Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice

Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant topological metals and to physically realize them. Here we, for the first time, establish a rigorous classification of topological metals that are protected by the PT symmetry using KO-theory. As a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D Brillouin zone is constructed, whose topological stability is revealed through its PT-symmetry-protected nontrivial Z2 topological charge. Based on these exact results, we propose an experimental scheme to realize and to detect tunable PT-invariant topological NL states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent 3D OL and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. Such a realistic cold-atom setup can yield topological NL states, having a tunable ring-shaped band-touching line with the two-fold degeneracy in the bulk spectrum and non-trivial surface states. The states are actually protected by the combined PT symmetry even in the absence of both P and T symmetries, and are characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we demonstrate with numerical simulations that (i) the characteristic NL can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological NL states in cold atom systems may provide a unique experimental platform for exploring exotic PT-invariant topological physics.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.

Transitions To the Long-Resident State in coupled chaotic oscillators

The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits of the two oscillators get close becomes faster with increasing the coupling strength; (3) The diffusion of two oscillator's phase difference is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.Comment: 3 pages, 5 figure

Quantum theory of electronic double-slit diffraction

The phenomena of electron, neutron, atomic and molecular diffraction have been studied by many experiments, and these experiments are explained by some theoretical works. In this paper, we study electronic double-slit diffraction with quantum mechanical approach. We can obtain the results: (1) When the slit width $a$ is in the range of $3\lambda\sim 50\lambda$ we can obtain the obvious diffraction patterns. (2) when the ratio of $\frac{d+a}{a}=n (n=1, 2, 3,\cdot\cdot\cdot)$, order $2n, 3n, 4n,\cdot\cdot\cdot$ are missing in diffraction pattern. (3)When the ratio of $\frac{d+a}{a}\neq n (n=1, 2, 3,\cdot\cdot\cdot)$, there isn't missing order in diffraction pattern. (4) We also find a new quantum mechanics effect that the slit thickness $c$ has a large affect to the electronic diffraction patterns. We think all the predictions in our work can be tested by the electronic double-slit diffraction experiment.Comment: 9pages, 14figure

Total Reaction Cross Section in an Isospin-Dependent Quantum Molecular Dynamics (IDQMD) Model

The isospin-dependent quantum molecular dynamics (IDQMD) model is used to study the total reaction cross section $\sigma_R$. The energy-dependent Pauli volumes of neutrons and protons have been discussed and introduced into the IDQMD calculation to replace the widely used energy-independent Pauli volumes. The modified IDQMD calculation can reproduce the experimental $\sigma_R$ well for both stable and exotic nuclei induced reactions. Comparisons of the calculated $\sigma_R$ induced by $^{11}Li$ with different initial density distributions have been performed. It is shown that the calculation by using the experimentally deduced density distribution with a long tail can fit the experimental excitation function better than that by using the Skyrme-Hartree-Fock calculated density without long tails. It is also found that $\sigma_R$ at high energy is sensitive to the long tail of density distribution.Comment: 4 page, 4 fig

Entanglement in spin-one Heisenberg chains

By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.Comment: 7 pages and 4 figure

Testing the viability of the interacting holographic dark energy model by using combined observational constraints

Using the data coming from the new 182 Gold type Ia supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, and the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey, $H(z)$ and lookback time measurements, we have performed a statistical joint analysis of the interacting holographic dark energy model. Consistent parameter estimations show us that the interacting holographic dark energy model is a viable candidate to explain the observed acceleration of our universe.Comment: 15 pages, 9 figures, accepted for publication in JCA

Wavelength scaling of high-order harmonic yield from an optically prepared excited state atom

Wavelength scaling law for the yield of high-order harmonic emission is theoretically examined for excited state atoms which are optically prepared by simultaneously exposing to an extreme ultraviolet pulse at the resonant wavelength and an infrared pulse at a variable wavelength in the range of 0.8\mum-2.4\mum. Numerical simulations are performed based on the three-dimensional time-dependent Schrodinger equation (3D TDSE) for Ne and H. We confirm that the harmonic yield follows a \lambda^-{4-6} scaling with the single fundamental driving laser pulse; whereas for the optically prepared excited state atoms, a \lambda^-{2-3} scaling for the harmonic yield is revealed.Comment: 20 pages, 3 figure