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<jats:p>Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer (i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér–Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference (i.e., the <jats:inline-formula> <jats:tex-math><?CDATA ${\hat{J}}_{z}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mover accent="true"> <mml:mi>J</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> <mml:mi>z</mml:mi> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_120303_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the <jats:inline-formula> <jats:tex-math><?CDATA ${\hat{J}}_{z}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mover accent="true"> <mml:mi>J</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> <mml:mi>z</mml:mi> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_120303_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.</jats:p>

<jats:p>We propose a family of Hardy-type tests for an arbitrary <jats:italic>n</jats:italic>-partite system, which can detect different degrees of non-locality ranging from standard to genuine multipartite non-locality. For any non-signaling <jats:italic>m</jats:italic>-local hidden variable model, the corresponding tests fail, whereas a pass of this type of test indicates that this state is <jats:italic>m</jats:italic> non-local. We show that any entangled generalized GHZ state exhibits Hardy’s non-locality for each rank of multipartite non-locality. Furthermore, for the detection of <jats:italic>m</jats:italic> non-localities, a family of Bell-type inequalities based on our test is constructed. Numerical results show that it is more efficient than the inequalities proposed in [<jats:italic>Phys. Rev. A</jats:italic> <jats:bold>94</jats:bold> 022110 (2016)].</jats:p>

<jats:p>We investigate the teleportation of an entangled state via a couple of quantum channels, which are composed of a spin-1/2 Heisenberg dimer in two infinite Ising–Heisenberg chains. The heterotrimetallic coordination polymer Cu<jats:sup>II</jats:sup>Mn<jats:sup>II</jats:sup>(L<jats:sup>1</jats:sup>)][Fe<jats:sup>III</jats:sup>(bpb)(CN)<jats:sub>2</jats:sub>]·ClO<jats:sub>4</jats:sub> · H<jats:sub>2</jats:sub>O (abbreviated as Fe–Mn–Cu) can be regarded as an actual material for this chain. We apply the transfer-matrix approach to obtain the density operator for the Heisenberg dimer and use the standard teleportation protocol to derive the analytical expression of the density matrix of the output state and the average fidelity of the entanglement teleportation. We study the effects of the temperature <jats:italic>T</jats:italic>, anisotropy coupling parameter <jats:italic>Δ</jats:italic>, Heisenberg coupling parameter <jats:italic>J</jats:italic> <jats:sub>2</jats:sub> and external magnetic field <jats:italic>h</jats:italic> on the quantum channels. The results show that anisotropy coupling <jats:italic>Δ</jats:italic> and Heisenberg coupling <jats:italic>J</jats:italic> <jats:sub>2</jats:sub> can favor the generation of the output concurrence and expand the scope of the successful average fidelity.</jats:p>

<jats:p>The Landau damping which reveals the characteristic of relaxation dynamics for an equilibrium state is a universal concept in the area of complex system. In this paper, we study the Landau damping in the phase oscillator system by considering two types of coupling heterogeneity in the Kuramoto model. We show that the critical coupling strength for phase transition, which can be obtained analytically through the balanced integral equation, has the same formula for both cases. The Landau damping effects are further explained in the framework of Laplace transform, where the order parameters decay to zero in the long time limit.</jats:p>

<jats:p>Dynamics of the Au + H<jats:sub>2</jats:sub> reaction are studied using time-dependent wave packet (TDWP) and quasi-classical trajectory (QCT) methods based on a new potential energy surface [<jats:italic>Int. J. Quantum Chem.</jats:italic> <jats:bold>118</jats:bold> e25493 (2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available. The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.</jats:p>

<jats:p>We propose a simple pump-coupling-seed scheme to examine the optical <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{\Sigma }_{{\rm{g}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">X</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">g</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>–A<jats:sup>2</jats:sup>Π<jats:sub>u</jats:sub> coupling in <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{N}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn6.gif" xlink:type="simple" /> </jats:inline-formula> lasing. We produce the <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{N}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn7.gif" xlink:type="simple" /> </jats:inline-formula> lasing at 391 nm, corresponding to the <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{B}}}^{2}{\Sigma }_{{\rm{u}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">B</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">u</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn8.gif" xlink:type="simple" /> </jats:inline-formula>(<jats:italic>v</jats:italic>′ = 0)–<jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{\Sigma }_{{\rm{g}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">X</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">g</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn9.gif" xlink:type="simple" /> </jats:inline-formula>(<jats:italic>v</jats:italic> = 0) transition, by externally seeding the <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{N}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn10.gif" xlink:type="simple" /> </jats:inline-formula> gain medium prepared by irradiation of N<jats:sub>2</jats:sub> with an intense pump pulse. We then adopt a weak coupling pulse in between the pump and seed pulses, and show that the intensity of the 391-nm lasing can be efficiently modulated by varying the polarization direction of the coupling pulse with respect to that of the pump pulse. It is found that when the polarization directions of the pump and coupling pulses are perpendicular, the 391-nm lasing intensity is more sensitive to the coupling laser energy, which reflects the inherent nature of the perpendicular <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{\Sigma }_{{\rm{g}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">X</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">g</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_12_123301_ieqn11.gif" xlink:type="simple" /> </jats:inline-formula>–A<jats:sup>2</jats:sup>Π<jats:sub>u</jats:sub> transition.</jats:p>

<jats:p>We review the recently improved quantitative rescattering theory for nonsequential double ionization, in which the lowering of threshold due to the presence of electric field at the time of recollision has been taken into account. First, we present the basic theoretical tools which are used in the numerical simulations, especially the quantum theories for elastic scattering of electron as well as the processes of electron impact excitation and electron impact ionization. Then, after a brief discussion about the properties of the returning electron wave packet, we provide the numerical procedures for the simulations of the total double ionization yield, the double-to-single ionization ratio, and the correlated two-electron momentum distribution.</jats:p>

<jats:p>In the framework of the Thomas–Fermi (TF) approach, a model for the p-type double-<jats:italic>δ</jats:italic>-doped (DDD) system in GaAs is presented. This model, unlike other works in the literature, takes into account that the Poisson equation associated with the system is nonlinear. The electronic structure is calculated for heavy and light holes. The changes in the electronic structure result of the distance <jats:italic>d</jats:italic> between the doped layers are studied. In particular, the relative absorption coefficient as well as the relative refractive index change is calculated as a function of the incident photon energy for heavy holes. The effect of the interlayer distance exhibits, in the absorption coefficient, a red shift of the peak position and a decrease in amplitude when the distance increases. In addition, the relative refractive index change node has a red shift as well as the interlayer distance increases. The calculations show that the effect of the separation between layers has a greater influence on the linear terms. These results are very important for theoretical calculations and engineering of optical and electronic devices based in <jats:italic>δ</jats:italic>-doped GaAs.</jats:p>

<jats:p>A switchable autostereoscopic 3-dimensional (3D) display device with wide color gamut is introduced in this paper. In conjunction with a novel directional quantum-dot (QD) backlight, the precise scanning control strategy, and the eye-tracking system, this spatial-sequential solution enables our autostereoscopic display to combine all the advantages of full resolution, wide color gamut, low crosstalk, and switchable 2D/3D. And also, we fabricated an autostereoscopic display prototype and demonstrated its performances effectively. The results indicate that our system can both break the limitation of viewing position and provide high-quality 3D images. We present two working modes in this system. In the spatial-sequential mode, the crosstalk is about 6%. In the time-multiplexed mode, the viewer should wear auxiliary and the crosstalk is about 1%, just next to that of a commercial 3D display (BENQ XL2707-B and View Sonic VX2268WM). Additionally, our system is also completely compatible with active shutter glasses and its 3D resolution is same as its 2D resolution. Because of the excellent properties of the QD material, the color gamut can be widely extended to 77.98% according to the ITU-R recommendation BT.2020 (Rec.2020).</jats:p>

<jats:p>We theoretically construct a rectangular phononic crystal (PC) structure surrounded by water with <jats:italic>C</jats:italic> <jats:sub>2<jats:italic>v</jats:italic> </jats:sub> symmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms: the vertical type, in which the distance <jats:italic>s</jats:italic> between the center of the scatterer and its right-angle point is greater than 0.5<jats:italic>a</jats:italic>, and the transverse type, in which <jats:italic>s</jats:italic> is smaller than 0.5<jats:italic>a</jats:italic> (where <jats:italic>a</jats:italic> is the crystal constant in the <jats:italic>x</jats:italic> direction). Each rectangular scatterer has three variables: length <jats:italic>L</jats:italic>, width <jats:italic>D</jats:italic>, and rotation angle <jats:italic>θ</jats:italic> around its centroid. We find that, when <jats:italic>L</jats:italic> and <jats:italic>D</jats:italic> change and <jats:italic>θ</jats:italic> is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary <jats:italic>θ</jats:italic> and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.</jats:p>