The dissociation pathways of N2+ in intense femtosecond laser fields

Using a neutral N2 beam as target,this paper studies the dissociation of N2+ in intense femtosecond laser fields(45 fs,～1×10 16 W/cm 2) at the laser wavelength of 800 nm based on the time-of-flight mass spectra of N + fragment ions.The angular distributions of N+ and the laser power dependence of N + yielded from different dissociation pathways show that the dissociation mechanisms mainly proceed through the couplings between the metastable states(A,B and C) and the upper excited states of N2+.A coupling model of light-dressed potential energy curves of N+2 is used to interpret the kinetic energy release of N+.     

New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix | ξ ₁ ,ξ ₂ >_C,DC,D< ξ ₁ ,ξ ₂ | is a Radon transform of Wigner operator.     

Quantum Marginal Inequalities and the Conjectured Entropic Inequalities

A conjecture – the modified super-additivity inequality of relative entropy – was proposed in Zhang et al. (Phys. Lett. A 377:1794–1796, 2013): There exist three unitary operators \(U_{A}\in \mathrm {U}(\mathcal {H}_{A}), U_{B}\in \mathrm {U}(\mathcal {H}_{B})\) , and \(U_{AB}\in \mathrm {U}(\mathcal {H}_{A}\otimes \mathcal {H}_{B})\) such that $$\mathrm{S}\left(U_{AB}\rho_{AB}U^{\dagger}_{AB}||\sigma_{AB}\right)\geqslant \mathrm{S}\left(U_{A}\rho_{A}U^{\dagger}_{A}||\sigma_{A}\right) + \mathrm{S}\left(U_{B}\rho_{B}U^{\dagger}_{B}||\sigma_{B}\right), $$ where the reference state σ is required to be full-ranked. A numerical study on the conjectured inequality is conducted in this note. The results obtained indicate that the modified super-additivity inequality of relative entropy seems to hold for all qubit pairs.     

Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time τ1 and τ2 by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. （1） The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate μ decides that the selection is propitious to gene A haploid or gene B haploid. （2） The additive coloured noise intensity and the correlation time τ2 play opposite roles. It is noted that α and τ2 can not separate the single peak, while can make the peak disappear and ~-2 can make the peak be sharp. （3） The multiplicative coloured noise intensity D and the correlation time τ1 can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing D and decreasing τ1.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.     

Copper ion beam emission in solid electrolyte Rb4Cu16I6.5Cl13.5

Copper ion conducting solid electrolyte Rb$_{4}$Cu$_{16}$I$_{6.5}$Cl$_{13.5 }$ was prepared by means of mechano-chemical method. The structure and morphology of the powder was investigated by x-ray diffraction and scanning electron microscopy. The grain size was estimated to be 0.2-0.9 μm and the ionic conductivity at room temperature was approximately 0.206 S/cm. The solid electrolyte Rb$_{4}$Cu$_{16}$I$_{6.5}$Cl$_{13.5 }$ was exploited for copper ion beam generation. The copper ion emission current of several nA was successfully obtained at acceleration voltages of 15 kV and temperature of 197 $^\circ$C in vacuum of 2.1$\times10^{-4}$ Pa. A good linear correlation between the logarithmic ion current $(\log I)$ and the square root of the acceleration voltage ($U_{\rm acc}$) at high voltage range was obtained, suggesting the Schottky emission mechanism in the process of copper ion beam generation.     

Entanglement and Berry Phase in a (3×3)-dimensional Yang-Baxter System

A 9×9 unitary \breveR\breve{R} -matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of \breveR\breve{R} -matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via \breveR\breve{R} -matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary \breveR\breve{R} -matrix. Then the geometric properties of this system is studied. The results showed that the Berry phase of this system can be represented under the framework of SU(2) algebra.     

Entanglement in a generalized Jaynes--Cummings model

We investigate the pairwise entanglement and global entanglement in a generalized Jaynes--Cummings model, which can be used to realize Greenberger--Horne--Zeilinger (GHZ) entangled state (Zheng S B 2001 {\it Phys. Rev. Lett.} {\bf 87} 230404). Our results show that the W-type entangled states cannot be generated based on the model. The dependences of entanglement on Rabi frequency $\lambda$ and dipole--dipole coupling strength ${\it \Omega}$ are given. It is found that there exists the quantum phase transition when $\lambda={\it \Omega}$. For typical experimental data, the critical temperature for pairwise entanglement is on the order of $10^{-6}$\,K. Based on these results, two strategies that overcome decoherence are proposed.     

Analytic solutions for degenerate Raman-coupled model

The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference W, modulus B of the Bloch vector, and entropy E. We find that the time evolutions of these quantities are periodic with a period of π. The maxima of W and B appear at the scaled interaction time points τ- = kπ（k = 0, 1, 2,...）. At these time points, E = 0, which shows that the atom and the field are not entangled. Between these time points, E ≠ 0, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of W is a Gaussian function with a variance of 1/（4n^-）（n^- is the mean number of photons）. Under the envelope, W oscillates at a frequency of n^-/π. When the field is initially in a thermal state, near the maxima, W is a Lorentz function with a width of 1/n^-.     

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average $\pi_{4}$ and geometric average $\varPi_{4}$ is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter $r$ goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter $r$ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy $S_{\text{ABCDI}}$, $S_{\text{ABCIDI}}$, $S_{\text{ABICIDI}}$ and $S_{\text{AIBICIDI}}$ always decrease with the controllable angle $\theta$, while the entropies $S_{3-3~\rm non}$, $S_{3-2~\rm non}$, $S_{3-1~\rm non}$ and $S_{3-0~\rm non}$ first increase with the angle $\theta$ and then decrease with it.     

Mottness,phase string,and high-Tc superconductivity

It is a great discovery in physics of the twentieth century that the elementary particles in nature are dictated by gauge forces, characterized by a nonintegrable phase factor that an elementary particle of charge $q$ acquires from $A$ to $B$ points: $P \exp \left( \text{i} \frac q {\hbar c}\int_A^B A_{\mu}\text{d} x^{\mu}\right),$ where $A_{\mu}$ is the gauge potential and $P$ stands for path ordering. In a many-body system of strongly correlated electrons, if the so-called Mott gap is opened up by interaction, the corresponding Hilbert space will be fundamentally changed. A novel nonintegrable phase factor known as phase-string will appear and replace the conventional Fermi statistics to dictate the low-lying physics. Protected by the Mott gap, which is clearly identified in the high-$T_{\rm c}$ cuprate with a magnitude $> 1.5$ eV, such a singular phase factor can enforce a fractionalization of the electrons, leading to a dual world of exotic elementary particles with a topological gauge structure. A non-Fermi-liquid "parent" state will emerge, in which the gapless Landau quasiparticle is only partially robust around the so-called Fermi arc regions, while the main dynamics are dominated by two types of gapped spinons. Antiferromagnetism, superconductivity, and a Fermi liquid with full Fermi surface can be regarded as the low-temperature instabilities of this new parent state. Both numerics and experiments provide direct evidence for such an emergent physics of the Mottness, which lies in the core of a high-$T_{\rm c}$ superconducting mechanism.     

Entanglement Swapping Transform Rule of Entangled Wigner Operators

For mixed input fields quantum information processing, it is very convenient to investigate a specified protocol by employ quasi-probability functions and characteristic functions in phase space. In this work, considering a nonlocal swapping operation labelled by  $\hat{E}_{s}$ , we derive the entanglement swapping transform rule for entangled Wigner operators. The same rule can be obtained by implementing this nonlocal swapping operation via two entangled pairs channels. And then we apply this rule to examine how does the Wigner function for output states change to demonstrate the entanglement swapping. As a result, this transform rule can be utilized to investigate swapping operation for any two-body entangled system.     

Quantum entanglement and control in a capacitively coupled charge qubit circuit

The macroscopic quantum entanglement in capacitively coupled SQUID (superconducting quantum interference device)-based charge qubits is investigated theoretically. The entanglement characteristic is discussed by employing the quantum Rabi oscillations and the concurrence. An interesting conclusion is obtained, i.e., the magnetic fluxes Ф_x1 and Ф_x2 through the superconducting loops can adjust the entanglement degree between the qubits.     

High-performance coherent population trapping clock based on laser-cooled atoms

We present a coherent population trapping clock system based on laser-cooled $^{87}$Rb atoms. The clock consists of a frequency-stabilized CPT interrogation laser and a cooling laser as well as a compact magneto-optical trap, a high-performance microwave synthesizer, and a signal detection system. The resonance signal in the continuous wave regime exhibits an absorption contrast of $\sim 50$%. In the Ramsey interrogation method, the linewidth of the central fringe is 31.25 Hz. The system achieves fractional frequency stability of ${2.4\times }{{10}}^{{-11}}/\sqrt \tau $, which goes down to ${1.8\times }{{10}}^{{-13}}$ at 20000 s. The results validate that cold atom interrogation can improve the long-term frequency stability of coherent population trapping clocks and holds the potential for developing compact/miniature cold atoms clocks.     

On entanglement invariant for a double Jaynes-Cummings model

In a recent paper [Phys. Rev. A 76 042313 （2007）], Sainz and Bjork introduced an entanglement invariant ε under evolution for a system of four qubits interacting through two isolated Jaynes-Cummings Hamiltonians. This paper proves that this entanglement invariant ε is closely connected with the linear entropy between two independent subsystems.     

Luminescent characteristics of Tm3+/Tb3+/Eu3+ tri-doped Na5Y9F32 single crystals for white emission with high thermal stability

By using an improved Bridgman method, 0.3 mol% Tm$^{3+}/0.6$ mol% Tb$^{3+}/y$ mol% Eu$^{3+}$ ($y = 0$, 0.4, 0.6, 0.8) doped Na$_{5}$Y$_{9}$F$_{32}$ single crystals were prepared. The x-ray diffraction, excitation spectra, emission spectra and fluorescence decay curves were used to explore the crystal structure and optical performance of the obtained samples. When excited by 362 nm light, the cool white emission was realized by Na$_{5}$Y$_{9}$F$_{32}$ single crystal triply-doped with 0.3 mol% Tm$^{3+}/0.6$ mol% Tb$^{3+}/0.8$ mol% Eu$^{3+}$, in which the Commission Internationale de l'Eclairage (CIE) chromaticity coordinate was (0.2995, 0.3298) and the correlated color temperature (CCT) was 6586 K. The integrated normalized emission intensity of the tri-doped single crystal at 448 K could keep 62% of that at 298 K. The internal quantum yield (QY) was calculated to be $\sim 15.16$% by integrating spheres. These results suggested that the single crystals tri-doped with Tm$^{3+}$, Tb$^{3+}$ and Eu$^{3+}$ ions have a promising potential application for white light-emitting diodes (w-LEDs).     

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method (ATMM) is applied to calculating the critical radius $r_{\rm c}$ and the dipole polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen atom and the Hulth\'{e}n potential. We find that there exists a linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$ for a fixed angular quantum number $l$, moreover, the three bounds of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$, $\alpha_{\rm d}^{U}$) satisfy an inequality: $\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.     

Ground state for CH2 and symmetry for methane decomposition

Using the different level of methods B3P86, BLYP, B3PW91, HF, QCISD、 CASSCF （4,4） and MP2 with the various basis functions 6-311G^＊＊, D95, cc-pVTZ and DGDZVP, the calculations of this paper confirm that the ground state is X^-3B1 with C2v group for CH2. Furthermore, the three kinds of theoretical methods, i.e. B3P86、 CCSD（T, MP4） and G2 with the same basis set cc-pVTZ only are used to recalculate the zero-point energy revision which are modified by scaling factor 0.989 for the high level based on the virial theorem, and also with the correction for basis set superposition error. These results are also contrary to X^-3∑^-g for the ground state of CH2 in reference. Based on the atomic and molecular reaction statics, this paper proves that the decomposition type （1） i.e. CH4 →CH2＋H2, is forbidden and the decomposition type （2） i.e. CH4→CHa＋H is allowed for CH4. This is similar to the decomposition of SiH4.