Relativistic symmetries of Deng Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ^28Si

The interacting boson model with isospin （IBM-3） has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ^28Si nucleus. The theoretical calculations show that the 24^＋ state is the lowest mixed symmetry state in ^28Si and the 43＋ state is also a mixed symmetry state.     

Ground-State Properties of Superfluid Fermi Gas in Fourier-Synthesized Optical Lattices

By employing the balance condition between the lattice potential and the interatomic interaction, we study the ground state solutions of superfluid Fermi gases in Fourier-synthesized （FS） optical lattices. The average energy of the ground state, the atoms number, and the atom density distribution of the Fermi system are analytically derived along the Bose–Einstein condensation （BEC） side to the Bardeen–Cooper–Schrieffer （BCS） side. We analyze the properties of ground state solutions at both the BEC limit and unitarity in FS optical lattices. It is found that the relative phase α between the two lattice harmonics impacts greatly on the properties of the ground state of the superfluid Fermi gas. Especially in the BCS limit, when α=π/2, the average energy presents an exponential form with the increase of the potential depth of the lattice harmonics v2. Meanwhile, there exits a minimal value. Moreover, due to the Fermi pressure, the atom density distribution at unitarity is more outstretched than that in the BEC limit. The average energy at unitarity is apparently larger than that in the BEC limit. The properties of the ground state solution exhibit very different behaviors when the system transits from the BEC side to the BCS side.     

Coherent Destruction of Tunneling of Dipolar Bosonic Gas

The tunneling dynamics of a dipolar bosonic gas with repulsive interactions in a periodically driven triple- well are investigated. Because of the coupled effect of long-range dipole-dipole interaction and the short-range of on-site interaction, the increase of the repulsive atomic interactions can either suppress tunneling or enhance tunneling and, thus, the system experiences rich coherent tunneling（CT）-coherent destruction of tunneling （CDT） transitions. In particular, as the repulsive atomic interactions increase, the system can undergo CT-CDT-CT- CDT or CDT-CT-CDT-CT-CDT transitions. This cannot occur in non-dipolar gas, where the increase of the repulsive atomic interaction only suppress tunneling and the system can only undergo CT-CDT transition. We further present a good understanding of the results with the help of the quasi-energy spectrum of the system.     

Collective Excitation and Quantum Depletion of a Bose-Einstein Condensate in a Periodic Array of Quantum Wells

With the help of a set of exact closed-form solutions to the stationary Gross–Pitaevskii （GP） equation, we calculate the collective excitation and quantum depletion of a weakly interacting Bose gas in the presence of a periodic array of quantum wells. The excitation spectrum （Bogoliubov spectrum） is obtained from the solution of the linearized time-dependent GP equation, which develops energy bands hωj（ p） periodic in quasi-momentum space. Moreover, we calculate the excitation strengths Zj（ p） relative to the density operator and then the dynamic structure factor S（ p,ω）. Accordingly, the analytical expressions of quantum depletion of the system are obtained. We find that the quantum depletion is enhanced when the interatomic interactions become larger and the potential is sufficiently deep. The conditions for the possible experimental realization of our scenario are also proposed.     

Hadronic Scenarios for Gamma-Ray Emission from Three Supernova Remnants Interacting with Molecular Clouds

GeV γ-rays detected with the large area telescope on board the Fermi Gamma-ray space telescope in the direc- tion of HB21, MSH 17-39 and G337.0-0.1 have been recently reported. The three supernova remnants （SNRs） show interactions with molecular clouds, and they are effective gamma-ray emitters as the relativistic protons accelerated by the SNR shocks inelastically colliding with the dense gas in the clouds. The origin of the observed γ-rays for the three remnants is investigated in the scenario of the diffusive shock acceleration. In the model, a part of the SNR shock transmits into the nearby molecular clouds, and the shock velocity is greatly reduced. As a result, a shock with a relatively low Alfven Mach number is generated, and the spectra of the accelerated protons and thee＇γ-ray photons produced via proton-proton interaction can be obtained. The results show that the observed γ-ray spectra for the three SNRs interacting with the molecular clouds can be reproduced. It can be concluded that the hadronic origin of the γ-rays for the three SNRs is approved, and the ability of SNR shocks to accelerate protons is also supported.     

Carrier Envelope Phase Effect of a Long Duration Pulse in the Low Frequency Region

Using the characteristic of small energy difference between two high Rydberg states, we theoretically investigate the carrier envelope phase （CEP） effect in a bound-bound transition of an atom in a low-frequency long laser pulse with tens of optical cycles. Particularly, we first prepare a Rydberg state of a hydrogen-like atom by a laser field with the resonant frequency between this state and the ground state. Then by using a low-frequency long laser pulse interacting with this Rydberg atom, we calculate the population of another Rydberg state nearby this Rydberg state at the end of the laser pulse and find that the population changes dramatically with the CEP of the low-frequency pulse. This CEP effect is attributed to the interference between the positive-frequency and negative-frequency components in one-photon transition. These results may provide a method to measure the CEP value of a long laser pulse with low frequency.     

The Heisenberg Model after an Interaction Quench

In accordance with the recent experimental progress of the controllable spin-spin interactions, the Heisenberg model after an interaction quench is discussed. The Hamiltonian of the system out of equilibrium is introduced and treated by the flow equation method. As a result, the spectrum and zero-point spin deviation are obtained with the help of time-evolved operators. Additionally, other methods are applied to verify the results in mathematics. It is found that the observables show an oscillating behavior. The feasible experimental scheme of the concerned scenario is also mentioned.     

An Exotic Type of Fulde-Ferrel-Larkin-Ovchinnikov States in Spin-Orbit Coupled Condensates

We find for the first time that a model Hamiltonian or s-wave superconductors in tne presence or spm-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, a novel type of Fulde Ferrel-Larkin-Ovchinnikov ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also generalize our exact analysis to the spin-orbit- coupled Bose-Einstein condensate.     

Interactions between Solitons and Cnoidal Periodic Waves of the Gardner Equation

The Gardner equation is one of the most important prototypic models in nonlinear physics. Many scholars pay much attention to the Gardner equation and various nonlinear excitations of the Gardner equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this work, with the help of the Riccati equation, the Gardner equation is solved by the consistent Riccati expansion. Furthermore, we obtain the soliton-cnoidal wave interaction solutions of the Gardner equation.