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 Select Parameters of Isotope Shifts for $2s2p{}^{3,1}\!P_{1} \to 2s^{2}{}^{1}\!S_0$ Transitions in Heavy Be-Like Ions Xiang Zhang, Jian-Peng Liu, Ji-Guang Li, Hong-Xin Zou Chin. Phys. Lett.    2019, 36 (11): .   DOI: 10.1088/0256-307X/36/11/113101 Abstract   HTML   PDF (669KB) The field shift and mass shift parameters of the 2$s2p\,{}^{3,1}\!P_{1}\to 2s^{2}\,{}^{1}\!S_0$ transitions in Be-like ions ($70 \le Z \le 92$) are calculated using the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections. We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-$Z$ range due to the relativistic nuclear recoil effects. A minimum value exists for the specific mass shift parameters around $Z=80$, especially for the 2$s2p\,{}^{3}\!P_{1}\to 2s^{2}\,{}^{1}\!S_0$ transition. In addition, the field shifts and mass shifts of these two transitions are estimated using an empirical formula, and their contributions are compared along the isoelectronic sequence.
 Select Manipulating the Flipping of Water Dipoles in Carbon Nanotubes Dang-Xin Mao, Xiao-Gang Wang, Guo-Quan Zhou, Song-Wei Zeng, Liang Chen, Jun-Lang Chen, Chao-Qing Dai Chin. Phys. Lett.    2019, 36 (10): .   DOI: 10.1088/0256-307X/36/10/103101 Abstract   HTML   PDF (1208KB) Flipping of water dipoles in carbon nanotubes is of great importance in many physical and biological applications, such as signal amplification, molecular switches and nano-gates. Ahead of these applications, understanding and inhibiting the non-negligible thermal noise is essential. Here, we use molecular dynamics simulations to show that the flipping frequency of water dipoles increases with the rising temperature, and the thermal noise can be suppressed by imposed charges and external uniform electric fields. Furthermore, the water dipoles flip periodically between two equiprobable and stable states under alternating electric fields. These two stable states may be adopted to store 0 and 1 bits for memory storage or molecular computing.
 Select Towards the Same Line of Liquid–Liquid Phase Transition of Dense Hydrogen from Various Theoretical Predictions Binbin Lu, Dongdong Kang, Dan Wang, Tianyu Gao, Jiayu Dai Chin. Phys. Lett.    2019, 36 (10): 103102.   DOI: 10.1088/0256-307X/36/10/103102 Abstract   HTML   PDF (1985KB) For a long time, there have been huge discrepancies between different models and experiments concerning the liquid–liquid phase transition (LLPT) in dense hydrogen. We present the results of extensive calculations of the LLPT in dense hydrogen using the most expensive first-principle path-integral molecular dynamics simulations available. The nonlocal density functional rVV10 and the hybrid functional PBE0 are used to improve the description of the electronic structure of hydrogen. Of all the density functional theory calculations available, we report the most consistent results through quantum Monte Carlo simulations and coupled electron-ion Monte Carlo simulations of the LLPT in dense hydrogen. The critical point of the first-order LLPT is estimated to be above 2000 K according to the equation of state. Moreover, the metallization pressure obtained from the jump of dc electrical conductivity almost coincides with the plateau of equation of state.
 Select Experimental Realization of Degenerate Fermi Gases of $^{87}$Sr Atoms with 10 or Two Spin Components Wei Qi, Ming-Cheng Liang, Han Zhang, Yu-Dong Wei, Wen-Wei Wang, Xu-Jie Wang, Xibo Zhang Chin. Phys. Lett.    2019, 36 (9): .   DOI: 10.1088/0256-307X/36/9/093701 Abstract   HTML   PDF (852KB) We report the experimental realization of quantum degenerate Fermi gases of $^{87}$Sr atoms under controlled 10- and dual-nuclear-spin configurations. Based on laser cooling and evaporative cooling, we achieve an ultracold Fermi gas of 10$^{5}$ atoms equally distributed over 10 spin states, with a temperature of $T/T_{\rm F}=0.21$. We further prepare a dual-spin gas by optically pumping atoms to the $m_{\rm F}=9/2$ and $m_{\rm F}=7/2$ states and observe a slightly lower $T/T_{\rm F}$ than that for a 10-spin gas under the same trapping condition, showing efficient evaporative cooling under a decreasing number ${\cal N}$ of spin states (${\cal N}\geqslant 2$) despite the increasing importance of Pauli exclusion. Given that rethermalization becomes less efficient with ${\cal N}$ approaching unity, we evaporatively cool an almost polarized gas to 130 nK. The simple and efficient preparation of ultracold Fermi gases of $^{87}$Sr with tunable spin configurations provides a first step towards engineering topological quantum systems.
 Select Influence of Debye Plasma on the KLL Dielectronic Recombination of H-Like Helium Ions Deng-Hong Zhang, Lu-You Xie, Jun Jiang, Chen-Zhong Dong Chin. Phys. Lett.    2019, 36 (8): .   DOI: 10.1088/0256-307X/36/8/083401 Abstract   HTML   PDF (619KB) Using the Debye shielding model, the effects of plasma shielding on the dielectronic recombination processes of the H-like helium ions are investigated. It is found that plasma shielding causes a remarkable change in the Auger decay rate of the doubly excited $2p^2$ $^3P_2$ state. As a result, the dielectronic recombination cross sections from the doubly excited $2p^2$ $^3P_2$ state increases with the decreasing Debye shielding length.
 Select Measurement of S-Wave Scattering Length between $^6$Li and $^{88}$Sr Atoms Using Interspecies Thermalization in an Optical Dipole Trap Xiao-Bin Ma, Zhu-Xiong Ye, Li-Yang Xie, Zhen Guo, Li You, Meng Khoon Tey Chin. Phys. Lett.    2019, 36 (7): .   DOI: 10.1088/0256-307X/36/7/073401 Abstract   HTML   PDF (708KB) We report the creation of the first mixture of $^6$Li and $^{88}$Sr atoms in an optical dipole trap. Using this mixture, a measurement of the interspecies thermalization process is carried out and the previously unknown interspecies s-wave scattering length between $^6$Li and $^{88}$Sr atoms is extracted to be $|a_{\rm ^6Li-^{88}Sr}|=(380^{+160}_{-100})a_0$ with $a_0$ being the Bohr radius from the rate of interspecies thermalization.
 Select Secular Motion Frequencies of $^{9}$Be$^{+}$ Ions and $^{40}$Ca$^{+}$ Ions in Bi-component Coulomb Crystals Hai-Xia Li, Min Li, Qian-Yu Zhang, Xin Tong Chin. Phys. Lett.    2019, 36 (7): .   DOI: 10.1088/0256-307X/36/7/073701 Abstract   HTML   PDF (659KB) We obtain bi-component Coulomb crystals using laser-cooled $^{40}$Ca$^{+}$ ions to sympathetically cool $^{9}$Be$^{+}$ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled $^{40}$Ca$^{+}$ is impervious to the sympathetically cooled $^{9}$Be$^{+}$ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction.
 Select Carrier Envelope Phase Description for an Isolated Attosecond Pulse by Momentum Vortices Meng Li, Gui-zhong Zhang, Xin Ding, Jian-quan Yao Chin. Phys. Lett.    2019, 36 (6): .   DOI: 10.1088/0256-307X/36/6/063201 Abstract   HTML   PDF (1790KB) As a crucial parameter for a few-cycle laser pulse, the carrier envelope phase (CEP) substantially determines the laser waveform. We propose a method to directly describe the CEP of an isolated attosecond pulse (IAP) by the vortex-shaped momentum pattern, which is generated from the tunneling ionization of a hydrogen atom by a pair of time-delayed, oppositely and circularly polarized IAP-IR pulses. Superior to the angular streaking method that characterizes the CEP in terms of only one streak, our method describes the CEP of an IAP by the features of multiple streaks in the vortex pattern. The proposed method may open the possibility of capturing sub-cycle extreme ultraviolet dynamics.
 Select 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): .   DOI: 10.1088/0256-307X/36/4/043201 Abstract   HTML   PDF (672KB) 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.
 Select 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): .   DOI: 10.1088/0256-307X/36/4/043202 Abstract   HTML   PDF (2055KB) 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.
 Select Analysis of Transition Mechanism of Cubic Boron Nitride Single Crystals under High Pressure-High Temperature with Valence Electron Structure Calculation Mei-Zhe Lv, Bin Xu, Li-Chao Cai, Feng Jia, Xing-Dong Yuan Chin. Phys. Lett.    2019, 36 (1): .   DOI: 10.1088/0256-307X/36/1/013101 Abstract   HTML   PDF (535KB) The possibilities of hexagonal boron nitride (hBN) and lithium boron nitride (Li$_{3}$BN$_{2}$) transition into cubic boron nitride (cBN) under synthetic pressure 5.0 GPa and synthetic temperature 1700 K are analyzed with the use of the empirical electron theory of solids and molecules. The relative differences in electron density are calculated for dozens of bi-phase interfaces hBN/cBN, Li$_{3}$BN$_{2}$/cBN. These relative differences of hBN/cBN are in good agreement with the first order of approximation ($<$10%), while those of Li$_{3}$BN$_{2}$/cBN are much greater than 10%. This analysis suggests that Li$_{3}$BN$_{2}$ is impossible to be intermediate phase but is a catalyst and cBN should be directly transformed by hBN.
 Select Sub-Doppler Laser Cooling of $^{23}$Na in Gray Molasses on the $D_{2}$ Line Zhenlian Shi, Ziliang Li, Pengjun Wang, Zengming Meng, Lianghui Huang, Jing Zhang Chin. Phys. Lett.    2018, 35 (12): .   DOI: 10.1088/0256-307X/35/12/123701 Abstract   HTML   PDF (730KB) We report on the efficient gray molasses cooling of sodium atoms using the $D_{2}$ optical transition at 589.1 nm. Thanks to the hyperfine split about 6${\it \Gamma}$ between $|F'=2\rangle$ and $|F'=3\rangle$ in the excited state 3$^{2}P_{3/2}$, this atomic transition is effective for the gray molasses cooling mechanism. Using this cooling technique, the atomic sample in $F=2$ ground manifold is cooled from 700 $\mu$K to 56 $\mu$K in 3.5 ms. We observe that the loading efficiency into magnetic trap is increased due to the lower temperature and high phase space density of atomic cloud after gray molasses. This technique offers a promising route for the fast cooling of the sodium atoms in the $F=2$ state.
 Select Simulation of Intermediate State Absorption Enhancement in Rare-Earth Ions by Polarization Modulated Femtosecond Laser Field Wen-Jing Cheng, Shi-Hua Zhao Chin. Phys. Lett.    2018, 35 (11): .   DOI: 10.1088/0256-307X/35/11/113201 Abstract   HTML   PDF (534KB) We extend the third perturbation theory to study the polarization control behavior of the intermediate state absorption in Nd$^{3+}$ ions. The results show that coherent interference can occur between the single-photon and three-photon excitation pathways, and depends on the central frequency of the femtosecond laser field. Moreover, single-photon and three-photon absorptions have different polarization control efficiencies, and the relative weight of three-photon absorption in the whole excitation processes can increase with increasing the laser intensity. Therefore, the enhancement or suppression of the intermediate state absorption can be realized and manipulated by properly designing the intensity and central frequency of the polarization modulated femtosecond laser field. This research can not only enrich theoretical research methods for the up-conversion luminescence manipulation of rare-earth ions, but also can provide a clear physical picture for understanding and controlling multi-photon absorption in a multiple energy level system.
 Select Theoretical Investigation on the Low-Lying States of LaP Molecule Nagat Elkahwagy, Atif Ismail, S. M. A. Maize, K. R. Mahmoud Chin. Phys. Lett.    2018, 35 (10): .   DOI: 10.1088/0256-307X/35/10/103101 Abstract   HTML   PDF (477KB) The completely unexplored LaP molecule is investigated by ab initio methods. Potential energy curves for the low-lying states of LaP are constructed by means of the diffusion Monte Carlo method combined with three different trial functions. Spectroscopic constants are also numerically derived and the ground state is assigned, looking forward to experimental comparisons. Moreover, variations of the permanent dipole moments as a function of the internuclear separation for the two lowest states of the diatomic LaP are studied and analyzed.
 Select Transition Dipole Moment Measurements of Ultracold Photoassociated $^{85}$Rb$^{133}$Cs Molecules by Depletion Spectroscopy Juan-Juan Cao, Ting Gong, Zhong-Hao Li, Zhong-Hua Ji, Yan-Ting Zhao, Lian-Tuan Xiao, Suo-Tang Jia Chin. Phys. Lett.    2018, 35 (10): .   DOI: 10.1088/0256-307X/35/10/103301 Abstract   HTML   PDF (762KB) The transition dipole moments (TDMs) of ultracold $^{85}$Rb$^{133}$Cs molecules between the lowest vibrational ground level, $X^{1}{\it \Sigma}^{+}$ ($v=0$, $J=1$), and the two excited rovibrational levels, $2^{3}{\it \Pi}_{0^{+}}$ ($v'=10$, $J'=2$) and $2^{1}{\it \Pi}_{1}$ ($v'=22$, $J'=2$), are measured using depletion spectroscopy. The ground-state $^{85}$Rb$^{133}$Cs molecules are formed from cold mixed component atoms via the $2^{3}{\it \Pi}_{0^{-}}$ ($v=11$, $J=0$) short-range level, then detected by time-of-flight mass spectrum. A home-made external-cavity diode laser is used as the depletion laser to couple the ground level and the two excited levels. Based on the depletion spectroscopy, the corresponding TDMs are then derived to be 3.5(2)$\times$$10^{-3}$$ea_{0}$ and 1.6(1)$\times$$10^{-2}$$ea_{0}$, respectively, where $ea_{0}$ represents the atomic unit of electric dipole moment. The enhance of TDM with nearly a factor of 5 for the $2^{1}{\it \Pi}_{1}$ ($v'=22$, $J'=2$) excited level means that it has stronger coupling with the ground level. It is meaningful to find more levels with much more strong coupling strength by the represented depletion spectroscopy to realize direct stimulated Raman adiabatic passage transfer from scattering atomic states to deeply molecular states.
 Select First-Principles Study of Magnetic Properties of TM$_{13}$ and TM$_{13}$@Au$_{32}$ Clusters (TM=Mn, Co) Yi-Bo Li, Li-Jin Zeng, Chun-Xiang Zhao, Chun-Yao Niu Chin. Phys. Lett.    2018, 35 (10): .   DOI: 10.1088/0256-307X/35/10/103601 Abstract   HTML   PDF (830KB) The structural and magnetic properties of TM$_{13}$ and TM$_{13}$@Au$_{32}$ clusters (TM=Mn, Co) are studied by first-principles calculations. We find that the Au$_{32}$ cluster can tune not only the magnetic moment but also the magnetic coupling properties between the TM atoms of the TM cluster. The Au$_{32}$ cluster can increase the net magnetic moment of Mn$_{13}$ clusters while reducing that of Co$_{13}$ clusters. The interaction between Au and Mn atoms induces more Mn atoms to form spin parallel coupling, resulting in an increase of the total magnetic moment of Mn$_{13}$ clusters, while for the Co$_{13}$ clusters, the interaction between Au and Co atoms does not change the magnetic coupling states between the Co atoms, but reduces the magnetic moment of the Co atoms, leading to a decrease of the total magnetic moment of this system. Our findings indicate that the encapsulation of Au$_{32}$ clusters can not only raise the chemical stability of TM clusters, but also can tune their magnetic coupling properties and magnetic moment, which enables such systems to be widely applied in fields of spintronics and medical science.
 Select Experimental Study on Double Resonance Optical Pumping Spectroscopy in a Ladder-Type System of $^{87}$Rb Atoms Yi-Hong Li, Shao-Hua Li, Jin-Peng Yuan, Li-Rong Wang, Lian-Tuan Xiao, Suo-Tang Jia Chin. Phys. Lett.    2018, 35 (9): .   DOI: 10.1088/0256-307X/35/9/093201 Abstract   HTML   PDF (734KB) Double resonance optical pumping spectroscopy has an outstanding advantage of high signal-to-noise ratio, thus having potential applications in precision measurement. With the counter propagated 780 nm and 776 nm laser beams acting on a rubidium vapor cell, the high resolution spectrum of $5S_{1/2}-5P_{3/2}-5D_{5/2}$ ladder-type transition of $^{87}$Rb atoms is obtained by monitoring the population of the $5S_{1/2}$ ground state. The dependence of the spectroscopy lineshape on the probe and coupling fields are comprehensively studied in theory and experiment. This research is helpful for measurement of fundamental physical constants by high resolution spectroscopy.
 Select Lithium/Silver-Doped Cu$_{2}$ZnSnS$_{4}$ with Tunable Band Gaps and Phase Structures: a First-Principles Study Jun Zhang, Jun Liao, Le-Xi Shao, Shu-Wen Xue, Zhi-Guo Wang Chin. Phys. Lett.    2018, 35 (8): .   DOI: 10.1088/0256-307X/35/8/083101 Abstract   HTML   PDF (1504KB) Doping is an effective approach for improving the photovoltaic performance of Cu$_{2}$ZnSnS$_{4}$ (CZTS). The doping by substitution of Cu atoms in CZTS with Li and Ag atoms is investigated using density functional theory. The results show that the band gaps of Li$_{2x}$Cu$_{2(1-x)}$ZnSnS$_{4}$ and Ag$_{2x}$Cu$_{2(1-x)}$ZnSnS$_{4}$ can be tuned in the ranges of 1.30–3.43 and 1.30–1.63 eV, respectively. The calculation also reveals a phase transition from kesterite to wurtzite-kesterite for Li$_{2x}$Cu$_{2(1-x)}$ZnSnS$_{4}$ as $x$ is larger than 0.9. The tunable band gaps of Li$_{2x}$Cu$_{2(1-x)}$ZnSnS$_{4}$ and Ag$_{2x}$Cu$_{2(1-x)}$ZnSnS$_{4}$ make them beneficial for achieving band-gap-graded solar cells.
 Select Measurement of Zeeman Shift of Cesium Atoms Using an Optical Nanofiber Chuan-Biao Zhang, Dian-Qiang Su, Zhong-Hua Ji, Yan-Ting Zhao, Lian-Tuan Xiao, Suo-Tang Jia Chin. Phys. Lett.    2018, 35 (8): .   DOI: 10.1088/0256-307X/35/8/083201 Abstract   HTML   PDF (973KB) Nanofibers have many promising applications because of their advantages of high power density and ultralow saturated light intensity. We present here a Zeeman shift of the Doppler-broadened cesium D$_2$ transition using a tapered optical nanofiber in the presence of a magnetic field. When a weak magnetic field is parallel to the propagating light in the nanofiber, the Zeeman shift rates for different circularly polarized spectra are observed. For the $\sigma^{+}$ component, the typical linear Zeeman shift rates of $F=3$ and $F=4$ ground-state cesium atoms are measured to be 3.10($\pm$0.19) MHz/G and 3.91($\pm$0.16) MHz/G. For the $\sigma^{-}$ component, the values are measured to be $-$2.81($\pm$0.25) MHz/G, and $-$0.78($\pm$0.28) MHz/G. The Zeeman shift using the tapered nanofiber can help to develop magnetometers to measure the magnetic field at the narrow local region and the dispersive signal to lock laser frequency.
 Select Influence on the Lifetime of $^{87}$Rb Bose–Einstein Condensation for Far-Detuning Single-Frequency Lasers with Different Phase Noises Peng Peng, Liang-hui Huang, Dong-hao Li, Peng-jun Wang, Zeng-ming Meng, Jing Zhang Chin. Phys. Lett.    2018, 35 (6): .   DOI: 10.1088/0256-307X/35/6/063201 Abstract   HTML   PDF (656KB) We study the influence of the phase noises of far detuning single frequency lasers on the lifetime of Bose–Einstein condensation (BEC) of $^{87}$Rb in an optical dipole trap. As a comparison, we shine a continuous-wave single-frequency Ti:sapphire laser, an external-cavity diode laser and a phase-locked diode laser on BEC. We measure the heating and lifetime of BEC in two different hyperfine states: $|F=2,m_{F}=2\rangle$ and $|F=1,m_{F}=1\rangle$. Due to the narrow linewidth and small phase noise, the continuous-wave single-frequency Ti:sapphire laser has less influence on the lifetime of $^{87}$Rb BEC than the external-cavity diode laser. To reduce the phase noise of the external-cavity diode laser, we use an optical phase-locked loop for the external-cavity diode laser to be locked on a Ti:sapphire laser. The lifetime of BEC is increased when applying the phase-locked diode laser in contrast with the external-cavity diode laser.
 Select Multi-Electron Effects in Attosecond Transient Absorption of CO Molecules Bin Zhang, Jian Zhao, Zeng-Xiu Zhao Chin. Phys. Lett.    2018, 35 (4): .   DOI: 10.1088/0256-307X/35/4/043201 Abstract   HTML   PDF (600KB) Using the fully propagated time-dependent Hartree–Fock method, we identify that both the dynamic core polarization and multiorbital contributions are important in the attosecond transient absorption of CO molecules. The dynamics of core electrons effectively modifies the behaviors of electrons in the highest occupied molecular orbital, resulting in the modulation of intensity and position of the absorption peaks. Depending on the alignment angles, different inner orbitals are identified to contribute, and even dominate the total absorption spectra. As a result, multi-electron fingerprints are encoded in the absorption spectra, which shed light on future applications of attosecond transient absorption in complex systems.
 Select Kramers–Henneberger Form of Strong Field Theory with the Correction of Dipole Approximation Yi-Ning Huo, Jian Li, Feng-Cai Ma Chin. Phys. Lett.    2018, 35 (4): .   DOI: 10.1088/0256-307X/35/4/043202 Abstract   HTML   PDF (649KB) We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined as the photoelectron longitudinal momentum distributions (PLMD), in tunneling regime ($\gamma_{\rm K}\ll 1$), based on the strong field approximation theory. The nondipole Hamiltonian for photoelectrons interacting with laser fields from a hydrogen-like atom is transformed into the Kramers–Henneberger frame in our model. To introduce the correction of dipole approximation, the spatial variable is kept in a vector potential ${\boldsymbol A}({\boldsymbol r},t)$, demonstrating that the breakdown of dipole approximation is the major reason for the shift of the peak in PLMD. The nondipole effects are apparent when circularly polarized lasers are adopted to ionize the atoms, and clear tendency to increase offsets is found for increasing laser intensities.
 Select Experimental Determination of the Landé $g$-Factors for 5$s^{2}$$^{1}\!S and 5s5p$$^{3}\!P$ States of the $^{87}$Sr Atom Ben-quan Lu, Yebing Wang, Yang Guo, Qinfang Xu, Mojuan Yin, Jiguang Li, Hong Chang Chin. Phys. Lett.    2018, 35 (4): .   DOI: 10.1088/0256-307X/35/4/043203 Abstract   HTML   PDF (733KB) We present an experimental determination on the Landé $g$-factors for the 5$s^{2}$ $^{1}\!S_{0}$ and $5s5p$ $^{3}\!P_{0}$ states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the $^{87}$Sr optical lattice clock. The Zeeman shift of the $5s5p$ $^{3}\!P_{0}$–5$s^{2}$ $^{1}\!S_{0}$ forbidden transition is measured with the $\pi$-polarized and $\sigma^{\pm}$-polarized interrogations at different magnetic field strengths. Moreover, in the $g$-factor measurement with the $\sigma^{\pm}$-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5$s^{2}$ $^{1}\!S_{0}$ $g$-factor for the $^{87}$Sr atom is $-1.306(52)\times10^{-4}$, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential $g$-factor $\delta g$ between the $5s5p$ $^{3}\!P_{0}$ state and the 5$s^{2}$ $^{1}\!S_{0}$ state of the $^{87}$Sr atoms is measured in the experiment as well, which are $-7.67(36)\times10^{-5}$ with $\pi$-transition spectra and $-7.72(43)\times10^{-5}$ with $\sigma^{\pm}$-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential $g$-factor of the clock states for the optical clocks based on other atoms.
 Select Experimental Observation of Spin-Exchange in Ultracold Fermi Gases Peng Peng, Liang-Hui Huang, Dong-Hao Li, Zeng-Ming Meng, Peng-Jun Wang, Jing Zhang Chin. Phys. Lett.    2018, 35 (3): .   DOI: 10.1088/0256-307X/35/3/033401 Abstract   HTML   PDF (1233KB) We experimentally study the spin exchange collision in ultracold $^{40}$K Fermi gases. The quadratic Zeeman shift, trap potential and temperature of atomic cloud will influence on the spin changing dynamics. Dependences of the spin components populations on the external bias magnetic field, the optical trap depth and the temperature of atomic cloud are experimentally investigated. The spin exchange from the initial states to the final state are observed for different initial states. This work shows an interesting process of reaching equilibrium by redistribution among the spin states with the spin exchange collision in an ultracold large-spin Fermi gas.
 Select Enhanced Loading of $^{40}$K from Natural Abundance Potassium Source with a High Performance 2D$^{+}$ MOT Jiang-Ling Yang, Yun Long, Wei-Wei Gao, Lan Jin, Zhan-Chun Zuo, Ru-Quan Wang Chin. Phys. Lett.    2018, 35 (3): .   DOI: 10.1088/0256-307X/35/3/033701 Abstract   HTML   PDF (477KB) $^{40}$K is one of the most important atomic species for ultra-cold atomic physics. Due to the extremely low concentration (0.012%) of $^{40}$K in natural abundance of potassium, most experiments use 4–10% enriched potassium source, which have greatly suffered from the extremely low annual production and significant price hikes in recent years. Using naturally abundant potassium source, we capture $5.4\times10^{6}$ cold $^{40}$K atoms with the help of a high performance of two-dimensional magneto-optical trap (2D$^{+}$ MOT), which is almost three orders of magnitude greater than previous results without the 2D$^{+}$ MOT. The number of the $^{40}$K atoms is sufficient for most ultra-cold $^{40}$K experiments, and our approach provides an ideal alternative for the field.
 Select Ab Initio Studies of Radicals HB$X$ ($X$=H, F, Cl, Br): Molecular Structure, Vibrational Frequencies and Potential Energy Qi-Xin Liu, Min Liang, Quan Miao, Jin-Juan Zhang, Er-Ping Sun, Ting-Qi Ren Chin. Phys. Lett.    2018, 35 (1): .   DOI: 10.1088/0256-307X/35/1/013101 Abstract   HTML   PDF (635KB) We describe high-level ab initio calculations on the BH$_{2}$, HBF, HBCl and HBBr radicals. Molecular structure, vibrational frequencies and potential energy curves of the ground state and the first excited state, which are two Renner–Teller components for a $^2{\it \Pi}$ state at linearity, are studied using the basis sets aug-cc-pVTZ and icMRCI+Q technique. On the basis of the potential energy curves, a reliable potential energy barrier to dissociation HB+$X$ ($X$=F, Cl, Br) fragments and to linearity are given. The ab initio results will add some understanding on the spectrum and the photo-dissociation dynamics of the series of radicals.
 Select Nonadiabatic Population Transfer in a Tangent-Pulse Driven Quantum Model Guang Yang, Wei Li, Li-Xiang Cen Chin. Phys. Lett.    2018, 35 (1): .   DOI: 10.1088/0256-307X/35/1/013201 Abstract   HTML   PDF (455KB) Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangent-pulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.
 Select Width-Dependent Optical Properties for Zigzag-Edge Silicene Nanoribbons Hai-Rui Bao, Wen-Hu Liao, Xin-Cheng Zhang, Min Zuo Chin. Phys. Lett.    2018, 35 (1): .   DOI: 10.1088/0256-307X/35/1/013301 Abstract   HTML   PDF (542KB) We study theoretically the optical response for perfect zigzag-edge silicene nanoribbons with $N$ silicon atoms of the A and B sublattices ($N$-ZSiNRs) under the irradiation of an external electromagnetic field at low temperatures. The 8- and 16-ZSiNRs are demonstrated to exhibit a broad energy regime of absorption coefficient, refractive index, extinction coefficient, and reflectivity from infrared to ultraviolet, utilizing the dipole-transition theorem for semiconductors. The optical spectra for 8- and 16-ZSiNRs may be classified into two types of the transitions, one between valence and conduction subbands with the same parity, and the other among the edge state and bulk state subbands. With the increase of the ribbon width, the optical spectra for ZSiNRs are proved to exhibit red shift and blue shift at the lower and higher energy regimes, respectively. The obtained novel features are believed to be of significance in designs of silicene-based optoelectronic devices.
 Select Probe Knots and Hopf Insulators with Ultracold Atoms Dong-Ling Deng, Sheng-Tao Wang, Kai Sun, L.-M. Duan Chin. Phys. Lett.    2018, 35 (1): 013701.   DOI: 10.1088/0256-307X/35/1/013701 Abstract   HTML   PDF (1726KB) Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.
 Select An Isotropic Empirical Intermolecular Potential for Solid H$_{2}$ and D$_{2}$: A Classical Molecular Calculation Li Yang , Hui Liu, Hui-Ling Zhou, Qing-Qiang Sun, Shu-Ming Peng, Xing-Gui Long, Xiao-Song Zhou, Xiao-Tao Zu, Fei Gao Chin. Phys. Lett.    2017, 34 (12): .   DOI: 10.1088/0256-307X/34/12/123401 Abstract   HTML   PDF (1198KB) We develop an isotropic empirical potential for molecular hydrogen (H$_{2}$) and deuterium (D$_{2}$) by fitting to solid-state data, which is appropriate for classical molecular dynamics (CMD) approach. Based on the prior isotropic intermolecular potential used in self-consistent phonon approximation, a zero-point energy term and an embedded energy term are introduced to describe the H$_{2}$–H$_{2}$ and D$_{2}$–D$_{2}$ interactions in CMD simulations. The structure, cohesive energy and elastic properties of solid H$_{2}$ (D$_{2})$ are used as the fitting database. The present method is tested by calculating the melting point of solid H$_{2}$, and the pressure and bulk elastic modulus as a function of volume. The developed potentials well reproduce many properties of solid H$_{2}$ and D$_{2}$.
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