Synthetic spin-orbit (SO) coupling, an important ingredient for quantum simulation of many exotic condensed matter physics, has recently attracted considerable attention. The static and dynamic properties of a SO coupled Bose-Einstein condensate (BEC
) have been extensively studied in both theory and experiment. Here we numerically investigate the generation and propagation of a textit{dynamical} spin-density wave (SDW) in a SO coupled BEC using a fast moving Gaussian-shaped barrier. We find that the SDW wavelength is sensitive to the barriers velocity while varies slightly with the barriers peak potential or width. We qualitatively explain the generation of SDW by considering a rectangular barrier in a one dimensional system. Our results may motivate future experimental and theoretical investigations of rich dynamics in the SO coupled BEC induced by a moving barrier.
We show that Bogoliubovs quasiparticle in superfluid $^3He-B$ undergoes the Zitterbewegung, as a free relativistic Diracs electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of th
e Diracs electron. In particular, the Zitterbewegung of Bogoliubovs quasiparticle has a frequency approximately $10^5$ lower than that of an electron, rendering a more promising experimental observation.
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mas
s. They have the symmetries which are similar to the corresponding ones, and can be solved by using the algebraic method.
The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding
systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(dot{r}=0)$.
We investigate the orientation dependence of molecular high-order harmonic generation (HHG) both numerically and analytically. We show that the molecular recollision electronic wave packets (REWPs) in the HHG are closely related to the ionization pot
ential as well as the particular orbital from which it ionized. As a result, the spectral amplitude of the molecular REWP can be significantly different from its reference atom (i.e., with the same ionization potential as the molecule under study) in some energy regions due to the interference between the atomic cores of the molecules. This finding is important for molecular orbital tomography using HHG[Nature textbf{432}, 867(2004)].
