Abstract:
We study the effect of parametric excitations on systems of confined ultracold Bose atoms in periodically modulated optical lattices. In the regime where Mott insulating and Superfluid domains coexist, we show that the dependence of the energy absorbed by the system on the frequency of the modulation serves as an experimental probe for the existence and properties of Mott insulating-Superfluid domains.

Abstract:
The evolution of two-component cold atoms on a ring with spin-orbit coupling has been studied analytically for the case with N noninteracting particles. Then, the effect of interaction is evaluated numerically via a two-body system. Two cases are considered: (i) Starting from a ground state the evolution is induced by a sudden change of the laser field, and (ii) Starting from a superposition state. Oscillating persistent spin-currents have been found. A set of formulae have been derived to describe the period and amplitude of the oscillation. Based on these formulae the oscillation can be well controlled via adjusting the parameters of the laser beams. In particular, it is predicted that movable stripes might emerge on the ring.

Abstract:
The evolution of two-component cold atoms on a ring with quasispin-orbit (qSO) coupling and spin-flip has been studied analytically (for arbitrary particle number $ N $ without interaction) and numerically (for a few-body system with interaction). Counter-propagating and oscillating persistent spin-currents have been found. The regularity governing the period and amplitude of oscillation has been clarified. When the strengths for the qSO coupling and spin-flip are fixed, the frequency of oscillation can be effectively tuned by the Raman detuning, while the amplitude can be tuned by either changing the initial status and/or the Raman detuning. When the initial numbers of atoms of the two-components $N_{1}$ and $N_{2}$ are close to each other, the oscillation will be seriously suppressed. The condition for maximizing the amplitude of oscillation is given.

Abstract:
This study investigates the dynamical response of dark matter (DM) halos to recurrent starbursts in forming less-massive galaxies to solve the core-cusp problem. The gas, which is heated by supernova feedback after a starburst, expands and the star formation then terminates. This expanding gas loses energy by radiative cooling and then falls back toward the galactic center. Subsequently, the starburst is enhanced again. This cycle of expansion and contraction of the interstellar gas leads to a repetitive change in the gravitational potential of the gas. The resonance between DM particles and the density wave excited by the oscillating potential plays a key role in understanding the physical mechanism of the cusp-core transition of DM halos. DM halos effectively gain kinetic energy from the baryon potential through the energy transfer driven by the resonance between the particles and density waves. We determine that the critical condition for the cusp-core transition is such that the oscillation period of the gas potential is approximately the same as the local dynamical time of DM halos. We present the resultant core radius of a DM halo after the cusp-core transition induced by the resonance by using the conventional mass density profile predicted by the cold dark matter models. Moreover, we verify the analytical model by using $N$-body simulations, and the results validate the resonance model.

Abstract:
We demonstrate the possibility of energy-selective removal of cold atoms from a tight optical trap by means of parametric excitation of the trap vibrational modes. Taking advantage of the anharmonicity of the trap potential, we selectively remove the most energetic trapped atoms or excite those at the bottom of the trap by tuning the parametric modulation frequency. This process, which had been previously identified as a possible source of heating, also appears to be a robust way for forcing evaporative cooling in anharmonic traps.

Abstract:
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone (BZ). Furthermore, we introduce two experimental schemes including the spin-resolved Bloch oscillation to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.

Abstract:
The dynamic behaviors of microRNA and mRNA under external stress are studied with biological experiments and mathematics models. In this study, we developed a mathematic model to describe the biological phenomenon and for the first time reported that, as responses to external stress, the expression levels of microRNA and mRNA sustained oscillation. And the period of the oscillation is much shorter than several reported transcriptional regulation negative feedback loop.

Abstract:
We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation (OPG) and amplification (OPA) of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.

Abstract:
We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms, and into the dynamics of driven clouds of cold trapped atoms.

Abstract:
Cold atoms from a magneto-optic trap have been used as a nonlinear medium in a nearly resonant cavity. Squeezing in a probe beam passing through the cavity was demonstrated. The measured noise reduction is 40% for free atoms and 20% for weakly trapped atoms.