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Chin. Phys. Lett.  
  Chin. Phys. Lett.--2016, 33 (07)   Published: 22 June 2016
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Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

Jin-Tao Tan, Yun-Rong Luo, Zheng Zhou, Wen-Hua Hai
Chin. Phys. Lett. 2016, 33 (07): 070302 doi: 10.1088/0256-307X/33/7/070302
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We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular 'island' of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical 'chaotic sea', which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.

Distillation of Atmospherically Disturbed Continuous Variable Quantum Entanglement with Photon Subtraction

Sheng-Li Zhang, Jian-Sheng Guo, Jian-Hong Shi, Xu-Bo Zou
Chin. Phys. Lett. 2016, 33 (07): 070303 doi: 10.1088/0256-307X/33/7/070303
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Entanglement distillation is a probabilistic quantum operation which tries to repair entanglement after environment-induced decoherence. All known distillations of continuous variable entanglement always assume that the entanglement is distributed via a standard attenuating channel with fixed photon loss rate, which is fairly idealized without many realistic effects taken into account. Here we investigate the problem of distillation of entanglement transmitted via atmospheric channel, with transmittance being highly probabilistic and unfixed. Two typical distillation schemes, i.e., single-sided photon subtraction and bi-sided photon subtraction, are investigated.

Noiseless Linear Amplification with General Local Unitary Operations

Song Yang, Ning-Juan Ruan, Yun Su, Xu-Ling Lin, Zhi-Qiang Wu
Chin. Phys. Lett. 2016, 33 (07): 070304 doi: 10.1088/0256-307X/33/7/070304
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Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state $|n\rangle\rightarrow g^n|n\rangle$, with $g$ being the amplification gain. We here give a general framework for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0–1 photon subspace. In particular, we study if the local unitary is composed of single mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.

Information Leakage Problem in High-Capacity Quantum Secure Communication with Authentication Using Einstein–Podolsky–Rosen Pairs

Zhi-Hao Liu, Han-Wu Chen, Wen-Jie Liu
Chin. Phys. Lett. 2016, 33 (07): 070305 doi: 10.1088/0256-307X/33/7/070305
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The information leakage problem often exists in bidirectional quantum secure direct communication or quantum dialogue. In this work, we find that this problem also exists in the one-way quantum secure communication protocol [Chin. Phys. Lett. 32 (2015) 050301]. Specifically, the first bit of every four-bit message block is leaked out without awareness. A way to improve the information leakage problem is given.

Signature of Critical Point in Momentum Profile of Trapped Ultracold Bose Gases

Qiang Zhu, Bing Wang, De-Zhi Xiong, Bao-Long Lü
Chin. Phys. Lett. 2016, 33 (07): 070306 doi: 10.1088/0256-307X/33/7/070306
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We present a new method to identify the critical point for the Bose–Einstein condensation (BEC) of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped $^{87}$Rb gases.

Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom–Cavity Couplings

Hong-Mei Zou, Mao-Fa Fang
Chin. Phys. Lett. 2016, 33 (07): 070307 doi: 10.1088/0256-307X/33/7/070307
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Based on the time-convolutionless master-equation approach, the entropic uncertainty in the presence of quantum memory is investigated for a two-atom system in two dissipative cavities. We find that the entropic uncertainty can be controlled by the non-Markovian effect and the atom–cavity coupling. The results show that increasing the atom–cavity coupling can enlarge the oscillating frequencies of the entropic uncertainty and can decrease the minimal value of the entropic uncertainty. Enhancing the non-Markovian effect can reduce the minimal value of the entropic uncertainty. In particular, if the atom–cavity coupling or the non-Markovian effect is very strong, the entropic uncertainty will be very close to zero at certain time points, thus Bob can minimize his uncertainty about Alice's measurement outcomes.

The Stability of Some Viable Stars and Electromagnetic Field

M. Azam, S. A. Mardan, M. A. Rehman
Chin. Phys. Lett. 2016, 33 (07): 070401 doi: 10.1088/0256-307X/33/7/070401
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We examine the impact of electromagnetic field on the stability of compact stars corresponding to embedded class one metric using the concept of cracking. For this purpose, we develop the generalized hydrostatic equilibrium equation for charged perfect fluid distribution of compact stars and perturb it by means of local density perturbation scheme to check the stability of inner matter configuration. We investigate the cracking of Her X-1, PSR 1937+21, PSR J 1614-2230, PSR J 0348+0432 and RX J 1856-37. We conclude that PSR J 0348+0432 and RX J 1856-37 exhibit cracking when charge is introduced on these astrophysical objects.

The Ott–Antonsen Ansatz in Globally Coupled Phase Oscillators

Nian-Ping Wu, Hong-Yan Cheng, Qiong-Lin Dai, Hai-Hong Li
Chin. Phys. Lett. 2016, 33 (07): 070501 doi: 10.1088/0256-307X/33/7/070501
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The Ott–Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscillators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott–Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of $\alpha(\omega)$, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency $\omega_{\rm e}(\omega)$ of desynchronous oscillators, and the structure of the graph $\omega_{\rm e}(\omega)$.

Hertz-Level Clock Spectroscopy of $^{171}$Yb Atoms in a One-Dimensional Optical Lattice

Meng-Jiao Zhang, Hui Liu, Xi Zhang, Kun-Liang Jiang, Zhuan-Xian Xiong, Bao-Long LÜ, Ling-Xiang He
Chin. Phys. Lett. 2016, 33 (07): 070601 doi: 10.1088/0256-307X/33/7/070601
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An ultra-narrow spectroscopy of clock transition with high signal-to-noise ratio is crucial for a high-performance atomic optical clock. We present a detailed study about how to obtain a Hertz-level clock transition spectrum of $^{171}$Yb atoms. About $4\times10^{4}$ atoms are loaded into a one-dimensional optical lattice with a magic wavelength of 759 nm, and a long lifetime of 3 s is realized with the lattice power of 1 W. Through normalized shelving detection and spin polarization, $^{171}$Yb clock spectroscopy with a Fourier-limited linewidth of 5.9 Hz is obtained. Our work represents a key step toward an ytterbium optical clock with high frequency stability.

A Single Folded Beam Magneto-Optical Trap System for Neutral Mercury Atoms

Kang-Kang Liu, Ru-Chen Zhao, Wei Gou, Xiao-Hu Fu, Hong-Li Liu, Shi-Qi Yin, Jian-Fang Sun, Zhen Xu, Yu-Zhu Wang
Chin. Phys. Lett. 2016, 33 (07): 070602 doi: 10.1088/0256-307X/33/7/070602
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Mercury is a promising candidate for the optical lattice clock, due to its low sensitivity to the blackbody radiation. We develop a single folded beam magneto-optical trap for the neutral mercury optical lattice clock, with a 253.7 nm frequency quadrupled laser. Up to $1.7\times10^{6}$ ($^{202}$Hg) or $1.5\times10^{6}$ ($^{199}$Hg) atoms can be captured, and the atom temperature is lowered to 170 μK ($^{202}$Hg) or 50 μK ($^{199}$Hg). The cold atom signals of all six rich abundant isotopes are observed in this system.


Constraints on the First Generation Scalar Leptoquarks

Xiao-Min Wang, Chong-Xing Yue, Zhi-Cheng Liu
Chin. Phys. Lett. 2016, 33 (07): 071401 doi: 10.1088/0256-307X/33/7/071401
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Inspired by the CMS excess in $eejj$ and $e\nu jj$ channels and possible interpretation using the first generation scalar leptoquarks (SLQs), we consider their contributions to non-standard neutrino interaction and the pion meson leptonic decay $\pi\rightarrow l\nu$. Compared with the relevant experimental data, the constraints on the first generation SLQs are obtained. Their corrections to the anomalous magnetic moment $a_{\mu}$ are further calculated and the numerical results show that it is possible to explain the deviation from its standard model prediction.

A Common Optical Potential for $^{4}$He+$^{12}$C at Intermediate Energies

Li-Yuan Hu, Yu-Shou Song, Ying-Wei Hou, Hui-Lan Liu
Chin. Phys. Lett. 2016, 33 (07): 072401 doi: 10.1088/0256-307X/33/7/072401
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A common optical potential for $^4$He+$^{12}$C at intermediate bombarding energies, which is essential in analyzing exotic nuclei with $^4$He clusters, is obtained based on the São Paulo potential. Among systematic optical potentials for $^4$He+$^{12}$C, this potential has the merit of using a fixed imaginary part of the Woods–Saxon form. By optical-model calculations, this potential reproduces the experimental elastic scattering angular distributions of $^4$He+$^{12}$C well within the energy range of 26$A$–60$A$ MeV. It is also applied successfully in calculations of the breakup reactions of $^6$Li+$^{12}$C and $^6$He+$^{12}$C with a three-body continuum discretized coupled-channel method.

A Gaussian Model for Anisotropic Strange Quark Stars

H. Panahi, R. Monadi, I. Eghdami
Chin. Phys. Lett. 2016, 33 (07): 072601 doi: 10.1088/0256-307X/33/7/072601
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For studying the anisotropic strange quark stars, we assume that the radial pressure inside an anisotropic star can be obtained simply by isotropic pressure plus an additional Gaussian term with three free parameters ($A$, $\mu$ and $\chi$). According to recent observations, a pulsar in a mass range of 1.97$\pm$0.04$M_{\odot}$ has been measured. Hence, we take this opportunity to set the free parameters of our model. We fix $\chi$ by applying boundary and stability conditions and then search the $A-\mu$ parameter space for a maximum mass range of $1.9M_{\odot} < M_{\max} < 2.1M_{\odot}$. Our results indicate that anisotropy increases the maximum mass $M_{\max}$ and also its corresponding radius $R$ for a typical strange quark star. Furthermore, our model shows magnetic field and electric charge increase the anisotropy factor ${\it \Delta}$. In fact, ${\it \Delta}$ has a maximum on the surface and this maximum goes up in the presence of magnetic field and electric charge. Finally, we show that anisotropy can be more effective than either magnetic field or electric charge in raising maximum mass of strange quark stars.

Beam Dynamics Design of a 50mA D$^{+}$ RFQ

Fang-Jian Jia, Kun Zhu, Yuan-Rong Lu, Zhi Wang, Zhi-Yu Guo, Qi Fu, Yuan He
Chin. Phys. Lett. 2016, 33 (07): 072901 doi: 10.1088/0256-307X/33/7/072901
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A new 973 project was proposed by Peking University and Institute of Modern Physics of Chinese Academy of Sciences recently. The project requires a 50 mA, 162.5 MHz, cw mode radio frequency quadrupole (RFQ) to accelerate the D$^{+}$ to 1 MeV. In a high-current linear accelerator, the strong space charge effect causes the growth of envelope and emittance along with heavy beam losses. In the beam dynamics design of this RFQ, beam envelope mismatching is discussed and a matching dynamics method is proposed to minimize the envelope and emittance growth. The influence of limiting current on the beam transmission is discussed and used in the optimization of transverse and longitudinal parameters. After the optimization, the beam transmission efficiency reaches higher than 98%.

Magic Wavelengths for the $1S$–$2S$ and $1S$–$3S$ Transitions in Hydrogen Atoms

Dong Yin, Yong-Hui Zhang, Cheng-Bin Li, Xian-Zhou Zhang
Chin. Phys. Lett. 2016, 33 (07): 073101 doi: 10.1088/0256-307X/33/7/073101
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The dynamic dipole polarizabilities for $1S$, $2S$ and $3S$ states of the hydrogen atom are calculated using the finite B-spline basis set method, and the magic wavelengths for $1S$–$2S$ and $1S$–$3S$ transitions are identified. In comparison of the solutions from the Schrödinger and Dirac equations, the relativistic corrections on the magic wavelengths are of the order of $10^{-2}$ nm. The laser intensities for a 300-$E_{\rm r}$-deep optical trap and the heating rates at 514 and 1371 nm are estimated. The reliable prediction of the magic wavelengths would be helpful for the experimental design on the optical trapping of the hydrogen atoms, and in turn, it would be helpful to improve the accuracy of the measurements of the hydrogen $1S$–$2S$ and $1S$–$3S$ transitions.

Signature of Single Binary Encounter in Intermediate Energy He$^{2+}$–Ar Collisions$^*$

Yong Gao, Xiao-Long Zhu, Shao-Feng Zhang, Rui-Tian Zhang, Wen-Tian Feng, Da-Long Guo, Bin Li, Dong-Mei Zhao, Han-Bing Wang, Zhong-Kui Huang, Shun-Cheng Yan, Dong-Bin Qian, Xin-Wen Ma
Chin. Phys. Lett. 2016, 33 (07): 073401 doi: 10.1088/0256-307X/33/7/073401
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We experimentally observe the signature of electron emission resulting from a single binary encounter mechanism in the intermediate collision energy regime of 30 keV/u He$^{2+}$ on argon. Electron emission spectra in the transfer ionization are obtained and compared with classical calculations from a two-step model considering the initial electron velocity and re-scattering of the binary encounter electron in the recoil potential. Although the present reaction is actually a four-body problem, the model starting from a binary encounter gives out surprisingly good agreement with the experimental data. Our studies show that orbital velocities of the electron affect the emission patterns of ionized electrons significantly.

Polarization-Insensitive Magnetic Quadrupole-Shaped and Electric Quadrupole-Shaped Fano Resonances Based on a Plasmonic Composite Structure

Chen Dong, Bao Li, Han-Xiao Li, Hui Liu, Meng-Qi Chen, Dong-Dong Li, Chang-Chun Yan, Dao-Hua Zhang
Chin. Phys. Lett. 2016, 33 (07): 074201 doi: 10.1088/0256-307X/33/7/074201
Full Text: [PDF 835 KB] (Downloads:47)
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A combined structure with the unit cell consisting of four sub-units with 90$^{\circ}$ rotation in turn is designed. Each of sub-units is composed of two gold rods in transverse arrangement and one gold rod in longitudinal arrangement. Simulating electromagnetic responses of the structure, we verify that the structure exhibits the double Fano resonances, which originate from the coupling between magnetic quadrupoles and electric dipoles and the coupling between electric quadrupoles and electric dipoles. Simulation results also demonstrate that the structure is polarization-insensitive and shows an analogue of electromagnetically induced transparency at the two Fano resonances. Such a plasmonic structure has potential applications in photoelectric elements.

Anderson Localization in the Induced Disorder System

Fei-Fei Lu, Chun-Fang Wang
Chin. Phys. Lett. 2016, 33 (07): 074202 doi: 10.1088/0256-307X/33/7/074202
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We propose a coherently prepared three-level atomic medium that can provide a flexible disordered scheme for realizing the Anderson localization. Different disorder levels can be attained by modulating the intensity ratio between the two control beams. Due to the real-time tunability, the localization of the signal beam is observable and controllable. The influences of the induced disorder level, atomic density and the initial waist radius of the signal beam on the Anderson localization in the medium are also discussed.

Passively Q-Switched Nd,Cr:YAG Laser Simultaneous Dual-Wavelength Operation at 946nm and 1.3µm

Bin Lin, Qiu-Lin Zhang , Dong-Xiang Zhang , Bao-Hua Feng, Jing-Liang He, Jing-Yuan Zhang
Chin. Phys. Lett. 2016, 33 (07): 074203 doi: 10.1088/0256-307X/33/7/074203
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A diode-end-pumped Q-switched high-efficiency Nd,Cr:YAG laser with simultaneous dual-wavelength emission at 946 nm and 1.3 µm is demonstrated. The maximum output power of 1.93 W with simultaneous dual-wavelength operation is achieved at an absorbed pump power of 13.32 W and an absorbed slope efficiency of 15.15%. The maximum optical–optical efficiency is 14.49% with pulse widths of 16.38 ns at 946 nm and 26.65 ns at 1.3 µm. A maximum total repetition rate of 43.25 kHz is obtained.

Inhibition of Atomic Decay in Strongly Coupled Photonic Crystal Cavities

Yan-Li Xue, Ke Zhang, Bao-Hua Feng, Zhi-Yuan Li
Chin. Phys. Lett. 2016, 33 (07): 074204 doi: 10.1088/0256-307X/33/7/074204
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We discuss the evolution dynamics of a quantum system consisting of two two-level atoms separately embedded within two strongly coupled photonic crystal cavities. Although the quantum system is subjected to dissipation and decoherence from the cavity leakage and the atomic decay, it does allow for eigenstates that are not influenced by one of the two dissipation channels and results in dissipation-inhibition quantum states. These dissipation-free quantum states can help to achieve an extremely long photon and atom storage lifetime and provide a new perspective to realize efficient quantum information storage via reducing the negative influence of the dissipation from the environment.

Autler–Townes Splitting in a ${\it \Delta}$-Type Quantum Three-Level System

Qi-Chun Liu, Han Cai, Ying-Shan Zhang, Jian-She Liu, Wei Chen
Chin. Phys. Lett. 2016, 33 (07): 074205 doi: 10.1088/0256-307X/33/7/074205
Full Text: [PDF 517 KB] (Downloads:56)
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We observe the Autler–Townes splitting effect in a ${\it \Delta}$-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.

Angle Compensation and Asymmetry Effect of Light Diffracted by Millimeter Liquid Surface Slosh Wave

Yang Miao, Can Wu, Ning Wang, Jia-Qi You
Chin. Phys. Lett. 2016, 33 (07): 074206 doi: 10.1088/0256-307X/33/7/074206
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The angle compensation method is adopted to detect sloshing waves by laser diffraction, in the case that the wavelength of the sloshing waves is much greater than that of the incident light. The clear diffraction pattern is observed to be of asymmetry, involving orders, position and interval of the diffraction spots that are discovered during the light grazing incidence. It is found that the larger the angle of incidence is, the more obvious the asymmetry is. The higher the negative diffraction orders are, the smaller the intervals between spots are. On the contrary, in the positive region, the higher the diffraction orders are, the larger the spot intervals are. The positive interval is larger than that of the same negative diffraction order. If the incident angle reaches 1.558 rad in the experiment, all positive diffraction orders completely vanish. Based on the mechanism of phase modulation and with the Fourier transform method, the relations between the incident angle and position, interval spaces, and orders of diffraction spots are derived theoretically. The theoretical calculations are compared with the experimental data, and the comparison shows that the theoretical calculations are in good agreement with the experimental measurement.

Stimulated Brillouin Scattering Enhancement Factor Improvement in a 11.6-GHz-Linewidth 1.5-kW Yb-Doped Fiber Amplifier

Guang-Bo Liu, Yi-Feng Yang, Jian-Hua Wang, Ye Zheng, Xiao-Long Chen, Kai Liu, Chun Zhao, Yun-Feng Qi, Bing He, Jun Zhou
Chin. Phys. Lett. 2016, 33 (07): 074207 doi: 10.1088/0256-307X/33/7/074207
Full Text: [PDF 656 KB] (Downloads:31)
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The stimulated Brillouin scattering (SBS) threshold enhancement factor in a pure white noise linewidth broadening Yb-doped fiber amplifier (YDFA) with a short large mode area fiber is theoretically and experimentally studied. We demonstrate a 1064.08 nm, 11.6 GHz linewidth, 1.5 kW output power YDFA with an SBS threshold enhancement of $\sim$57 (26 W SBS threshold with single frequency seed). The output beam is near-diffraction limited with a beam quality factor of $M^{2}=1.15$ and a slope efficiency of up to 87%. No SBS or stimulated Raman scattering effects are observed in the whole power range. Further power scaling is limited by the available pump power in our system.

Q-Switched Raman Fiber Laser with Molybdenum Disulfide-Based Passive Saturable Absorber

N. Hisamuddin, U. N. Zakaria, M. Z. Zulkifli, A. A. Latiff, H. Ahmad, S. W. Harun
Chin. Phys. Lett. 2016, 33 (07): 074208 doi: 10.1088/0256-307X/33/7/074208
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We demonstrate a Q-switched Raman fiber laser using molybdenum disulfide (MoS$_{2})$ as a saturable absorber (SA). The SA is assembled by depositing a mechanically exfoliated MoS$_{2}$ onto a fiber ferrule facet before it is matched with another clean ferrule via a connector. It is inserted in a Raman fiber laser cavity with a total cavity length of about 8 km to generate a Q-switching pulse train operating at 1560.2 nm. A 7.7-km-long dispersion compensating fiber with 584 ps$\cdot$nm$^{-1}$km$^{-1}$ of dispersion is used as a nonlinear gain medium. As the pump power is increased from 395 mW to 422 mW, the repetition rate of the Q-switching pulses can be increased from 132.7 to 137.4 kHz while the pulse width is concurrently decreased from 3.35 µs to 3.03 µs. The maximum pulse energy of 54.3 nJ is obtained at the maximum pump power of 422 mW. These results show that the mechanically exfoliated MoS$_{2}$ SA has a great potential to be used for pulse generation in Raman fiber laser systems.

Optimization Design for the Sandwich Piezoelectric Transmitters in Acoustic Logging

Qian Wei, Xiu-Ming Wang, Cheng-Xuan Che, Jian-Sheng Cong,
Chin. Phys. Lett. 2016, 33 (07): 074301 doi: 10.1088/0256-307X/33/7/074301
Full Text: [PDF 392 KB] (Downloads:26)
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An optimized transducer prototype with a sandwich structure vibrated longitudinally is proposed for a transmitter in acoustic logging, especially in acoustic logging while drilling, by taking account of drilling environments with high temperature and pressure, as well as strong collar drilling vibration during the drilling process. Aimed to improve the transmitting performance, numerical and experimental studies for the transducer optimization are conducted. The impact of location and length of the piezoelectric stack on resonance characteristics and effective electromechanical coupling coefficient is calculated and analyzed. Admittance and transmitting performance of the proposed transducer are measured in laboratory experiments, and the results are compared with simulated ones. It is shown that the newly proposed transducer has higher transmitting performance with lower resonance frequencies. This work provides theoretical and experimental bases for transducer designing and acoustic wave measurements in acoustic logging, especially in acoustic logging while drilling.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

Shu-Zeng Zhang, Xiong-Bing Li, Hyunjo Jeong
Chin. Phys. Lett. 2016, 33 (07): 074302 doi: 10.1088/0256-307X/33/7/074302
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This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Origin of Initial Current Peak in High Power Impulse Magnetron Sputtering and Verification by Non-Sputtering Discharge

Zhong-Zhen Wu, Shu Xiao, Sui-Han Cui, Ricky K. Y. Fu, Xiu-Bo Tian, Paul K. Chu, Feng Pan
Chin. Phys. Lett. 2016, 33 (07): 075201 doi: 10.1088/0256-307X/33/7/075201
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A non-sputtering discharge is utilized to verify the effect of replacement of gas ions by metallic ions and consequent decrease in the secondary electron emission coefficient in the discharge current curves in high-power impulse magnetron sputtering (HiPIMS). In the non-sputtering discharge involving hydrogen, replacement of ions is avoided while the rarefaction still contributes. The initial peak and ensuing decay disappear and all the discharge current curves show a similar feature as the HiPIMS discharge of materials with low sputtering yields such as carbon. The results demonstrate the key effect of ion replacement during sputtering.

High-Pressure Preparation of High-Density Cu$_{2}$ZnSnS$_{4}$ Materials

Yi-Ming Li, Li-Xia Qiu, Zhan-Hui Ding, Yong-Feng Li, Bin Yao, Zhen-Yu Xiao, Pin-Wen Zhu
Chin. Phys. Lett. 2016, 33 (07): 076101 doi: 10.1088/0256-307X/33/7/076101
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High-density Cu$_{2}$ZnSnS$_{4 }$ (CZTS) materials are prepared via the mechanical alloying and high pressure sintering method using Cu$_{2}$S, ZnS and SnS$_{2}$ as the raw materials. The morphological, structural, compositional and electrical properties of the materials are investigated by using x-ray diffraction, scanning electron microscopy, and energy dispersive x-ray spectroscopy, as well as by the Raman scattering and the Hall Effect measurements. The CZTS synthesized under 5 GPa and 800$^\circ\!$C shows a p-type conductivity, with a resistivity of $9.69\times10^{-2}$ $\Omega \cdot$cm and a carrier concentration of $1.45\times10^{20}$ cm$^{-3}$. It is contributed to by the large grains in the materials reducing the grain boundaries, thus effectively reducing the recombination of the charge carriers.

Hot-Carrier Effects on Total Dose Irradiated 65nm n-Type Metal-Oxide-Semiconductor Field-Effect Transistors

Qi-Wen Zheng, Jiang-Wei Cui, Hang Zhou, De-Zhao Yu, Xue-Feng Yu, Qi Guo
Chin. Phys. Lett. 2016, 33 (07): 076102 doi: 10.1088/0256-307X/33/7/076102
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The influence of total dose irradiation on hot-carrier reliability of 65 nm n-type metal-oxide-semiconductor field-effect transistors (nMOSFETs) is investigated. Experimental results show that hot-carrier degradations on irradiated narrow channel nMOSFETs are greater than those without irradiation. The reason is attributed to radiation-induced charge trapping in shallow trench isolation (STI). The electric field in the pinch-off region of the nMOSFET is enhanced by radiation-induced charge trapping in STI, resulting in a more severe hot-carrier effect.

Production of Rubidium Bose–Einstein Condensate in an Optically Plugged Magnetic Quadrupole Trap

Dong-Fang Zhang, Tian-You Gao, Ling-Ran Kong, Kai Li, Kai-Jun Jiang
Chin. Phys. Lett. 2016, 33 (07): 076701 doi: 10.1088/0256-307X/33/7/076701
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We experimentally produce the rubidium Bose–Einstein condensate in an optically plugged magnetic quadrupole trap. A far blue-detuned focused laser beam with a wavelength of 532 nm is plugged in the center of the magnetic quadrupole trap to increase the number of trapped atoms and to suppress the heating. An rf evaporative cooling in the magneto-optical hybrid trap is applied to decrease the atom temperature into degeneracy. The atom number of the condensate is $1.2(0.4)\times10^5$ and the temperature is below 100 nK. We also study characteristic behaviors of the condensate, such as phase space density, condensate fraction and anisotropic expansion.

Effect of Terraces at the Interface on the Structural and Physical Properties of La$_{0.8}$Sr$_{0.2}$MnO$_{3}$ Thin Films

Ya-Qing Feng, Kui-Juan Jin, Chen Ge, Xu He, Lin Gu, Zhen-Zhong Yang, Hai-Zhong Guo, Qian Wan, Meng He, Hui-Bin Lu, Guo-Zhen Yang
Chin. Phys. Lett. 2016, 33 (07): 076801 doi: 10.1088/0256-307X/33/7/076801
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Employing atomic force microscopy, transmission electron microscopy and the second harmonic generation technique, we carefully explore the structural properties of 6-unit-cell-thick La$_{0.8}$Sr$_{0.2}$MnO$_{3}$ films grown on SrTiO$_{3}$ with atomically flat TiO$_{2}$-terminated terraces on the surface. The results clearly demonstrate that the terraces on the surface of TiO$_{2}$-terminated SrTiO$_{3}$ can improve the layer-by-layer epitaxial growth of the manganite films, which results in uniform film coverage at the beginning of growth and thus reduces the substrate-induced disorder at or near the interface. Comparing the magnetic and transport properties of La$_{0.8}$Sr$_{0.2}$MnO$_{3}$ films with the thicknesses varying from 6 unit cells to 80 unit cells grown respectively on as-received SrTiO$_{3}$ and TiO$_{2}$-terminated SrTiO$_{3}$, it is found that these atomically flat terraces on the surface of TiO$_{2}$-terminated SrTiO$_{3}$ can greatly enhance the Curie temperature and conductivities of the ultrathin La$_{0.8}$Sr$_{0.2}$MnO$_{3}$ films with thickness less than 50 unit cells, while no obvious difference is detected in the magnetic and transport properties of the 80 unit-cell thick films.

White Light Emission from ZnS:Mn Thin Films Deposited on GaN Substrates by Pulsed Laser Deposition

Cai-Feng Wang, Qing-Shan Li, Ji-Suo Wang, Feng-Zhou Zhao , Li-Chun Zhang
Chin. Phys. Lett. 2016, 33 (07): 076802 doi: 10.1088/0256-307X/33/7/076802
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ZnS:Mn thin films are grown on GaN substrates by pulsed laser deposition. The structure, morphology and optical properties are investigated by x-ray diffraction, scanning electron microscopy and photoluminescence (PL). The obtained ZnS:Mn thin films are grown in preferred orientation along $\beta$-ZnS (111) direction corresponding to crystalline structure of cubic phase. The deposition temperature has an obvious effect on the structure, surface morphology and optical properties of ZnS:Mn thin films. PL measurements show that there are two emission bands located at 440 nm and 595 nm when the films are deposited at temperatures from 100$^{\circ}\!$C to 500$^{\circ}\!$C. The relative integrated intensity of the blue emission and orange-red emission is determined by the deposition conditions. At the proper deposition temperature of 300$^{\circ}\!$C, the color coordinate is closest to (0.33, 0.33). The ZnS:Mn films on GaN substrates can exhibit white light emission.

Phase Transition and Band Structure Tuned by Strains in Al$_{1/2}$Ga$_{1/2}$N Alloy of Complex Structure

Li-Xia Qin, Rong-Li Jiang
Chin. Phys. Lett. 2016, 33 (07): 077101 doi: 10.1088/0256-307X/33/7/077101
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Phase transition and band structure tuned by uniaxial and biaxial strains are systematically investigated based on the density-functional theory for ordered Al$_{1/2}$Ga$_{1/2}$N alloys of complex structures. Although the structural transformations to graphite-like from wurtzite are energetically favorable for both types of strain, the phase transitions are different in nature: the second-order transition induced by uniaxial strain is jointly driven by the mechanical and dynamical instabilities and the first-order transition by biaxial strain only by the mechanical instability. The wurtzite phase always shows the direct band gap, while the band gap of the graphite-like phase is always indirect. Furthermore, the band gaps of the wurtzite phase can be reduced by both types of strain, while that of the graphite-like phase is enhanced by uniaxial strain and is suppressed by biaxial strain.

Adsorption Regularity and Characteristics of $sp^{3}$-Hybridized Gas Molecules on Anatase TiO$_{2}$ (101) Surface

Yong-Hong Gu, Qing Feng, Jian-Jun Chen, Yan-Hua Li, Cong-Zhong Cai
Chin. Phys. Lett. 2016, 33 (07): 077102 doi: 10.1088/0256-307X/33/7/077102
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We report the anatase titanium dioxide (101) surface adsorption of $sp^{3}$-hybridized gas molecules, including NH$_{3}$, H$_{2}$O and CH$_{4}$, using first-principles plane-wave ultrasoft pseudopotential based on the density functional theory. The results show that it is much easier for a surface with oxygen vacancies to adsorb gas molecules than it is for a surface without oxygen vacancies. The main factor affecting adsorption stability and energy is the polarizability of molecules, and adsorption is induced by surface oxygen vacancies of the negatively charged center. The analyses of state densities and charge population show that charge transfer occurs at the molecule surface upon adsorption and that the number of transferred charge reduces in the order of N, O and C. Moreover, the adsorption method is chemical adsorption, and adsorption stability decreases in the order of NH$_{3}$, H$_{2}$O and CH$_{4}$. Analyses of absorption and reflectance spectra reveal that after absorbed CH$_{4}$ and H$_{2}$O, compared with the surface with oxygen vacancy, the optical properties of materials surface, including its absorption coefficients and reflectivity index, have slight changes, however, absorption coefficient and reflectivity would greatly increase after NH$_{3}$ adsorption. These findings illustrate that anatase titanium dioxide (101) surface is extremely sensitive to NH$_{3}$.

Performance and Stability of Polymer Solar Cells Based on the Blends of Poly(3-Hexylthiophene) and Indene-C$_{60}$ Bis-Adduct

Min-Nan Guo, Shao-Wei Liu, Na Guo, Li-Ying Yang, Wen-Jing Qin, Shou-Gen Yin
Chin. Phys. Lett. 2016, 33 (07): 077201 doi: 10.1088/0256-307X/33/7/077201
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The performance and morphology stability of polymer bulk heterojunction solar cells based on poly(3-hexylthiophene) (P3HT) as the donor and indene-C$_{60}$ bisadduct (ICBA) or methanofullerene [6,6]-phenyl C$_{61}$-butyric acid methyl ester (PCBM) as the acceptor are compared. Effect of the different donor and acceptor weight ratios on photovoltaic performance of the P3HT:ICBA device is studied. The optimal device achieved power conversion efficiency of 5.51% with $J_{\rm sc}$ of 10.86 mA/cm$^{2}$, $V_{\rm oc}$ of 0.83 V, and fill factor (FF) of 61.1 % under AM 1.5 G (100 mW/cm$^{2})$ simulated solar illumination. However, the stability measurement shows that cells based on P3HT:ICBA are less stable than those of the device based on P3HT:PCBM. Atomic force microscope results reveal that the morphology of the P3HT:ICBA film changed considerably during the storage periods due to unstable interpenetrating D-A network. This observation can be explained by the fact that there is lack of intermolecular hydrogen bonds in the P3HT:ICBA system. However, in the P3HT:PCBM system the molecules in the blend film are firmly held together in the solid state by means of intermolecular hydrogen bonds originating from C-H$\cdots$Os bonds (where Os comes from the singly-bonded O atom of PCBM), forming a stable three-dimensional network. The measured PL decay lifetimes for P3HT:PCBM and P3HT:ICBA systems are 33.66 ns and 35.34 ns, respectively, indicating that the P3HT:ICBA system has a less efficient exciton separation efficiency than that of P3HT:PCBM, which may result in the interfacial photogenerated charges accumulated on the D: A interface. Such progressive phase segregation between P3HT and ICBA eventually leads to the degradation in performance and deteriorates the stability of the device. We also present an approach to enhance the stability of P3HT:ICBA systems by adding PCBM as the second acceptor. Our results show that by carefully tuning the contents of PCBM as the second acceptor, more stable polymer solar cells can be obtained.

Interaction of Two Parallel Cracks in REBCO Bulk Superconductors under Applied Magnetic Field

Zhao-Xia Zhang, Feng Xue, Xiao-Fan Gou
Chin. Phys. Lett. 2016, 33 (07): 077401 doi: 10.1088/0256-307X/33/7/077401
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Interactions of two collinear and parallel $a/b$-plane cracks in REBCO (where RE is a rare-earth element and usually Y is adopted) bulk superconductors under the Lorentz force resulted from the applied magnetic field are studied. By using the derived boundary integral equation for the crack problem of a cylindrical bulk superconductor under the applied magnetic field, we comprehensively investigate the stress intensity factor (SIF) of modes I and II at the crack tips of the two collinear and parallel cracks with their sizes, relative positions and the applied magnetic field. The calculated results show that in most cases, the SIF of mode I is found to be about tens of times of the one of mode II, and all the SIFs are always proportional to increase in the applied magnetic field, and the cracks near the center are more dangerous due to the larger Lorentz force.

Common Electronic Features and Electronic Nematicity in Parent Compounds of Iron-Based Superconductors and FeSe/SrTiO$_3$ Films Revealed by Angle-Resolved Photoemission Spectroscopy

De-Fa Liu, Lin Zhao, Shao-Long He, Yong Hu, Bing Shen, Jian-Wei Huang, Ai-Ji Liang, Yu Xu, Xu Liu, Jun-Feng He, Dai-Xiang Mou, Shan-Yu Liu, Hai-Yun Liu, Guo-Dong Liu, Wen-Hao Zhang, Fang-Sen Li, Xu-Cun Ma, Qi-Kun Xue, Xian-Hui Chen, Gen-Fu Chen, Li Yu, Jun Zhang, Zu-Yan Xu, Chuang-Tian Chen, Xing-Jiang Zhou
Chin. Phys. Lett. 2016, 33 (07): 077402 doi: 10.1088/0256-307X/33/7/077402
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We report comprehensive angle-resolved photoemission investigations on the electronic structures and nematicity of the parent compounds of the iron-based superconductors including CeFeAsO, BaFe$_2$As$_2$, NaFeAs, FeSe and undoped FeSe/SrTiO$_3$ films with 1, 2 and 20 layers. While the electronic structure near the Brillouin zone center ${\it \Gamma}$ varies dramatically among different materials, the electronic structure near the Brillouin zone corners ($M$ points), as well as their temperature dependence, are rather similar. The electronic structure near the zone corners is dominated by the electronic nematicity that gives rise to a band splitting of the $d_{xz}$ and $d_{yz}$ bands below the nematic transition temperature. A clear relation is observed between the band splitting magnitude and the onset temperature of nematicity. Our results may shed light on the origin of nematicity, its effect on the electronic structures, and its relation with superconductivity in the iron-based superconductors.

Analytical Descriptions of Magnetic Properties and Magnetoresistance in n-Type HgCr$_2$Se$_4$

Chao-Jing Lin, You-Guo Shi, Yong-Qing Li
Chin. Phys. Lett. 2016, 33 (07): 077501 doi: 10.1088/0256-307X/33/7/077501
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We present a detailed investigation of magnetic properties of colossal magnetoresistance material HgCr$_2$Se$_4$. While spontaneous magnetization and zero-field magnetic susceptibility are found to follow asymptotic scaling laws for a narrow range of temperatures near the critical point, two methods with connections to the renormalization group theory provide analytical descriptions of the magnetic properties for much wider temperature ranges. Based on this, an analytical formula is obtained for the temperature dependence of the low field magnetoresistance in the paramagnetic phase.

Tuning Martensitic Phase Transition by Non-Magnetic Atom Vacancy in MnCoGe Alloys and Related Giant Magnetocaloric Effect

Li-Fu Bao, Wen-Deng Huang, Ya-Jie Ren
Chin. Phys. Lett. 2016, 33 (07): 077502 doi: 10.1088/0256-307X/33/7/077502
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The effects of non-magnetic atom vacancy on structural, martensitic phase transitions and the corresponding magnetocaloric effect in MnCoGe$_{1-x}$ alloys are investigated using x-ray diffraction and magnetic measurements. The introduction of non-magnetic atom vacancy leads to the decrease of the martensitic transition temperature and realizes a temperature window where magnetic and martensitic phase transitions can be tuned together. Moreover, the giant magnetocaloric effect accompanied with the coupled magnetic-structural transition is obtained. It is observed that the peak values of magnetic entropy change of MnCoGe$_{0.97}$ are about $-$13.9, $-$35.1 and $-$47.4 J$\cdot$kg$^{-1}$K$^{-1}$ for $\Delta H=2$, 5, 7 T, respectively.

Self-Consistent Spin-Wave Analysis of the 1/3 Magnetization Plateau in the Kagome Antiferromagnet

Zhong-Chao Wei, Hai-Jun Liao, Jing Chen, Hai-Dong Xie, Zhi-Yuan Liu, Zhi-Yuan Xie, Wei Li, B. Normand, Tao Xiang
Chin. Phys. Lett. 2016, 33 (07): 077503 doi: 10.1088/0256-307X/33/7/077503
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We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisenberg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers $S$. The values of the critical magnetic fields and the widths of the magnetization plateaus are fully consistent with the recent numerical results from exact diagonalization and infinite projected entangled paired states.

Highly Efficient and Stable Hybrid White Organic Light Emitting Diodes with Controllable Exciton Behavior by a Mixed Bipolar Interlayer

Yuan-Yuan Hou, Jiang-Hong Li, Xiao-Xiang Ji, Ya-Feng Wu, Wei Fan, Igbari Femi
Chin. Phys. Lett. 2016, 33 (07): 077801 doi: 10.1088/0256-307X/33/7/077801
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Highly efficient and stable hybrid white organic light-emitting diodes (HWOLEDs) with a mixed bipolar interlayer between fluorescent blue and phosphorescent yellow emitting layers are demonstrated. The bipolar interlayer is a mixture of p-type diphenyl (10-phenyl-10H-spiro [acridine-9,9'-fluoren]-3'-yl) phosphine oxide and n-type 2',2"-(1,3,5-benzinetriyl)-tris(1-phenyl-1-H-benzimidazole). The electroluminance and Commission Internationale de l'Eclairage (CIE1931) coordinates' characteristics can be modulated easily by adjusting the ratio of the hole-predominated material to the electron-predominated material in the interlayer. The hybrid WOLED with a p-type:n-type ratio of 1:3 shows a maximum current efficiency and power efficiency of 61.1 cd/A and 55.8 lm/W, respectively, with warm white CIE coordinates of (0.34, 0.43). The excellent efficiency and adaptive CIE coordinates are attributed to the mixed interlayer with improved charge carrier balance, optimized exciton distribution, and enhanced harvesting of singlet and triplet excitons.

Growth of Ag on Pb Island with Si(111) Substrate

Xiao-Peng Hu, Rui Zhu, Jun Xu, Shuai-Hua Ji, Xi Chen, Qi-Kun Xue, Da-Peng Yu
Chin. Phys. Lett. 2016, 33 (07): 078101 doi: 10.1088/0256-307X/33/7/078101
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We study the growth of Ag on Pb island surface with low temperature scanning tunnelling microscopy. Two growth modes, the subsurface island mode and the surface alloy mode, are observed on the substrate at room temperature and at 100 K, respectively. In the surface alloy mode, the perfect alloy AgPb$_2$ is formed on the Pb island surface after annealing. The two growth modes at different substrate temperatures are attributed to the existence of an exchange barrier of Ag atoms on the Pb island surface. The modulation of the exchange barrier by the quantum well states is also observed on the Pb island.

Copper Ion Beam Irradiation-Induced Effects on Structural, Morphological and Optical Properties of Tin Dioxide Nanowires

M. A. Khan, A. Qayyum, I. Ahmed, T. Iqbal, A. A. Khan, R. Waleed, B. Mohuddin, M. Malik
Chin. Phys. Lett. 2016, 33 (07): 078102 doi: 10.1088/0256-307X/33/7/078102
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The 0.8 MeV copper (Cu) ion beam irradiation-induced effects on structural, morphological and optical properties of tin dioxide nanowires (SnO$_{2}$ NWs) are investigated. The samples are irradiated at three different doses $5\times10^{12}$ ions/cm$^{2}$, $1\times10^{13}$ ions/cm$^{2}$ and $5\times10^{13}$ ions/cm$^{2}$ at room temperature. The XRD analysis shows that the tetragonal phase of SnO$_{2}$ NWs remains stable after Cu ion irradiation, but with increasing irradiation dose level the crystal size increases due to ion beam induced coalescence of NWs. The FTIR spectra of pristine SnO$_{2}$ NWs exhibit the chemical composition of SnO$_{2}$ while the Cu–O bond is also observed in the FTIR spectra after Cu ion beam irradiation. The presence of Cu impurity in SnO$_{2}$ is further confirmed by calculating the stopping range of Cu ions by using TRM/SRIM code. Optical properties of SnO$_{2}$ NWs are studied before and after Cu ion irradiation. Band gap analysis reveals that the band gap of irradiated samples is found to decrease compared with the pristine sample. Therefore, ion beam irradiation is a promising technology for nanoengineering and band gap tailoring.

A Novel Real-Time State-of-Health and State-of-Charge Co-Estimation Method for LiFePO$_{4}$ Battery

Rong-Xue Qiao, Ming-Jian Zhang, Yi-Dong Liu, Wen-Ju Ren, Yuan Lin, Feng Pan
Chin. Phys. Lett. 2016, 33 (07): 078201 doi: 10.1088/0256-307X/33/7/078201
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The state of charge (SOC) and state of health (SOH) are two of the most important parameters of Li-ion batteries in industrial production and in practical applications. The real-time estimation for these two parameters is crucial to realize a safe and reliable battery application. However, this is a great problem for LiFePO$_{4}$ batteries due to the large constant potential plateau in the charge/discharge process. Here we propose a combined SOC and SOH co-estimation method based on the experimental test under the simulating electric vehicle working condition. A first-order resistance-capacitance equivalent circuit is used to model the battery cell, and three parameter values, ohmic resistance ($R_{\rm s})$, parallel resistance ($R_{\rm p})$ and parallel capacity ($C_{\rm p})$, are identified from a real-time experimental test. Finally we find that $R_{\rm p}$ and $C_{\rm p}$ could be utilized to make a judgement on the SOH. More importantly, the linear relationship between $C_{\rm p}$ and the SOC is established to make the estimation of the SOC for the first time.

Numerical Simulation on Thermal-Electrical Characteristics and Electrode Patterns of GaN LEDs with Graphene/NiO$_x$ Hybrid Electrode

Quan-Xi Yan, Shu-Fang Zhang, Xing-Ming Long, Hai-Jun Luo, Fang Wu, Liang Fang, Da-Peng Wei, Mei-Yong Liao
Chin. Phys. Lett. 2016, 33 (07): 078501 doi: 10.1088/0256-307X/33/7/078501
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The thermal-electrical characteristic of a GaN light-emitting diode (LED) with the hybrid transparent conductive layers (TCLs) of graphene (Gr) and NiO$_x$ is investigated by a finite element method. It is indicated that the LED with the compound TCL of 3-layer Gr and 1 nm NiO$_x$ has the best thermal-electrical performance from the view point of the maximum temperature and the current density deviation of multiple quantum wells, and the maximum temperature occurs near the n-electrode rather than p-electrode. Furthermore, to depress the current crowding on the LED, the electrode pattern parameters including p- and n-electrode length, p-electrode buried depth and the distance of n-electrode to active area are optimized. It is found that either increasing p- or n-electrode length and buried depth or decreasing the distance of n-electrode from the active area will decrease the temperature of the LED, while the increase of the n-electrode length has more prominent effect. Typically, when the n-electrode length increases to 0.8 times of the chip size, the temperature of the GaN LED with the 1 nm NiO$_x$/3-layer-Gr hybrid TCLs could drop about 7 K and the current density uniformity could increase by 23.8%, compared to 0.4 times of the chip size. This new finding will be beneficial for improvement of the thermal-electrical performance of LEDs with various conductive TCLs such as NiO$_x$/Gr or ITO/Gr as current spreading layers.

Cosmic Constraints to the $w$CDM Model from Strong Gravitational Lensing

Jie An, Bao-Rong Chang, Li-Xin Xu
Chin. Phys. Lett. 2016, 33 (07): 079801 doi: 10.1088/0256-307X/33/7/079801
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We study the cosmic constraint to the $w$CDM (cold dark matter with a constant equation of state $w$) model via 118 strong gravitational lensing systems which are compiled from SLACS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances $D^{\rm obs}=D_{\rm A}(z_{\rm l},z_{\rm s})/D_{\rm A}(0,z_{\rm s})$ is taken as a cosmic observable. To obtain this ratio, we adopt two strong lensing models: one is the singular isothermal sphere model (SIS) and the other one is the power-law density profile (PLP) model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index $\gamma$. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of ${\it \Omega}_{\rm m}=0.31^{+0.44}_{-0.24}$ by the SIS model is compatible with that obtained by Planck2015: ${\it \Omega}_{\rm m}=0.313\pm0.013$. However, the value of ${\it \Omega}_{\rm m}=0.15^{+0.13}_{-0.11}$ based on the PLP model is smaller and has $1.25\sigma$ tension with that obtained by Planck2015.
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