The effects of optically induced non-Abelian gauge field in cold atoms

We show that $N-1$ degenerate dark states can be generated by coupling $N$-fold degenerate ground states and a common excited state with $N$ laser fields. Interferences between light waves with different frequencies can produce laser fields with time-dependent amplitudes, which can induce not only U(N) non-Abelian vector fields but also the scalar ones for the adiabatic motion of atoms in such laser fields. As an example, a time-periodic gauge potential is produced by applying specific laser fields to a tripod system. Some features of the Landau levels and the ground-state phase diagram of a rotating Bose-Einstein condensate for a concrete gauge field are also discussed.Comment: Revtex 6 pages, 2 figures, version to be published in PR

Krylov projection methods for linear Hamiltonian systems

We study geometric properties of Krylov projection methods for large and sparse linear Hamiltonian systems. We consider in particular energy preservation. We discuss the connection to structure preserving model reduction. We illustrate the performance of the methods by applying them to Hamiltonian PDEs.Comment: 16 pages, 17 figure

Stark Effect of Doped Two-Dimensional Transition Metal Dichalcogenides

The band gap of two-dimensional (2D) semiconductors can be efficiently tuned by gate electric field, which is so called the Stark effect. We report that doping, which is essential in realistic devices, will substantially change the Stark effect of few-layer transition metal dichalcogenides in unexpected ways. Particularly in bilayer structures, because of the competition between strong quantum confinement and intrinsic screening length, electron and hole dopings exhibit surprisingly different Stark effects: doped electrons actively screen the external field and result in a nonlinear Stark effect; however, doped holes do not effectively screen the external field, causing a linear Stark effect that is the same as that of undoped materials. Our further analysis shows that this unusual doping effect is not limited within transition metal dichalcogenides but general for 2D structures. Therefore, doping plays a much more crucial role in functional 2D devices and this unusual Stark effect also provides a new degree of freedom to tune band gaps and optical properties of 2D materials.Comment: 12 pages with 4 figure