Generation of Two-Flavor Vortex Atom Laser from a Five-State Medium

Two-flavor atom laser in a vortex state is obtained and analyzed via electromagnetically induced transparency (EIT) technique in a five-level $M$ type system by using two probe lights with $\pm z$-directional orbital angular momentum $\pm l\hbar$, respectively. Together with the original transfer technique of quantum states from light to matter waves, the present result can be extended to generate continuous two-flavor vortex atom laser with non-classical atoms.Comment: 5 pages, 1 figure; The previous version (v2) is a wrong one; this is the published versio

On the connectedness of planar self-affine sets

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected. Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively collinear.Comment: 18 pages; 18 figure