth to moderate congestion, but decreases slowly when the traffic state switches from moderate congestion to serious congestion. These characteristics can be used to distinguish different traffic states, providing more perspective to understand different traffic scenarios. In this work we preliminarily study the attributes of traffic time series based on the proposed visibility graph method. Future efforts will continue to compare various methods of time series network construction to determine the pros and cons of each method for further analysis.

2017, 66 (23): 230102.
doi: 10.7498/aps.66.230102

Abstract +

With the development of computing technology, numerical exact diagonalization method plays a vital role in modern computational condensed matter physics, especially in the research area of strongly correlated electron systems:it becomes a benchmark for other numerical computational techniques, such as quantum Monte Carlo, numerical renormalization group, density matrix renormalization group, and dynamic mean field theory. In this paper, we first numerically exactly diagonalize the three-dimensional hydrogen atom with the combination of finite-difference method, and find that the numerical wave function of ground state is in good agreement with the analytical calculations. We then turn to discuss the space dimension confinement hydrogen system, two-dimensional hydrogen atom, and notice that the numerical wave function is no longer in agreement with the analytical calculation, where the ground state wave function has a numerical singularity as radius approaches to zero. Compared with the case of the three-dimensional hydrogen atom, this issue mainly comes from the nature of space dimension confinement. To resolve such an issue of numerical singularity in two-dimensional hydrogen atom, we need to construct a new discrete and normalized Bessel function as a basis to study the ground state behavior of dimension confinement system based on the framework of Lanczos-type numerical exact diagonalization. The constructed normalized Bessel basis is orthogonal and discrete, and thus becomes suitable for practical calculation. Besides, these prominent properties of such a Bessel basis greatly reduce the complexity and difficulty in practical calculation, and thus makes computing work efficient. In addition, Lanczos-type numerical exact diagonalization method can extremely speed up the process of solving the eigenvalue equation. As a result, such a high efficient calculation of our method demonstrates the consistence between numerical and analytical ground state energy value, and the corresponding wave function with enough truncated basis number. Since this kind of numerical singularity occurs in many space dimension confinement systems, our finding for constructing a new discrete Bessel basis function may be helpful in studying the quantum systems with numerical singularity behaviors in wavefunctions in future. On the other hand, it should be pointed out that the Bessel basis is incorporated into the linear augment plane wave method in the density functional theory to study the electronic band structure of the condensed material and obtain high accurate results, especially in the theoretical prediction of topological insulators and in experimental realization as well.

2017, 66 (23): 230301.
doi: 10.7498/aps.66.230301

Abstract +

The quantum reflection and interference of Bose-Einstein condensates (BECs) encountering a potential barrier or well is one of the most efficient ways of studying the exotic properties of macroscopic matter waves. As a matter of fact, one can reveal the quantum nature, coherence properties, and many-body effects as well as the potential applications of ultracold atomic gases by virtue of the quantum reflection and interference of BECs. Although there have been extensive investigations regarding the quantum reflection and interference of single-component BECs, so far there have been very few studies regarding those of multi-component BECs. In this work, we investigate the quantum reflections and interferences of spin-dependent BECs in semi-infinite potential wells by using the propagation method and the time-of-flight imaging scheme which is widely used in cold atom experiments. We obtain the exact analytical solutions of the spin-dependent condensate wave functions in the semi-infinite potential wells. It is shown that once the spin-dependent optical lattice is switched off the spin-dependent matter wave packets delocalized in different lattice sites interfere with each other during the free expansion. Consequently, the interference fringes with high contrast are formed. At the same time, the expanded spin-dependent matter waves encounter the hard wall of the semi-infinite potential well, which leads to a quantum reflection. There is a double interference between the reflected wave and the freely expanded incident wave, which is characterized by the significant modulation effect in the interference patterns. Concretely, there exist intense density oscillations in several symmetric and local regions of the interference fringes. Essentially, the double interference is a self-interference of BECs, and it results from the interference between the spin-dependent BEC and the BEC image, where the hard wall severs as a mirror plane. Therefore it is similar to Young's double-slit interference in wave optics, and a standing wave node is formed at the trap wall. In particular, the positions and the intervals of the local density oscillations in the interference patterns are determined by evolution time, laser wavelength and laser intensity, which is verified in the numerical simulations and calculations. In addition, the effects of spin state, transport distance, and relative phase on the interference fringes are analyzed and discussed. The present investigation is helpful in understanding the macroscopic quantum properties of the spin-dependent BECs, and provides a new scheme to test the theoretical model and physical mechanism of the condensate interference in a spin-dependent optical lattice.

2017, 66 (23): 230502.
doi: 10.7498/aps.66.230502

Abstract +

Because of simple schematic structure and complex dynamical behaviors, the Chua's system is considered as a paradigm for chaos research. Despite a great many of studies relating to the Chua's system, most of them focus on its positive parameter space. This is explained by the fact that the implementation of the Chua's circuit with negative parameters needs resistors, inductances and/or capacitors with negative values, and thus leads to physical impossibility. In order to extend the parameter space of the Chua's system to its negative side, where all system parameters are negative, an equivalent realization of the Chua's circuit is developed with off-the-shelf electronic components by an electronic analogy method. Recently, the research of fractional-order chaotic systems has received considerable interest. However, the theoretical and experimental studies of the fractional-order Chua's system with negative parameters are still lacking. In this study, we set up a model of the fractional-order Chua's system in negative parameter space. The stability of all equilibrium points is investigated with the fractional-order stability theory. Based on the Grnwald-Letnikov derivative, the dynamical behaviors dependent on the control parameter and the fractional orders are investigated by standard nonlinear analysis techniques including phase portraits, the largest Lyapunov exponents, and bifurcation diagrams. In order to further verify the dynamic behaviors of the fractional-order Chua's system with negative parameters, an experimental implementation of the Chua's circuit with negative parameters based on an electronic analogy is performed with off-the-shelf electronic components such as operational amplifiers, resistors and capacitors. The experimental tests are conducted on the resulting circuit. A period-doubling bifurcation route to chaos is successfully observed and some typical phase diagrams are captured by an oscilloscope, which are well consistent with theoretical analyses and numerical simulations. The numerical simulations and the experimental results show that the fractional-order Chua's system in negative parameter space can still exhibit rich dynamical behaviors. But it is worth noting that the classical double-scroll chaotic attractor emerging in a conventional Chua's system cannot be found in this system. This work focuses mainly on the dynamical behaviors of the fractional-order Chua's system with negative parameters, which was not reported previously. Thus the research results of this study will further enrich the dynamical behaviors of the Chua's system, and play a positive role in promoting the chaos-based applications of the Chua's system. Meanwhile, the results obtained in this work lead to the conjecture that there remain some unknown and striking behaviors in the Chua's system with negative parameters, which need further revealing.

2017, 66 (23): 230101.
doi: 10.7498/aps.66.230101

Abstract +

Wireless cellular networks all over the world are undergoing a profound transformation evolving from voice-oriented to data networks. Larger coverage area, better service quality, and lower energy cost are the key issues in the deployment of cellular networks. To achieve these goals, small cells, such as the femtocells and picocells, have become an important part of the current 4G and future 5G wireless cellular networks. Generally speaking, small cell networks are deployed according to the peak traffic load, which causes energy waste during low traffic periods. Against this background, energy efficiency optimization has become one of the research hotspots in wireless communications. In this paper, we focus on the energy efficiency problem in small cell networks in which a large number of small cells are spatially deployed in dense urban areas such as office buildings and shopping malls. We optimize the energy efficiency through small cell dormant mechanism under the constraints of average connection ratio (ACR) and average downlink channel capacity. First, we derive the mathematical expressions for average downlink channel capacity and ACR in three-dimensional (3D) small cell networks by Poisson point process (PPP) theory. Second, the monotonicities of channel capacity and ACR are analyzed in detail. Then, based on the results of monotonicity analysis, the optimal small cell dormant probability is calculated to satisfy the constraints of ACR and average downlink channel capacity respectively. Finally, we formulate a network energy consumption minimization problem subject to the constraints of ACR and channel capacity to determine the dormant probability. In addition, we also formulate an optimal maximum connection number of small cells, which minimizes the energy consumption subject to the joint constraints of ACR and channel capacity. Numerical results show that our 3D PPP model is more accurate than the traditional two-dimensional (2D) one in both channel capacity and ACR performance, and that the energy consumption of small cell networks can be reduced by about 21% of the total energy consumption with the dormant strategy in this paper. More importantly, the optimal dormant probability and appropriate configuration of the maximal number of connection can be effectively used to design small cell dormant strategy for 3D small cell networks.

2017, 66 (23): 230503.
doi: 10.7498/aps.66.230503

Abstract +

Aiming at the data security problem in big data environment, in this paper we propose a new chaotic encryption algorithm based on both big data platform named Hadoop and non-degenerate high-dimensional discrete hyperchaotic system. The algorithm utilizes the chaotic stream cryptography and reads the data from HDFS of Hadoop platform. After fragmentation processing and MapReduce programming, the data are encrypted and decrypted by Map function in parallel. The Reduce function implements the merging operation of the data and stores them on the HDFS. The algorithm has a better execution efficiency. Compared with the low-dimensional chaotic system based encryption algorithm, the non-degenerate high-dimensional discrete chaotic system based encryption algorithm can improve the system security performance. It can pass the strict TESTU01 test with better statistical properties and make sure that the correlation with the parallel ciphertext is very small. Numerous key parameters increase the difficulty in making estimation or identification. Under the closed-loop feedback in ciphertext, it has the ability to resist the known and chosen plaintext attacks.

2017, 66 (23): 230601.
doi: 10.7498/aps.66.230601

Abstract +

The accurate measurement of the weak geomagnetic field is of significance for different disciplines. It can provide sufficient navigation information for both human beings and different natural animal species. Inspired by avian magnetoreception models, we consider the feasibility of utilizing quantum coherence phenomena to measure weak static magnetic fields. We propose an experimentally feasible scheme to measure weak static magnetic fields with nitrogen-vacancy color center in diamond. Nitrogen-vacancy color centers are regarded as an ideal platform to study quantum science as a result of its long coherence time up to a millisecond timescale at room temperature. In a high-purity diamond, the hyperfine interaction with the surrounding 13C nuclear spins dominates the decoherence process. In this paper, by the cluster-correlation expansion, we numerically simulate the decoherence process between|0⟩ ightangle and|+1⟩ ightangle states of the individual nitrogen-vacancy color center electron spin in the 13C nuclear-spin baths with various magnitudes of external magnetic fields. By applying the Hahn echo pulse sequence to the system, we obtain the coherence of the nitrogen-vacancy color center electron spin as a function of total evolution time and magnetic field. Furthermore, we obtain the high-accuracy relationship between the three decoherence-characteristic timescales, i.e., TW, TR, T2, and magnetic field B. Finally, we draw a conclusion that TR has the highest sensitivity to the magnetic field in the three timescales. Thus, for a certain nitrogen-vacancy color center, TR can be the scale for the magnitude of the magnetic field, or rather, the component along the nitrogen-vacancy electronic spin axis. When measuring an unknown magnetic field, we adjust the nitrogen-vacancy axis to the three mutually orthogonal directions respectively. By this means, we obtain the three components of the magnetic field and thus the magnitude and direction of the actual magnetic field. The accuracy can reach as high as 60 nT·Hz-1/2, and can be further improved by using an ensemble of nitrogen-vacancy color centers or diamond crystals purified with 12C atoms. In summary, our scheme may provide an alternative method of accurately measuring the weak geomagnetic field by the nitrogen-vacancy color center under ambient condition.

2017, 66 (23): 230701.
doi: 10.7498/aps.66.230701

Abstract +

A series of Na2CaSiO4:Sm3+, Eu3+ phosphors is prepared by the high-temperature solid-state reaction method at 1150℃, and their crystal structures, luminescent properties and energy transfer phenomenon influenced by Sm3+ and Eu3+ are studied. The X-ray diffraction results indicate that the samples single-and co-doped with Sm3+ and Eu3+ keep single-phase and no impurity phases are observed. At the excitation wavelength of 404 nm, the Na2CaSiO4:Sm3+ samples emit narrow-band spectral fluorescence with lines composed of peak-to-peak values of 565, 602, 650, 713 nm, which correspond to the electronic transitions of Sm3+ from the ground state level 4G5/2 to 6H5/2, 6H7/2, 6H9/2, and 6H11/2. On the other hand, the Na2CaSiO4:Eu3+ sample exhibits red emission with a peak-to-peak value of 613 nm at the excitation wavelength of 395 nm. The analyses of the spectrum and lifetime of fluorescence show that with the increase of Eu3+ content, the emission intensity of Sm3+ decreases and the emission intensity of Eu3+ increases. Moreover, the lifetime corresponding to Sm3+ at 602 nm decreases gradually. It is indicated that the energy transfers from Sm3+ to Eu3+. The critical distance of energy transfer is 1.36 nm, which is calculated by the concentration quenching method. The energy transfer mechanism is ascribed to the quadrupole-quadrupole interaction. As the Eu3+ doping concentration increases, the transfer efficiency increases to 20.6%. In conclusion, the Na2CaSiO4:Sm3+, Eu3+ phosphors may be used as a red component for white light-emitting diodes.

## EDITOR'S SUGGESTION

2017, 66 (23): 230304.
doi: 10.7498/aps.66.230304

Abstract +

Quantum entanglement as an important resource in quantum computation and quantum information has attracted much attention in recent decades. The effect of temperature should be viewed as an external control in the preparation of entangled state, and the thermal entanglement of the Heisenberg spin model has been discussed intensively. Due to the quantum fluctuation and thermal effect, there have been found some interesting physical phenomena in the geometrically frustrated spin system at zero or a certain temperature. Meanwhile, the lattice spin system with triangular plaquettes is regarded as a general structure of magnetic material. In this paper, we theoretically analyze the thermal entanglement of Ising-Heisenberg chain with triangular plaquettes. The transfer matrix method is used to calculate numerically the thermal entanglement in the infinite Ising-Heisenberg chain. We consider three kinds of Heisenberg spin interaction models (i.e., XXX-Heisenberg model, XXZ-Heisenberg model and XYZ-Heisenberg model), and discuss the effects of magnetic field and temperature on the three models, respectively. The results show that temperature and magnetic field have important effects on the three models. Meanwhile, it is found that the XXX-Heisenberg model is more sensitive than the anisotropy model (i.e., XXZ-Heisenberg model or XYZ-Heisenberg model) when temperature rises. A certain magnetic field would promote the generation of the quantum entangled states in all the three cases when the thermal fluctuation suppresses the quantum effects of the systems. In addition, it is found that the entanglement of XYZ-Heisenberg model is more robust than the others at a higher temperature, especially when the anisotropy along the z axis is greater than that along the y axis. We also plot the variations of the critical temperature with magnetic field in the three models. From the critical temperature-magnetic field phase diagrams, we can obtain the range of parameters in which the pairwise entanglement of the system exists. We also find that the entanglement revival behaviors may occur in a specific range of the parameters. Therefore, the properties of the thermal entanglement of Ising-Heisenberg chain with triangular plaquettes can be controlled and enhanced by choosing and using suitable parameters of magnetic field and temperature.

###### ATOMIC AND MOLECULAR PHYSICS

2017, 66 (23): 233301.
doi: 10.7498/aps.66.233301

Abstract +

The forbidden transitions of I2+ may be used to measure the variations of α and μ constant in an enhanced sensitivity. We analyze the rotational spectrum of I2+ between 11860 and 13100 cm-1 and assign 5759 lines to 31 bands in an A2Π3/2-X2Π3/2 system. The accurate rotational molecular constants of 5 levels in X2Π3/2 state and 9 levels in A2Π3/2 state are obtained. On condition that the signal-to-noise ratio is limited by quantum projection noise and the linewidth is 1 Hz, the forbidden transition between X2Π3/2 and X2Π1/2 should be able to achieve the sensitivities of δα/α ≈ 2.37×10-19 a-1 and δμ/μ ≈ 1.18×10-18 a-1.

2017, 66 (23): 233101.
doi: 10.7498/aps.66.233101

Abstract +

Ultracold molecules have wonderfully potential applications in quantum system, precision measurement, and chemical dynamics, and so on. Thus, people have a strong desire for investigating the potential cooling candidates. Feasibility of laser cooled OH molecules is investigated by ab initio quantum chemistry. Potential energy curves for the ground state X2Π and low-lying excited state A2Σ+ of OH molecules are calculated by multi-reference configuration interaction method to develop an applicable cooling transition. In order to obtain more accurate results, the calculations involve Davidson corrections, scalar relativistic corrections, core-valence correlation, and spin-orbit coupling effects. Based on the obtained potential energy curves of Λ-S and Ω states, spectroscopic parameters are determined by solving the one-dimensional radial Schrödinger equation, which are in good agreement with available theoretical and experimental values. The permanent dipole moments, transition dipole moments, vibrational levels, Franck-Condon factors and radiative lifetimes of OH molecules are also calculated. The results indicate that the OH molecule has a highly diagonally distributed Franck-Condon factor (f_{00}=0.9053) for the A2Σ+ (ν'=0} ight) → X2Π (ν"=0} ight) transition and short radiative lifetime (τ00=5.8363×10-7 s) for the A2Σ+ state. It means that the OH molecule meets the criteria as a promising candidate for direct laser cooling, which can ensure rapid and efficient laser cooling. Finally, a specific scheme for laser cooling of OH molecules is proposed, and the scheme for the A2Σ+ → X2Π transition requires three laser wavelengths, i.e., main pump laser with λ00=307.1532 nm, two repumping lasers, with λ10=344.9163 nm and λ21=349.7659 nm, respectively. The data imply the probability of laser cooling OH molecules with three electronic levels. In addition, the calculated results also indicate that spin-orbit splitting of X2Π is much less than vibrational level, which leads to the conclusion that spin-orbit coupling has no effect on laser cooling scheme of OH molecules. The results above will provide an important theoretical basis for preparing ultracold OH molecule.

2017, 66 (23): 233701.
doi: 10.7498/aps.66.233701

Abstract +

Classical motion of a single damped ion confined in a Paul trap is usually described by a damped harmonic oscillator model. We report the treatment of quantum damping motion of the system via a non-Hermitian Hamiltonian with dipole and quadrupole imaginary potential. By deriving and analyzing the exact solution of the system, we obtain the different real energy spectra and stable quantum states for the PT symmetry and asymmetry cases, as well as the imaginary spectrum and decaying quantum state for the PT asymmetry case. The corresponding imaginary energy parameter region and the survival probability are investigated. We find that the non-Hermitian system parameters of the external filed uniquely determine the quantum stable states and lead to the new characteristic of the morphology of wave function. Based on these properties, we propose a method of incoherently manipulating quantum transitions between the quantum stable states. By setting the decayed expectation value of ion position to be the same as the decayed displacement of the classical damped harmonic oscillator, we obtain the correspondence between the imaginary potential strength and the classical damping parameters. The results will enrich the quantum dynamics of the damped trapped ions, which may be useful in a wide application field.

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

## EDITOR'S SUGGESTION

2017, 66 (23): 234201.
doi: 10.7498/aps.66.234201

Abstract +

In the three-dimensional (3D) scanning measurement based on structured light techniques, the strong reflection surface is easy to produce local specular reflection due to the illumination of the structured light, which will cause the camera to be over-exposed, and therefore the geometry information of strong reflection surface cannot be detected. Since the digital micromirror device (DMD) has the modulating characteristics of the spatial information of incident light, an adaptive high-dynamic-range imaging method based on DMD is proposed to solve the problem of visual imaging of strong reflection surface. Firstly, a novel and computational imaging system is designed and built, and its optical model is also established. Then, the matching and mapping methods between DMD micromirrors and CMOS pixels are described in detail and realized. Meanwhile, we analyze the theory of the high-dynamic-range imaging based on per-pixel coded exposure, and design a coding control algorithm of light intensity to achieve the adaptive precision modulation of the intensity of incident light, so that the incident light in the imaging system is always in appropriate exposure intensity. The experiments show that the method can break through the limited dynamic range of the ordinary digital camera, and accurately control the intensity of incident light in each region of the measured strong reflection surfaces, and thus it can obtain the high-quality images of the local over-exposure area of the strong reflection surface. More importantly, the research will provide a new solution to the problem of 3D point cloud loss caused by local over-exposure of the strong reflection surface.

2017, 66 (23): 234202.
doi: 10.7498/aps.66.234202

Abstract +

This paper presents a novel method of generating multiple Fresnel hologram watermarks of three-dimensional objects. Firstly, the original watermark signal is used as the layers of the virtual three-dimensional object, and the encrypted watermark signal is generated in the form of complex noise by using both the region multiplexing tomography and the Fresnel double random phase coding method. Then, the spectrum of the watermark signal is conjugate symmetrically arranged and inverse Fourier transform is performed to obtain the real-valued watermark. The spectrum of the watermark signal is set to be in a non-interested region of the host spectrum to reduce their influence on the digital reconstruction of the host hologram. Finally, the encoded watermark signal is superimposed on the host hologram with a certain intensity. The original host hologram is not required during watermark reconstruction, and blind extraction is achieved. The reconstructed quick response (QR) code from the host hologram can be scanned and identified. The simulation results show that the proposed scheme has good invisibility and robustness to various types of image attacking operations such as filtering, joint photographic experts group (JPEG) compression, Gaussian noise, cropping, and rotation. The proposed method has good digital reconstruction quality for both host hologram and watermark when suffering attacks, and the QR code in the reconstruction plane has good scan recognition. Diffraction interference problem among different watermark layers is solved by the controllable post-processing of the watermarks with adjustable reconstruction and no interference, and the watermark restruction quality is improved. Furthermore, the application of virtual optics enriches the watermarking signal design method and enhances the security of the algorithm.

2017, 66 (23): 234204.
doi: 10.7498/aps.66.234204

Abstract +

Optical chaos has conducted in-depth investigation and attracted widespread attention in recent years,owing to its important applications in chaos-based secure communication,fast physical random bit generation,chaotic laser radar, lidar,chaotic optical time domain reflectometer,distance measurement,and optical fiber sensor.The key to these applications is a compact and broadband chaotic light source,because the integrated circuits have an advantage over those setups composed of discrete components in some unique virtues such as smaller size,lower cost,better stability, and better reproducibility via mass production.In order to combine the advantages of the chaotic application and integrated circuits,the integrated chaotic external-cavity semiconductor laser has aroused great interest.Note that, the integrated chaotic external-cavity semiconductor laser can work in both short-and long-cavity mechanisms,which depends on the laser relaxation oscillation frequency.The output of chaotic external cavity semiconductor laser has obvious relaxation oscillation characteristic.When the relaxation oscillation frequency is less than the external-cavity oscillation frequency,the external-cavity semiconductor laser works in short-cavity mechanism.Otherwise,it works in long-cavity mechanism.In this paper,we comparatively analyze the effects of fine-tuning cavity length on the effective bandwidth of the integrated external-cavity semiconductor laser under both short-and long-cavity mechanisms.First,we comparatively analyze the effects of fine-tuning cavity length and external-cavity feedback rate on the effective bandwidth of the integrated external-cavity semiconductor laser when relaxation oscillation frequency is 5.6 GHz. At the same time,the injection current and carrier lifetime are adjusted to observably increase the relaxation oscillation frequency.Finally,we comparatively analyze the effects of fine-tuning cavity length and external-cavity feedback rate on the effective bandwidth of the integrated external-cavity semiconductor laser when relaxation oscillation frequency is 40 GHz.Results show that for short-cavity mechanism,the chaotic output is not stable:0.1-mm deviation will lead to the conversion from chaotic state into non-chaotic state.By contrast,for the long-cavity mechanism,the chaotic output is more stable and has a larger chaotic area.It proves that the long-cavity mechanism is more feasible and conducive to the continuous achievement of a broadband chaotic laser and broadband continuous chaotic region.According to this feature,we realize the transition from short to long cavity regime by adjusting the injection current and carrier lifetime to substantially increase the relaxation oscillation frequency at the same time.We realize the transition from short to long cavity regime in a cavity length range from 2 mm to 10 mm,and then analyze the influences of the external cavity rate and external cavity length on the spectrum bandwidth of the external cavity semiconductor laser.The results show that under the long cavity mechanism,it is more conducive to the achievement of a broadband continuous chaotic region in a cavity lengt range from 4 mm to 20 mm.Considering the refractive index of integrated material,the external-cavity length for long-cavity mechanism can be shortened to a range from 1 mm to 2 mm.This length fully conforms to the butterfly packaging size.

2017, 66 (23): 234205.
doi: 10.7498/aps.66.234205

Abstract +

Real-time high-speed physical random numbers are crucial for a broad spectrum of applications in cryptography, communications as well as numerical computations and simulations.Chaotic laser is promising to construct high-speed physical random numbers in real time benefitting from its complex nonlinear dynamics.However,the real-time generation rate of physical random numbers by using single-bit extraction is confronted with a bottleneck because of the bandwidth limitation caused by laser relaxation,which dominates the laser chaos and then limits the effective bandwidth only to a few GHz.Although some bandwidth-enhanced methods have been proposed to increase the single-bit generation rate, the potential is very limited,and meanwhile the defects of system complexity will be introduced.An alternative method is to construct high-speed physical random numbers by using the multi-bit extraction.In this method,each sampling point is converted to N digital bits by using multi-bit analog-to-digital converter (ADC) and their M(M 6 N) least significant bits are retained as an output of random bits,where N and M are the numbers of ADC bits and retained bits,respectively.The generation rate of random numbers is thus equal to M times sampling rate and can be greatly increased.Whereas,in the multi-bit extraction demonstrations,the intensity output of chaotic laser is usually digitized by the commercial oscilloscope and then processed with least-significant-bit retention followed by other postprocessing methods such as derivative,exclusive-OR,and bit-order reversal.These followed post-processing operations have to be implemented off-line and thus cannot support the real-time generation of random numbers.Resultantly,it is still an ongoing challenge to develop high-speed generation schemes of physical random numbers with the capability of real-time output.In this paper,a real-time high-speed generation method of physical random numbers by using multi-bit quantization of chaotic laser is proposed and demonstrated experimentally.In the proposed generation scheme,an external-cavity feedback semiconductor laser is utilized as a source of chaotic laser.Through quantizing the chaotic laser with 6-bit ADC, which is triggered by a clock at a sampling rate of 7 GHz,a binary sequence with six significant bits can be achieved. After the selection of the two least-significant bits and self-delayed exclusive-OR operation in the field-programmable gate array (FPGA),a real-time 14-Gb/s binary stream is finally achieved.This binary stream has good uniformity and independence,and has passed the industry-standard statistical test suite provided by the National Institute of Standards and Technology (NIST),showing a good statistical randomness.It is believed that this work provides an alternative method of generating the real-time high-speed random numbers and promotes its applications in the field of information security.

2017, 66 (23): 234206.
doi: 10.7498/aps.66.234206

Abstract +

Master oscillator power amplifier (MOPA) is a common configuration in fiber lasers to obtain high power output. Amplified spontaneous emission (ASE) is amplified stage by stage by MOPA, which may result in damage to the fiber amplifier. In the experiment of high-power fiber amplifier, thermal effect is one of the most critical issues. High temperature from significant thermal effect would restrict the further improvement of laser power and cause the fiber to damage. In most of the experiments, the gain fibers are broken usually at the place 10-50 cm away from the fused point of the pump injection end. To better understand in physics the highest temperature and the position of the burning point, we study the ASE and temperature characteristics by using the rate equation model of fiber laser and the thermal conduction model of gain fiber. We analyze the influences of seed power, pump power and pump absorption on Yb-doped double-cladding fiber amplifier. The results show that when magnification is relatively high and ASE is serious, the highest temperature point of the fiber amplifier is not at the fused point of the pump injection end but at the place 10-50 cm away from the fused point, which consists well with the experimental result. For studying the ASE suppression and the temperature control of the hottest point, we compare the three parameters in the 915 nm pumped case with those in the 975 nm pumped case, these being power ratio of ASE to the output laser, hottest location along the fiber, and the ratio of the temperature difference between the highest temperature and fusion point temperature to the latter one. It is concluded that the optimal parameters for the 915 nm pumped case are seed power larger than 7 W, pump power less than 1250 W, and pump absorption less than 20 dB. As to the 975 nm pumped case, it is suggested that the seed power should be not less than 8 W with an appropriate pump power. The research also implies that a better performance of fiber amplifier is pumped by 975 nm under the same condition. To prevent the local internal hot point from forming and the potential burnout risk from happening, the magnification of fiber amplifier needs to be set below 50-fold. In conclusion, this work presents a suggestion for optimizing the fiber amplifier design through using appropriate seed power, pump power, pump absorption, magnification and pump wavelength.

2017, 66 (23): 234208.
doi: 10.7498/aps.66.234208

Abstract +

Photocurrent power spectral density function of laser heterodyne detection is obtained by the statistical theory and Wiener-Khinchin theorem. For a short-range distance heterodyne system without considering atmospheric turbulence, we observe the relations between the photocurrent spectral line distribution and the laser linewidth, the intermediate-frequency signal, and the propagation delay time of signal light relative to local oscillator light. Theoretical formula of photocurrent power spectrum in relevant papers is revised to eliminate the effect of laser linewidth. Onedimensional probability distribution model of phase noise caused by laser linewidth is built based on the signal and noise theory. Accordingly we establish a mathematical model of limit detection accuracy based on laser wavelength, detection distance, and laser linewidth, which indicates the minimum detectable amplitude of heterodyne system. According to the numerical results, we find that the distribution of photocurrent spectral line intensities is greatly dependent on the relation between delay time and coherent time. And the minimum resolvable displacement increases with the detection distance and laser linewidth increasing. When the optical limited displacement resolution is 0.266 nm with a laser wavelength of 532 nm, a laser linewidth is 1 kHz, and a detection distance is 100 m. Experimental data in relevant papers agree well with the theoretical derivations. Our findings show that the research of displacement resolution might provide a quantitative reference for the theoretical research and engineering application of short-range heterodyne resolution.

2017, 66 (23): 234501.
doi: 10.7498/aps.66.234501

Abstract +

The transversal and longitudinal wave velocities, the acoustic attenuation coefficients, the nonlinear coefficients at different pressures and the acoustic attenuation coefficient as a function of frequency in a two-dimensional (2D) monodisperse disc system are numerically calculated. The results show that the transversal and longitudinal wave velocities both exhibit a piecewise power law with pressure P. When P -4, the velocity decreases with the increase of pressure in the 2D disc granular system, and when P > 10-4, the transversal wave velocity Vt and longitudinal wave velocity Vl show the scaling power laws, i.e., νt~P0.202 and vl~P0.338, respectively. The ratio of the shear modulus to the bulk modulus G/B shows a power law scaling with the pressure, G/B~P-0.502, implying that the system lies in an L glass state at low pressure, similar to that of a three-dimensional (3D) spherical granular system. The attenuation coefficients (αT, αL) of the horizontal excitation and vertical excitation also show the picecewise behaviors with the change of frequency f. When f f. When f > 0.05, α ∝ fTα, αL ∝ f. And when f > 0.35, αT ∝ f2 and αL ∝ f1.5. In addition, the nonlinear coefficient and the attenuation coefficient of the 2D disc granular system under the vertical and horizontal excitation both also show a piecewise law behavior with pressure, similar to that of the acoustic velocity. When P -4, only the transversal nonlinear coefficient changes according to βT ∝ P-0.230, while the other coefficient has no change. When P > 10-4, the attenuation coefficients and nonlinear coefficients decrease according to their power law with the increase of pressure, i.e., βT ∝ P-0.703, βL ∝ P-0.684, αT ∝ P-0.099, αL ∝ P-0.105. The characteristic length l*, which characterizes the disordered structure responsible for the scattering, also decreases according to power law with the increase of pressure, when P -4, l* ∝ P-0.595; when P > 10-4, l* ∝ P0.236.

2017, 66 (23): 234701.
doi: 10.7498/aps.66.234701

Abstract +

To investigate the stability and transition control mechanism of supersonic boundary layer, a coupled method of velocity/temperature control based on synthetic cold/hot jet is proposed. Based on the prior dual-synthetic jet actuator, a high performance synthetic cold/hot jet is achieved by adding a cooling/heating module. By placing the actuator under the flat-plate, periodic blow-suction is produced and low momentum jets are injected into the boundary layer to control the transition. Numerical simulations are conducted to study the propagation and evolvement of the unstable waves in the supersonic flat-plate boundary layer with Ma=4.5. Influences of wall blow-suction, synthetic jet temperature, perturbation frequency, and perturbation amplitude on control effect of the unstable wave are mainly studied. The flow field and control effect are analyzed using the temporal mode of linear stability theory. The results show that without jet control, the first and second mode perturbation wave coexist simultaneously with the second mode dominant in the two-dimensional wave. In the effect of the wall blow-suction, the second mode appears to be more unstable while the first mode is suppressed. Under the control of the coupled speed-temperature, the jet temperature has significant influences on the area of the unstable region and the growth rate of the perturbation mode. When the jet temperature is different from the inlet fluid temperature, the fluctuation of temperature accelerates the transition of laminar flow to turbulent flow, and the velocity profile becomes more full, which leads to a more stable flow field. The control effect of high frequency blow-suction disturbance on flow field are better than that of low frequency. When the control frequency is higher than 400 Hz, the imaginary part of the eigenvalue ω _i of the second mode disturbance wave decreases, and the disturbance component accelerates the correction between velocity profile and temperature profile of supersonic boundary layer, thus making a more stable second mode. When the disturbance amplitude decreases to 1% of the main flow speed, only the second mode is detected of low time growth rate, which results in a better control effect. However, as the disturbance amplitude further decreases, the first mode reemerges, and its wave number overlaps with that of the second mode at first, and then, separates from each other. The research results provide a new idea for supersonic boundary layer transition control from laminar flow to turbulent flow.

2017, 66 (23): 234203.
doi: 10.7498/aps.66.234203

Abstract +

Stimulated Brillouin scattering (SBS) currently limits the power scaling of narrow-linewidth amplifiers. To date, several techniques have been employed to suppress SBS. Within these SBS suppressing techniques, the phase modulation technique is a preferable approach to obtaining kilowatt-level narrow-linewidth laser sources. In this manuscript, we numerically investigate the influence of phase modulation signals on linewidth and SBS threshold, and discuss how to choose an appropriate modulation signal for suppressing SBS with less linewidth broadening. Three types of signals are studied, including sinusoidal signal, white noise signal (WNS), and pseudo-random binary sequence signal (PRBS). Signal parameters such as modulation frequency and modulation depth are also optimized. It is found that the linewidth increases linearly with the modulation frequency, and the linewidth is largest for WNS modulation for the same modulation frequency. Specially, the linewidth is approximate to the modulation frequency for PRBS modulation. In the case of sinusoidal modulation, the spectra exhibit a series of discrete sidebands at integer multiples of the modulation frequency while the spectral power density is almost continuous for WNS modulation. In the case of PRBS modulation, the spectra contain periodic features that are distributed as a function of modulation frequency and pattern length. The SBS threshold grows to a maximum at~100 MHz modulation frequency for the case of sinusoidal signal modulation, which can be further increased by increasing the modulation depth. The SBS threshold can be further increased by implementing the cascade sinusoidal signal modulation. When WNS modulation is employed, the SBS threshold increases almost linearly with the modulation frequency and has an S-shaped increase with the modulation depth. For the PRBS modulation, the pattern length has an optimal value for SBS suppressing:the SBS threshold increases almost linearly below a frequency, but keeps stable above that frequency. The PRBSs with longer pattern lengths tend to suppress SBS more effectively in higher modulation frequency regime than those with the shorter ones. In the commonly used 1-2 GHz frequency regimes, the PRBS with a pattern length of 7 provides the best SBS mitigation, and the pattern length should be longer when the frequency is higher than 2 GHz. It should also be noted that the SBS threshold is highest when the modulation depth is close to the half-wave voltage (π). From the aspect of SBS suppression, the PRBS is superior to other two modulation signals, which can achieve higher SBS threshold with less linewidth broadening. The investigation can present a reference for the phase modulation signal designing in the power scaling of the narrow-linewidth fiber amplifiers.

2017, 66 (23): 234207.
doi: 10.7498/aps.66.234207

Abstract +

Photonic band-gap of light wave in spatial frequency model depicts the linear propagation characteristics of the light wave in period structures, based on which the linear diffraction and refraction of light are defined. In this paper, we numerically study the non-diffraction propagation and anomalous refraction of light waves in honeycomb photonic lattices according to the diffraction relationship of the photonic band-gap.By calculating the photonic band-gap structure, the linear propagation characteristics in the first transmission band are analyzed. The first Brillouin zone of the honeycomb lattice can be divided into different diffraction (Dx and Dy) and refraction regions (Δx and Δy), according to the definitions of light diffraction and refraction along the x-and y-axis. Light wave can present normal, anomalous diffraction and even non-diffraction when the wave vector matches the regions of Dx, y Dx, y > 0 and Dx, y=0, respectively. And the wave experiences the positive, negative refractions, and non-deflection when the refraction region meets the conditions:Δx, y x, y > 0 and Δx, y=0, respectively.By matching the input wave vectors to the contour lines of Dx=0 and Dy=0, we can realize the non-diffraction propagation along the x-and y-axis, respectively. When the input wave vector is set to be (0, 0), the light wave experiences normal diffraction and beam size is broadened. When the wave vector matches the point where Dy=0, the diffraction in the y-axis is obviously suppressed. To totally restrain the beam diffraction, the wave vector is set to be at the point where Dx=Dy=0. There are six intersections on the contour lines of Dx=0 and Dy=0, and these intersections are named non-diffraction points.The refraction of light can be also controlled by adjusting the input wave vector. When the wave vector is located on the contours of Δy=0, light wave propagates along the x-axis, without shifting along the y-axis. To excite the negative refractions, we need to match the input light wave to the eigen modes of the lattice, and adjust the wave vector to the negative refraction regions. We set the input wave vector to be kx > 0 and ky > 0, so that the beam would be output in the first quadrant of the coordinate if refracted normally. The eigen modes are approximated by multi-wave superposition, and the wave vector is adjusted to different refraction regions. From the numerical results of the light propagations, it is clearly seen that the propagations of a good portion of light energy follow the preconceived negative refractions, and output field is in the fourth, third, second, and third quadrant, respectively. Notably, the light waves generated by multi-wave superposition not only contain the eigen modes we need, but also include other modes. As a result, there are also energy outputs arising from the undesired modes in the other quadrants.The above conclusions are expected to provide a reference for the optical mechanisms of graphene-like optical phenomena in honeycomb photonic lattices.

2017, 66 (23): 234301.
doi: 10.7498/aps.66.234301

Abstract +

In order to build an efficient underwater acoustic sensor network in the Arctic Ocean environment, transmission characteristics of under-ice acoustic channels need comprehensive understanding. The reflecting and scattering of acoustic waves from sea ices have great influences on under-ice acoustic channels. Both topology and structure of sea surface ices are very complex and variable. The physical dimension, acoustic property and interface roughness of sea ices depend not only on local environment, but also on climate and formation time. Therefore, it is of great significance to develop a model of reflecting and scattering of acoustic waves from sea ices for investigating the sound propagation in the under-ice environment. Assuming that sea ices are a multi-layered elastic solid medium and the ice-water interface is rough and satisfies the boundary condition of perturbation, we develop a system of linear equations to solve the coherent reflection coefficient of the incident sound wave from water to sea ice. The coherent reflection coefficient is a function of the frequency of sound wave and incident grazing angle, and is numerically evaluated. The influences of ice thickness and ice-water interface roughness on the coherent reflection coefficient are analyzed. Furthermore, the method of calculating scattering coefficient by using the power spectrum density of the scattering field is introduced. The scattering coefficient as a function of the scattering grazing angle is numerically evaluated. The influences of ice thickness and ice-water interface roughness on scattering coefficient are analyzed. The results show that both the coherent reflection coefficient and the scattering coefficient are dependent on the frequency of acoustic wave, ice thickness and grazing angle. The coherent reflection coefficient is close to 1.0 and the scattering coefficient is less than 0.01 when incident grazing angle is less than 15°. In addition, the frequency of acoustic wave and ice thickness have weak influences on them. However, the frequency of acoustic wave and ice thickness have significant influences on the coherent reflection coefficient and the scattering coefficient when the incident grazing angle is big, say, greater than 30°. In general, the thicker the ice is, the smaller the coherent reflection coefficient and the scattering coefficient are. The coherent reflection coefficient is less than 0.18 when the ice thickness is greater than 10.0 m and the frequency of acoustic waves is greater than 2 kHz. The ice-water interface roughness has great influences on both the coherent reflection coefficient and the scattering coefficient. The rougher of the ice-water interface is, the smaller the coherent reflection coefficient is, and the bigger the scattering coefficient is.

2017, 66 (23): 234702.
doi: 10.7498/aps.66.234702

Abstract +

Boundary integral simulation has been conducted to study the motion and deformation of bubbles with weak viscous and surface tension effects in fluid. Both normal and tangential stress boundary conditions are satisfied and the weak viscous effects are confined to the thin boundary layers around bubble surfaces, which is also known as boundary layer theory of bubble. By using this method, the influence of viscosity and surface tension of fluid on the motion of bubbles has been studied. Both axisymmetric and three-dimensional numerical results are compared with analytical results of Rayleigh-Plesset equation. Good agreement between them is achieved, which validates the numerical model. On this basis, interaction model between two vertically placed bubbles is established, by taking the surface tension, gravity, and viscous effects into consideration. Variations of physical quantities including bubble deformation, jet velocity, and energy of fluid are studied. Last but not least, the influence of viscosity and surface tension on the motion of a spherical bubble is investigated. It is found that viscous effects of fluid depress the pulsation of bubble and part of fluid energy is transformed into viscous dissipation energy. As a result, the development of bubble jet, the radius of the bubble, and the jet velocity are reduced gradually. On the other hand, the surface tension of fluid does not change the range of the bubble pulsation but reduces the period of the bubble pulsation and enhances the potential energy of the bubble. This model and numerical results aim to provide some references for bubble dynamics in bioengineering, chemical engineering, naval architecture, and ocean engineering, etc.

###### PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

2017, 66 (23): 235201.
doi: 10.7498/aps.66.235201

Abstract +

An important effect of the interfacial instability occurring at the interfaces of gases is to enhance the mixing of gases. In the present paper, the vortex/wall interactions at the late stage of the evolution of V shaped air/interface accelerated by weak shock wave in a duct is numerically simulated using high-resolution finite volume method with minimized dispersion and controllable dissipation (MDCD) scheme. The objective of the present paper is to study the mechanism of mixing enhancement due to the vortex/wall interactions. Because of the shock impingement, the Richtmyer-Meshkov instability is first developed. As a result, the baroclinic vorticity is deposited near the interface due to the misalignment of the density and pressure gradient right after the interaction of shock wave with V shaped interface, leading to the formation of vortical structures along the interface manifested by the Kelvin-Helmholtz instability. The vortices induce the rolling up and deformation of interface, and multi-scale vortical structures are generated because of the interaction and merging between vortices. This process eventually causes the turbulence mixing transition. The vortex induced velocity field drives the vortices to move to the lower/upper walls of the duct, leading to the complicated interaction between vortex and wall. It is observed in the numerical results that during the vortex/wall interaction, vortex is accelerated along the wall, leading to the stretching of material interface. Then the primary vortex will lift off from the wall and forms a second vortex. These two phenomena are the two main mechanisms of the mixing enhancement. Because of the inherent instability at the interface, the stretching of the interface will spread the area of instability. Furthermore, at the late stage of the interfacial instability, the flow near the interface is turbulent because of the rolling and pairing of the vortices. Therefore, the stretching of the interface will speed up the development of the interfacial turbulence and enhance the mixing. The vortex lifting off from the wall can directly speed up the mixing since it makes the heavy gas move directly into the light gas. To further determine which mechanism is dominant, we study the evolution of the mixing parameter derived from a fictitious fast chemical reaction model. It is shown that during the acceleration of the vortices along the wall and the stretching of the interface, the slope of the mixing parameter increases by a factor of 2, which indicates a significant mixing enhancement. And the vortices lifting off from the wall also shows considerable mixing enhancement but it is not so strong as the first mechanism.

###### CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

2017, 66 (23): 237401.
doi: 10.7498/aps.66.237401

Abstract +

The superconductivity has always been one of the important topics in condensed matter physics. Recently, the discovery of superconductivity in potassium-doped picene have opened the way to a new class of organic superconductor, and at the same time metal-doped aromatic hydrocarbons have attracted great interest of researchers in investigating their physical and chemical properties. In this paper, according to the plane wave and pseudopotential method in the framework of density functional theory, we systematically study the structural and electronic properties of the K/Ba-codoped phenanthrene, including the atomic structure, band structure, density of states, formation energy, and charge transfer between dopant and phenanthrene molecule, and three meaningful conclusions have been drawn as follows. At first, the van der Waals interaction is found to play an important role in determining the atomic structure of metal-doped molecular solid, so it is necessary to include the interactions in these calculations. Secondly, due to the similarity in ionic radius, the combination of K and Ba is the favorable scheme for multiple-metal codoped phenanthrene crystal compared with K/Ca and K/Sr codoping schemes. From the viewpoint of formation energy, K1Ba1-phenanthrene has a bigger formation energy (-0.25 eV) per doped metal atom than K1Sr1-phenanthrene (-0.13 eV) and K1Ca1-phenanthrene (-0.04 eV). Thirdly, in order to realize the -3 valent state of phenanthrene molecule in K/Ba-codoped phenanthrene, the codoping of monovalent and bivalent metals is the only viable option due to the narrow interstitial space in molecular crystal. The bands crossing the Fermi level are from the lowest unoccupied molecular orbital (LUMO) and LUMO+1 orbital, resulting in the metallic state of K1Ba1-phenanthrene. The large density of states at the Fermi level is 17.3 eV-1, and these electronic states are mainly from C 2p orbitals and a little contribution from Ba 5d orbitals. Our studies present the electronic structure of K1Ba1-phenanthrene and suggest that K/Ba-codoping is a rational scheme to synthesize the superconductive sample, which provides a new route to the exploration of the promising superconductivity in metal-doped aromatic hydrocarbons.

2017, 66 (23): 237801.
doi: 10.7498/aps.66.237801

Abstract +

Metal nanoparticles have potential applications in the fields of optical sensing and optoelectronic devices, due to the localized surface plasmon resonance (LSPR) which enhances the spontaneous emission rate of nearby fluorescent molecules. The LSPR of metal nanoparticles is closely related to its material, shape, size and ambient medium, which affects the applications of nanoparticles in specific devices. In this paper, the LSPR effect of silver nanoparticles (SNPs) with different shapes of sphere, ellipsoid, cube, and triangular-prism, is investigated by using a three-dimensional finite difference time domain. The absorption and scattering spectra of the individual SNPs are first calculated. The resonance peaks are red shifted and enhanced with sharpness increasing from the nano-sphere to the nano-triangular-prism because the surface charges accumulate in the sharp corners. Then the effects of SNPs on the radiation power of the dipole source and light extraction efficiency of the light-emitting diodes (LEDs) are studied. The dipole radiation power decreases near the resonance wavelength due to the absorptions of SNPs, while increases after the resonance wavelength because of the coupling between the SNP LSPR and the dipole radiation. The calculated electric field distribution shows that the LSPR electric field of the SNPs concentrate near the surface of the dielectric film because of the interaction between the SNPs and the film. The concentrated electric field helps to improve the coupling between the LSPR and the dipole, which enhances the dipole radiation power in the LED. In the several kinds of SNPs, nano-cube SNP shows the most significant improvement on the dipole radiation power because of the strongest interaction with the dielectric film. In addition, the scattering effect of the SNP reduces the internal total reflection of light and improves the light extraction efficiency of the LED. Nano-ellipsoid SNP significantly enhances the light extraction because of its strongest scattering intensity. Further, the influence of the refractive index of the dielectric film on the dipole radiation power is studied. It is found that a higher refractive index of dielectric film helps to enhance the interaction between the SNPs and the film and improves the dipole radiation power. The optimized value of refractive index is acquired through detailed calculation.

2017, 66 (23): 237101.
doi: 10.7498/aps.66.237101

Abstract +

Low-frequency noise in the hydrogenated amorphous silicon thin film transistor is investigated in this paper. The drain current noise spectral density shows a 1/fγ (γ ≈ 0.92, f represents frequency) behavior which ascribes to fluctuations of the interfacial trapped charges due to the dynamic trapping and de-trapping of free carriers into slow oxide traps and localized traps. The normalized noise has the power law dependence on overdrive voltage, and the power law coefficient is about -1 which illustrates that the flicker noise is dominated by mobility fluctuation mechanism. By considering the contact resistance, and emission and trapping processes of carriers between localized states in the Si/SiNx interface, the variation of low frequency noise with drain current is analyzed and fitted by use of the theory of carrier number fluctuation with correlated mobility fluctuation (ΔN-Δμ model). Furthermore, the relationship between surface band-bending and gate voltage is extracted based on subthreshold current-voltage characteristics, and thus the density of localized states is then extracted through the measurement of drain current noise power spectral density. The experimental results show an exponential localized state distribution in the band-gap while densities of two defect modes at the bottom of conduction band NT1 and NT2 are about 6.31×1018 and 1.26×1018 cm-3·eV-1, and corresponding characteristic temperatures TT1 and TT2 are about 192 and 290 K, which is similar to the reported distribution of tail states in the amorphous silicon layer. Finally, the average Hooge's parameter is extracted to estimate the quality of devices and materials.

###### INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

2017, 66 (23): 238101.
doi: 10.7498/aps.66.238101

Abstract +

The phase transition characteristics of tungsten-doped vanadium dioxide film driven by an applied voltage are studied in the paper.A high-quality film is successfully deposited on an FTO (F:SnO2) transparent conductive glass substrate by direct current magnetron sputtering and post-anneal processing.First of all,an FTO substrate is placed in the chamber of magnetron sputtering system after being cleaned and dried.Then W-doped vanadium film is fabricated on the substrate with V-W alloy target with 1.4% W by mass fraction.In the process of magnetron sputtering,the operating pressure is kept at 3.0×10-1 Pa,and the operating voltage and current are 400 V and 2 A,respectively.Finally,W-doped VO2 film with a thickness of about 310 nm is prepared by being annealed at 400℃ in air atmosphere for 2.5 h.In order to explore the crystal structure,element constituents,surface morphology,roughness and photoelectric properties of W-doped vanadium dioxide film,it is respectively characterized by X-ray photoelectron spectroscopy (XPS),X-ray diffraction (XRD),scanning electron microscope (SEM),atomic force microscope (AFM) and semiconductor parameter analyzer.The XPS analysis confirms that there are no other elements except vanadium,oxygen,carbon and tungsten on the surface of W-doped VO2 film.The XRD patterns illustrate that tungsten-doping exerts an influence on the crystal lattice of VO2,but the film still prefers the orientation (110).The SEM and AFM images display that the film with low roughness has a compact structure and irregular crystal particles.Tungsten-doping is found to be able to improve the surface morphology of VO2 thin film significantly.In addition,a remarkable change in electrical resistivity and a narrow thermal hysteresis loop are also obtained in the metal-semiconductor phase transition.Further,the influences of tungsten-doping on the phase transition properties of the film are analyzed.The experiment demonstrates that the threshold voltage at which the phase transition of W-doped VO2 film occurs is 4.2 V at room temperature when the film is driven by an applied voltage ranging from 0 V to 8 V.It can be observed clearly that the current changes abruptly by two orders of magnitude.As the ambient temperature rises,the threshold voltage of phase transition drops and the current varies slightly.The optical transmittance curves show the distinct differences under applied voltage at different temperatures.It is found that the infrared transmittance difference reaches up to a maximal value of 27% at 50℃ during phase transition,while it increases by only 23% at 20℃ in a wavelength range of 1100-1500 nm.All these outstanding features indicate that W-doped VO2 film has excellent properties of electrically-induced phase transition. Compared with undoped-VO2 film,the W-doped VO2 film is predicated to have a wide range of applications in the high-speed optoelectronic devices due to its advantages of lower phase transition temperature,resistivity and threshold voltage

2017, 66 (23): 238801.
doi: 10.7498/aps.66.238801

Abstract +

It is very important to accurately model Li-ion battery and estimate the corresponding parameters that can be used for battery management system (BMS) of electric vehicles (EVs). However, the rigorous pseudo-two-dimensional (P2D) model of Li-ion battery is too complicated to be adopted directly to online state estimation and real-time control of stage-of-charge in BMS applications. To solve this problem, in this study we present a simplified pseudo-two-dimensional (SP2D) model by the electrolyte dynamic behaviors of electrochemical battery model, which is based on the porous electrode theory and concentration theory. First, the classical concentration equations of Li-ion battery P2D model are investigated and introduced, based on which, the approximated method of describing the concentration distributions of Li-ion battery described by the SP2D model is given by ignoring the variation of Li-ion wall flux density across the electrode thickness; then, the Li-ion battery terminal output voltage, the solid phase concentration and potential diffusion, the electrolyte concentration and potential distribution can be calculated based on the averaged electrochemical dynamic behaviors of Li-ion battery. Moreover, by employing some concentration assumptions:1) the solid-phase lithium concentration in each electrode is constant in spatial coordinate x, and uniform in time; 2) the exchange current density can be approximated by its averaged value; 3) the total amount of lithium in the electrolyte and in the solid phase is conserved; with the averaged dynamics of SP2D model, the simplified calculation expression for Li-ion battery terminal voltage is derived. Finally, a case study of Sony NMC 18650 Li-ion battery is conducted, and the simulated comparisons among the battery voltages at different-C-rate galvanostatic discharges, and the related electrolyte concentration of Li-ion at 1 C-rate are conducted. Moreover, the proposed SP2D model is used to predict the battery voltage and electrolyte concentration distribution with respect to the P2D model under hybrid pulse power characterization condition and urban dynamometer driving schedule condition, and the corresponding test data are used to verify the accuracy of the SP2D model. It is observed that the simulated data of SP2D model are in good accord with those of the P2D model and test curve under these two operation conditions, which further validates the effectiveness of the proposed electrochemical model of Li-ion battery. Accordingly, the proposed SP2D model in this paper can be used to estimate real-time state information in advanced battery management system applications, and can improve the calculation efficiency significantly and still hold higher accuracy simultaneously than that from the P2D model.

2017, 66 (23): 238501.
doi: 10.7498/aps.66.238501

Abstract +

Owing to the novel structure and rich electromagnetic properties, graphene shows very great promise in developing future nano-electronic devices and has thus attracted ever-increasing attention. Its isomorph-single layer, hexagonal boron-nitride (h-BN), in which carbon atoms in graphene are replaced with alternating boron and nitrogen atoms in the sp2 lattice structure, has led to a new research boom in condensed matter physics and material science. Although an h-BN layer has a similar structure to graphene, it possesses a number of properties different from its carbon counterpart. In this work, the first-principles method based on density functional theory is used to study the structural stability, magneto-electronic properties and mechano-magnetic coupling effects for an armchair BN nanoribbon doped with different transition metals (ABNNR-TM). The calculated binding energy and molecular dynamic stimulation suggest that these structures are stable. Meanwhile, the calculated results show that ABNNR-TM holds diverse magneto-electronic properties upon different TM doping. For example, they may be nonmagnetic metals, nonmagnetic semiconductors, magnetic metals, magnetic semiconductors, or bipolar magnetic semiconductors. In particular, the bipolar magnetic semiconductor is an important semiconducting material, which has promising applications in the fields of the giant magnetoresistance and the spin rectifying devices. Besides, the investigations on mechano-magnetic coupling effects indicate that magneto-electronic properties of ABNNR-TM are very sensitive to the stress, which can realize the phase transformation between the nonmagnetic metal, nonmagnetic semiconductor, magnetic metal, magnetic semiconductor, bipolar magnetic semiconductors, and half metal. Particularly, the obtained wide-gap half metal is of significance for developing novel spintronic devices. In short, this work demonstrates that it is possible to tune magneto-electronic properties of ABNNR-TM by mechanic method.

## EDITOR'S SUGGESTION

2017, 66 (23): 238701.
doi: 10.7498/aps.66.238701

Abstract +

Calcium ion (Ca2+) is a signal for both life and death in cells. Either directly or indirectly, Bcl-2 protein can regulate Ca2+ release from IP3R channel, thereby determining the cell fate. In this work, based on recent experimental results, a mathematical model is constructed to describe the signaling pathway of Ca2+ release regulated by Bcl-2 indirectly. The model output fits nicely to the experimental data. The model demonstrates that Bcl-2 can suppress Ca2+ signaling. After the robustness test of the model, the roles of some key components in the signaling pathway are predicted. Two-parameter bifurcation analyses of[IP3] and [Bcl-2] are conducted to show that Bcl-2 has a crucial role in the oscillatory region of Ca2+ signaling. Single-parameter bifurcation analyses of [PP1] and [PKA] reveal that the PP1 can inhibit Ca2+ from signaling potently, while PKA only promotes Ca2+ signaling to some extent. Our model also indicates that the different combinations of concentrations of IP3, Bcl-2 and PKA generate complex regulations on Ca2+ signaling. This work not only plays a guiding role in relevant biological experiments, but also provides some insights into the treatment of diseases caused by disruption of Ca2+ homeostasis.

###### CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

2017, 66 (23): 236201.
doi: 10.7498/aps.66.236201

Abstract +

Pressure-induced hydrogen bond symmetrization of InOOH as well as its effects on the elastic properties is investigated by first-principles simulation. The results indicate that the hydrogen bond in InOOH symmetrized at about 18 GPa, resulting in the pressure derivative of the b/c axial ratio changing from negative to positive. While the a/c axial ratio increases with the increasing pressure over a range of 0-40 GPa, its pressure derivative does not change significantly across the hydrogen bond symmetrization. In the text, A-InOOH denotes the asymmetric hydrogen bond phase and S-InOOH refers to the symmetric hydrogen bond phase. The compressional and off-diagonal elastic constants, bulk modulus B, Poisson's ratio , B/G (G represents shear modulus) and longitudinal wave velocity VP increase with the increasing pressure in both A-InOOH and S-InOOH. These properties of A-InOOH are significantly smaller than those of S-InOOH, and therefore they increase abnormally during the hydrogen bond symmetrization, such as a 20%-40% increase of the bulk modulus. Shear modulus G and Young's modulus E increase with the increasing pressure in A-InOOH, but decrease with the increasing pressure in S-InOOH, implying that hydrogen bond symmetrization would change their pressure evolution trends obviously. Shear elastic constant C44 and shear wave velocity VS decrease with the increasing pressure in both A-InOOH and S-InOOH, and more quickly in the latter, indicating that the structure change of hydrogen bond would change their pressure evolution rates. The Young's moduli along the[100],[010] and[001] directions increase with the increasing pressure in A-InOOH, while decrease with the increasing pressure in S-InOOH, and those along the[110],[110],[110] and[110] directions always increase with the increasing pressure over a range of 0-40 GPa. The anisotropy and toughness of InOOH increase with the increasing pressure in both A-InOOH and S-InOOH, and the hydrogen bond symmetrization results in abnormal increase. In the materials containing hydrogen bonds, the effects of hydrogen bond symmetrization on different compressional elastic constants depend on the hydrogen bond projection on corresponding axes:the bigger the projection, the more significant the effect is.
InOOH has an obviously smaller bulk modulus than -AlOOH. The dominant reason is that the In3+ radius (0.81 , 1 =0.1 nm) is larger than Al3+ radius (0.50 ), resulting in the weaker interaction between In3+ and O2- than that between Al3+ and O2-. In addition, InOOH has more vacancies than -AlOOH. Combining with previous investigations on other rutile-distorted MOOH (M= Al, Ga, Fe, Cr), we can infer that the axial ratios, elastic properties and wave velocities of all MOOH materials have similar pressure evolutions to those of InOOH, and the hydrogen bond symmetrization has similar effects on the properties of MOOH.