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Volume 36 Issue 4
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Finite-Key Analysis for a Practical High-Dimensional Quantum Key Distribution System Based on Time-Phase States
Ya-Hui Gan, Yang Wang, Wan-Su Bao, Ru-Shi He, Chun Zhou, Mu-Sheng Jiang
Chin. Phys. Lett. 2019, 36 (4): 040301 .   DOI: 10.1088/0256-307X/36/4/040301
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High-dimensional quantum states key distribution (HD-QKD) can enable more than one bit per photon and tolerate more noise. Recently, a practical HD-QKD system based on time-phase states has provided a secret key at Mbps over metropolitan distances. For the purposes of further improving the secret key rate of a practical HD-QKD system, we make two main contributions in this work. Firstly, we present an improved parameter estimation for this system in the finite-key scenario based on the Chernoff bound and the improved Chernoff bound. Secondly, we analyze how the dimension $d$ affects the performance of the practical HD-QKD system. We present numerical simulations about the secret key rate of the practical HD-QKD system based on different parameter estimation methods. It is found that using the improved Chernoff bound can improve the secret key rate and maximum channel loss of the practical HD-QKD system. In addition, a mixture of the 4-level and 8-level practical HD-QKD system can provide better performance in terms of the key generation rate over metropolitan distances.
Variational Approach to Study $\mathcal{PT}$-Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions
Wei Qi, Hai-Feng Li, Zhao-Xin Liang
Chin. Phys. Lett. 2019, 36 (4): 040501 .   DOI: 10.1088/0256-307X/36/4/040501
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Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a $\mathcal{PT}$-symmetric potential are discussed. In the framework of the variational approach, we investigate how the non-locality of interactions affects the self-localization and stability of a condensate with attractive two-body interactions. The results reveal that the non-locality of interactions dramatically influences the shape, width, and chemical potential of the condensate. Analytically variational computation also predicts that there exists a critical negative non-local interaction strength ($p_{\rm c} < 0$) with each fixed two-body interaction ($g_{0} < 0$), and there exists no bright soliton solution for $p_{0} < p_{\rm c}$. Furthermore, we study the effect of the non-locality interactions on the stability of the solitons using the Vakhitov–Kolokolov stability criterion. It is shown that for a positive non-local interaction ($p_{0}>0$), there always exist stable bright solitons in some appropriate parameter regimes.
Experimental Investigation of the Electromagnetically Induced-Absorption-Like Effect for an N-Type Energy Level in a Rubidium BEC
Khan Sadiq Nawaz, Cheng-Dong Mi, Liang-Chao Chen, Peng-Jun Wang, Jing Zhang
Chin. Phys. Lett. 2019, 36 (4): 043201 .   DOI: 10.1088/0256-307X/36/4/043201
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We study the electromagnetically induced-absorption-like (EIA-like) effect for an n-type system in an $^{87}$Rb Bose–Einstein condensate (BEC) using the absorption imaging technique for coupling and driving lasers operating at the $D_{1}$ and $D_{2}$ lines of $^{87}$Rb. The coherent effect is probed by measuring the number of atoms remaining after the BEC is exposed to strong driving fields and a weak probe field. The absorption imaging technique accurately reveals the EIA-like effect of the n-type system. This coherent effect in an n-type system is useful for optical storage, tunable optical switching, and so on.
Understanding Tunneling Ionization of Atoms in Laser Fields using the Principle of Multiphoton Absorption
Long Xu, Li-Bin Fu
Chin. Phys. Lett. 2019, 36 (4): 043202 .   DOI: 10.1088/0256-307X/36/4/043202
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The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although great efforts have been carried out within semiclassical models, there are few discussions describing the multiphoton absorption process within a quantum framework. Comparing the results obtained with the time-dependent Schrödinger equation (TDSE) and the Keldysh–Faisal–Reiss (KFR) theory, we study the nonperturbative effects of ionization dynamics beyond the KFR theory. The difference in momentum spectra between multiphoton and tunneling regimes is understood in a unified picture with virtual multiphoton absorption processes. For the multiphoton regime, the momentum spectra can be obtained by coherent interference of each periodic contribution. However, the interference of multiphoton absorption peaks will result in a complex structure of virtual multiphoton bands in the tunneling regime. It is shown that the virtual spectra will be almost continuous in the tunneling regime instead of the discrete levels found in the multiphoton regime. Finally, with a model combining the TDSE and the KFR theory, we try to understand the different effects of virtual multiphoton processes on ionization dynamics.
A Gain-Switched Fe:ZnSe Laser Pumped by a Pulsed Ho,Pr:LLF Laser
Ying-Yi Li, You-Lun Ju, Tong-Yu Dai, Xiao-Ming Duan, Chun-Fa Guo, Li-Wei Xu
Chin. Phys. Lett. 2019, 36 (4): 044201 .   DOI: 10.1088/0256-307X/36/4/044201
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We demonstrate a gain-switched Fe:ZnSe laser pumped by a 2958 nm pulsed Ho,Pr:LLF laser. The maximum single pulse energy is 16.4 $\mu$J with a minimum pulse duration of 13.9 ns at the pulse repetition frequency of 1 Hz when the Fe:ZnSe crystal is cooled to 77 K by liquid nitrogen, corresponding to a slope efficiency of 22.9%. The central wavelength and FWHM linewidth are 3957.4 nm and 23.2 nm, respectively. The output energy monotonically decreases as the crystal temperature increases in the range 77–293 K.
A High Conversion Efficiency Q-Switched Intracavity Nd:YVO$_{4}$/KTA Optical Parametric Oscillator under Direct Diode Pumping at 880nm
Li-Jiao He, Ke Liu, Nan Zong, Zhao Liu, Zhi-Min Wang, Yong Bo, Xiao-Jun Wang, Qin-Jun Peng, Da-Fu Cui, Zu-Yan Xu
Chin. Phys. Lett. 2019, 36 (4): 044202 .   DOI: 10.1088/0256-307X/36/4/044202
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We report a high conversion efficiency Q-switched Nd:YVO$_{4}$/KTiOAsO$_{4}$ (KTA) intracavity optical parametric oscillator (IOPO) operating near 3.5 μm based on direct 880 nm laser diode (LD) pumping. A maximum average idler output power of 2.6 W with a pulse width of about 7.9 ns is achieved under an absorbed LD power of 45.4 W at a pulse repetition rate (PRR) of 10 kHz. The maximum optical-optical conversion efficiency from LD power to OPO mid-infrared (MIR) output of 6.74% is achieved. To our knowledge, this is the highest conversion efficiency for a KTA-IOPO by exploiting a Q-switched laser as the parent fundamental pump source. The beam quality factors $M^{2}$ of the MIR beam at the full output power with a PRR of 10 kHz are within 2.12 in both the horizontal and vertical directions, indicating a near Gaussian mode.
Temperature-Dependent Dielectric Characterization of Magneto-Optical Tb$_{3}$Sc$_{2}$Al$_{3}$O$_{12}$ Crystal Investigated by Terahertz Time-Domain Spectroscopy
Ju-Geng Li, Sen-Miao Yang, Xin Chen, Nai-Feng Zhuang, Qi-Biao Zhu, An-Hua Wu, Xian Lin, Guo-Hong Ma, Zuan-Ming Jin, Jian-Quan Yao
Chin. Phys. Lett. 2019, 36 (4): 044203 .   DOI: 10.1088/0256-307X/36/4/044203
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Terbium scandium aluminum garnet (TSAG) crystals have been widely used in magneto-optical systems. We investigate the complex refractive index of the TSAG crystal in the terahertz frequency range using terahertz (THz) time-domain spectroscopy in the temperature range 100–300 K. It is observed that the refractive index and the absorption coefficient increase with the THz frequency. The refractive index increases with the temperature. We measure the temperature coefficient of the refractive index of the TSAG crystal in the frequency range 0.4–1.4 THz. Furthermore, the loss tangent, i.e., the ratio of experimental values of the imaginary and real part of the dielectric permittivity, is found to be almost independent of frequency. TSAG is very promising for applications in THz optoelectronics because it has a high dielectric constant, low loss, and low thermal coefficient of the dielectric constant.
The 10kW Level High Brightness Face-Pumped Slab Nd:YAG Amplifier with a Hybrid Cooling System
Shuai Li, Ya-Ding Guo, Zhong-Zheng Chen, Lin Zhang, Ke-Ling Gong, Zhi-Feng Zhang, Bao-Shan Wang, Jian Xu, Yi-Ting Xu, Lei Yuan, Yang Kou, Yang Liu, Yan-Yong Lin, Qin-Jun Peng, Zu-Yan Xu
Chin. Phys. Lett. 2019, 36 (4): 044204 .   DOI: 10.1088/0256-307X/36/4/044204
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We demonstrate a high power, high brightness, slab amplifier based on face-pumped Nd:YAG slab gain modules, having a high efficient hybrid cooling system of the conduction cooling and forced convection cooling. Using a single gain module, a laser output power up to 4.5 kW with a remarkable optical-optical conversion efficiency of 51% is realized, indicating an excellent lasing performance of the Nd:YAG slab module. The amplifier operates at a repetition rate of 700 Hz and delivers a maximum average output power exceeding 10.5 kW with pulse duration of 150 μs. A good beam quality factor is measured to be $\beta=1.9$. To the best of our knowledge, this is the highest brightness for a 10 kW level Nd:YAG slab amplifier.
Multi-Path Ghost Imaging by Means of an Additional Time Correlation
Rui Liu, Ling-Jun Kong, Yu Si, Zhou-Xiang Wang, Wen-Rong Qi, Chenghou Tu, Yongnan Li, Hui-Tian Wang
Chin. Phys. Lett. 2019, 36 (4): 044205 .   DOI: 10.1088/0256-307X/36/4/044205
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Ghost imaging functions achieved by means of the spatial correlations between two photons is a new modality in imaging systems. With a small number of photons, ghost imaging is usually realized based on the position correlation of photon pairs produced from the spontaneous parametric down-conversion process. Here we demonstrate a way to realize multi-path ghost imaging by introducing an additional time correlation. Different delays of paths will induce the shift of the coincidence peak, which carries the information about objects. By choosing the suitable coincidence window, we obtain images of three objects simultaneously, with a visibility of 87.2%. This method provides insights and techniques into multi-parameter ghost imaging. It can be applied to other correlated imaging systems, for example, quantum spiral imaging.
Acoustic Absorption Characteristics of New Underwater Omnidirectional Absorber
Cun Wang, Shan-De Li, Wei-Guang Zheng, Qi-Bai Huang
Chin. Phys. Lett. 2019, 36 (4): 044301 .   DOI: 10.1088/0256-307X/36/4/044301
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We investigate a new underwater omnidirectional absorber with acoustic black hole effect to realize a broadband omnidirectional acoustic wave absorption. Based on multiple scattering theory, a two-dimensional axisymmetric model of underwater omnidirectional absorber comprised of an acoustic gradient refractive index structure and a hollow core is developed, and the mechanisms of omnidirectional absorption and dissipation of acoustic waves are studied. The numerical results indicate that the omnidirectional absorber developed here can achieve the omnidirectional absorption of incident acoustic waves in a broadband frequency and can effectively reduce the backscattering of acoustic waves. It potentially provides a new notion for underwater acoustic coating design.
Source Ranging Using Ensemble Convolutional Networks in the Direct Zone of Deep Water
Yi-Ning Liu, Hai-Qiang Niu, Zheng-Lin Li
Chin. Phys. Lett. 2019, 36 (4): 044302 .   DOI: 10.1088/0256-307X/36/4/044302
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Using deep convolutional neural networks as primary learners and a deep neural network as meta-learner, source ranging is solved as a regression problem with the ensemble learning method. Simulated acoustic data from the acoustic propagation model are used as the training data. Real data from an experiment in the South China Sea are used as the test data to demonstrate the performance. The results indicate that in the direct zone of deep water, signals received by a very deep receiver can be used to estimate the range of underwater sound source. Within 30 km, the mean absolute error of the range predictions is 1.0 km and the mean absolute percentage error is 7.9%.
Impact of Sheath Boundary Conditions and Magnetic Flutter on Evolution and Distribution of Transient Particle and Heat Fluxes in the Edge-Localized Mode Burst by Experimental Advanced Superconducting Tokamak Simulation
Yan-Bin Wu, Tian-Yang Xia, Fang-Chuan Zhong, Bin Gui, EAST Team
Chin. Phys. Lett. 2019, 36 (4): 045201 .   DOI: 10.1088/0256-307X/36/4/045201
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To study the evolution and distribution of the transient particle and heat fluxes during the edge-localized modes (ELMs) burst on the experimental advanced superconducting tokamak (EAST), the BOUT$^{++}$ six-field two-fluid model with sheath boundary conditions (SBCs) and magnetic flutter terms in the parallel thermal conduction is used to simulate the evolution of the profiles and growing process of the fluxes at divertor targets. Although SBCs hardly play a role in the linear phase, in the nonlinear phase both SBCs and magnetic flutter can change the dominant toroidal mode. SBCs are able to broaden the frequency distribution of the turbulence. The magnetic flutter increases the ELM size from 2.8% to 8.4%, and it doubles the amplitudes of the radial heat and particle transport coefficients at outer midplane (OMP), at around 1.0 m$^{2}$s$^{-1}$. It is then able to increase the particle and heat flux at the divertor targets and to broaden the radial distribution of the parallel heat flux towards the targets.
Synthesis and Characteristics of Type Ib Diamond Doped with NiS as an Additive
Jian-Kang Wang, Shang-Sheng Li, Ning Wang, Hui-Jie Liu, Tai-Chao Su, Mei-Hua Hu, Fei Han, Kun-Peng Yu, Hong-An Ma
Chin. Phys. Lett. 2019, 36 (4): 046101 .   DOI: 10.1088/0256-307X/36/4/046101
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Large diamond single crystals doped with NiS are synthesized under high pressure and high temperature. It is found that the effects on the surface and shape of the synthesized diamond crystals are gradually enhanced by increasing the NiS additive amount. It is noted that the synthesis temperature is necessarily raised to 1280$^{\circ}\!$C to realize the diamond growth when the additive amount reaches 3.5% in the synthesis system. The results of Fourier transform infrared spectroscopy (FTIR) demonstrate that S is incorporated into the diamond lattice and exists in the form of C–S bond. Based on the FTIR results, it is found that N concentration in diamond is significantly increased, which are ascribed to the NiS additive. The analysis of x-ray photoelectron spectroscopy shows that S is present in states of C–S, S–O and C–S–O bonds. The relative concentration of S compared to C continuously increases in the synthesized diamonds as the amount of additive NiS increases. Additionally, the electrical properties can be used to characterize the obtained diamond crystals and the results show that diamonds doped with NiS crystals behave as n-type semiconductors.
Strain Induced Nanopillars and Variation of Magnetic Properties in La$_{0.825}$Sr$_{0.175}$MnO$_{3}$/LaAlO$_{3}$ Films
Xin Li, Jing-Zhi Han, Xiong-Zuo Zhang, Yin-Feng Zhang, Hai-Dong Tian, Ming-Zhu Xue, Kun Li, Xin Wen, Wen-Yun Yang, Shun-Quan Liu, Chang-Sheng Wang, Hong-Lin Du, Xiao-Dong Zhang, Xin-An Wang, Ying-Chang Yang, Jin-Bo Yang
Chin. Phys. Lett. 2019, 36 (4): 046102 .   DOI: 10.1088/0256-307X/36/4/046102
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To investigate the process of strain relaxation and resultant variation of microstructure and magnetic properties, low-doped La$_{0.825}$Sr$_{0.175}$MnO$_{3}$ epitaxial films with different thicknesses are deposited on LaAlO$_{3}$ substrates and strain induced nanopillars are discovered inside the La$_{0.825}$Sr$_{0.175}$MnO$_{3}$ film. Perpendicular oriented nanopillars mainly exist below 30 nm and tend to disappear above 30 nm. The distribution of nanopillars not only induce the variation of lattice parameters and local structural distortion but also lead to the deviation of easy magnetization axis from the perpendicular direction. Specifically, the out-of-plane lattice parameters of the film decrease quickly with the increase of the thickness but tend to be constant when the thickness is above 30 nm. Meanwhile, the variations of magnetic properties along in-plane and out-of-plane directions would also decline at first and they then remain nearly unchanged. Our work constructs the relationship between nanopillars and magnetic properties inside films. We are able to clearly reveal the effects of inhomogeneous strain relaxation.
High-Pressure Phase Transitions of Cubic Y$_{2}$O$_{3}$ under High Pressures by In-situ Synchrotron X-Ray Diffraction
Sheng Jiang, Jing Liu, Xiao-Dong Li, Yan-Chun Li, Shang-Ming He, Ji-Chao Zhang
Chin. Phys. Lett. 2019, 36 (4): 046103 .   DOI: 10.1088/0256-307X/36/4/046103
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High-pressure phase transitions of cubic Y$_{2}$O$_{3}$ are investigated using in situ synchrotron x-ray diffraction in a diamond anvil cell up to 36.3 GPa. The pressure-induced phase transitions of cubic Y$_{2}$O$_{3}$, which display apparent inconsistencies in previous studies, are verified to be from a cubic phase to a monoclinic phase and further to a hexagonal phase at 11.7 and 21.6 GPa, respectively. The hexagonal Y$_{2}$O$_{3}$ displays noticeable anisotropic compressibility due to its layered structure and it is stable up to the highest pressure in the present study. A third-order Birch–Murnaghan fit based on the observed pressure-volume data yields zero pressure bulk moduli of 180(3), 196(7) and 177(7) GPa for cubic, monoclinic and hexagonal phases, respectively.
Effects of Helium Implantation and Subsequent Electron Irradiation on Microstructures of Fe-11wt.% Cr Model Alloy
Bing-Sheng Li, Zhi-Guang Wang, Tie-Long Shen, Kong-Fang Wei, Yan-Bin Sheng, Tamakai Shibayama, Xi-Rui Lu, An-Li Xiong
Chin. Phys. Lett. 2019, 36 (4): 046104 .   DOI: 10.1088/0256-307X/36/4/046104
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Helium effects on dislocation and cavity formation of Fe-11 wt.% Cr model alloy are investigated. Single-beam (electron) and dual-beam (He$^{+}$/e$^{-}$) irradiations are performed at 350$^\circ\!$C and 400$^\circ\!$C using an ultra-high voltage electron microscope combined with ion accelerators. In-situ observation shows that the growth rate of dislocation loops is reduced in the helium pre-injected specimen. The mean size of cavities decreased in the helium pre-injected specimen. The possible mechanisms are discussed.
Negative Differential Resistance and Rectifying Effects of Diblock Co-Oligomer Molecule Devices Sandwiched between C$_{2}$N-$h$2D Electrodes
Meng Ye, Cai-Juan Xia, Bo-Qun Zhang, Yue Ma
Chin. Phys. Lett. 2019, 36 (4): 047101 .   DOI: 10.1088/0256-307X/36/4/047101
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Based on nonequilibrium Green's function method in combination with density functional theory, we study the electronic transport properties of dipyrimidinyl-diphenyl molecules embedded in a carbon atomic chain sandwiched between zigzag graphene nanoribbon and different edge geometries C$_{2}$N-$h$2D electrodes. Compared with the graphene electrodes, the C$_{2}$N-$h$2D electrode can cause rectifying and negative differential resistance effects. For C$_{2}$N-$h$2D with zigzag edges, a more remarkable negative differential resistance phenomenon appears, whereas armchair-edged C$_{2}$N-$h$2D can give rise to much better rectifying behavior. These results suggest that this system can be potentially useful for designs of logic and memory devices.
Effect of Post-Annealing on Structural and Electrical Properties of ZnO:In Films
Guo-Ping Qin, Hong Zhang, Hai-Bo Ruan, Jiang Wang, Dong Wang, Chun-Yang Kong
Chin. Phys. Lett. 2019, 36 (4): 047301 .   DOI: 10.1088/0256-307X/36/4/047301
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Indium-doped ZnO (ZnO:In) films are deposited on quartz substrates by rf magnetron sputtering. The effects of post-annealing on structural, electrical, optical and Raman properties are investigated by x-ray diffraction, Raman scattering, Hall measurement and first-principles calculation. The results indicate that all of the ZnO:In films have excellent crystallinity with a preferred ZnO (002) orientation. It is found that the incorporation of In can dramatically increase the intensity of the 274 cm$^{-1}$ Raman mode. However, both post-annealing treatment and increasing O$_{2}$ partial pressure in the process of preparing thin films can reduce the intensity of the 274 cm$^{-1}$ mode or even eliminate it, and relax compressive stress of the ZnO:In film judged by analyzing the shifts of the (002) Bragg peaks and $E_{2}$ (high) mode. Finally, the origin of the 274 cm$^{-1}$ mode is inferred to be the vibration of Zn interstitial (Zn$_{\rm i}$) defects, which play a crucial role in the high electron concentration and low resistivity of ZnO:In films annealed in an appropriate temperature range (450–600$^{\circ}\!$C).
The 0–$\pi$ Phase Transition in Epitaxial NbN/Ni$_{60}$Cu$_{40}$/NbN Josephson Junctions
Feng Li, Wei Peng, Zhen Wang
Chin. Phys. Lett. 2019, 36 (4): 047401 .   DOI: 10.1088/0256-307X/36/4/047401
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We fabricate high quality superconductor/ferromagnet/superconductor (SFS) Josephson junctions using epitaxial NbN/Ni$_{60}$Cu$_{40}$/NbN trilayer heterostructures. Both experimental measurements and theoretical calculations of the ferromagnet layer thickness dependence of the Josephson critical current are performed. We observe the damped oscillation behavior of the critical current as a function of the ferromagnetic layer thickness at 4.2 K, which shows a 0–$\pi$ phase transition in this type of magnetic Josephson junction. Clear 0–$\pi$ and reverse $\pi$–0 phase transitions occur around the Ni$_{60}$Cu$_{40}$ thicknesses of 3.2 and 6.7 nm. Numerical calculations based on the quasi-classical Usadel equation and the Green function fit well with the experimental results. Compared with the dirty limit, the intermediate regime without the dead layer gives better fit for our SFS Josephson junctions because of the epitaxial structure. Both of the 0- and $\pi$-phase junctions show the ideal magnetic field dependence with a Fraunhofer-like pattern at 4.2 K.
Double Resonance Raman Scattering in Single-Layer MoSe$_{2}$ under Moderate Pressure
Jian-mei Li, Yi-kun Yao, Li-huan Sun, Xin-yan Shan, Cong Wang, Xing-hua Lu
Chin. Phys. Lett. 2019, 36 (4): 048201 .   DOI: 10.1088/0256-307X/36/4/048201
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Pressure-dependent properties in layered transition-dichalcogenides are important for our understanding of their basic structures and applications. We investigate the electronic structure in MoSe$_{2}$ monolayer under external pressure up to 5.73 GPa by Raman spectroscopy and photoluminescence (PL) spectroscopy. The double resonance out-of-plane acoustic mode ($2ZA$) phonon is observed in Raman spectroscopy near 250 cm$^{-1}$, which presents pronounced intensity and pressure dependence. Significant variation in $2ZA$ peak intensity under different pressures reflects the change in electronic band structure as pressure varies, which is consistent with the blue shift in PL spectroscopy. The high sensitivity in both Raman and PL spectroscopy under moderate pressure in such a two-dimensional material may have many advantages for optoelectronic applications.
Neutrino Emission and Cooling of Dark-Matter-Admixed Neutron Stars
Wen-Bo Ding, Zi Yu, Yan Xu, Chun-Jian Liu, Tmurbagan Bao
Chin. Phys. Lett. 2019, 36 (4): 049701 .   DOI: 10.1088/0256-307X/36/4/049701
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The GW170817 binary neutron star merger event in 2017 has raised great interest in the theoretical research f neutron stars. The structure and cooling properties of dark-matter-admixed neutron stars are studied here using relativistic mean field theory and cooling theories. The non-self-annihilating dark matter (DM) component is assumed to be ideal fermions, among which the weak interaction is considered. The results show that pulsars J1614-2230, J0348+0432 and EXO 0748-676 may all contain DM with the particle mass of 0.2–0.4 GeV. However, it is found that the effect of DM on neutron star cooling is complicated. Light DM particles favor the fast cooling of neutron stars, and the case is converse for middle massive DM. However, high massive DM particles, around 1.0 GeV, make the low mass (around solar mass) neutron star still undergo direct Urca process of nucleons at the core, which leads the DM-admixed stars cool much more quickly than the normal neutron star, and cannot support the direct Urca process with a mass lower than 1.1 times solar mass. Thus, we may conjecture that if small (around solar mass) and super cold (at least surface temperature 5–10 times lower than that of the usual observed data) pulsars are observed, then the star may contain fermionic DM with weak self-interaction.
21 articles