Bloch - Zener oscillations 3 algebraic
نویسنده
چکیده
Abstract. It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian, a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed.
منابع مشابه
Bloch–Zener Oscillations in Graphene and Topological Insulators
We show that superlattices based on zero-gap semiconductors such as graphene and mercury telluride exhibit characteristic Bloch–Zener oscillations that emerge from the coherent superposition of Bloch oscillations and multiple Zener tunneling between the electron and hole branch. We demonstrate this mechanism by means of wave packet dynamics in various spatially periodically modulated nanoribbon...
متن کاملSurface acoustic BLOCH oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling in a solid.
We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The us...
متن کاملManipulation of matter waves using Bloch and Bloch–Zener oscillations
We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated singleand double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed transport with very little dispersion. The dynamics in the double-periodic system is dominated by Bloch–Zener oscillations, i.e. the interplay of Bloch oscillations a...
متن کاملBloch oscillations and Zener tunneling in two-dimensional photonic lattices.
We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap s...
متن کاملBloch-Zener oscillations across a merging transition of Dirac points.
Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition toward a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling proba...
متن کامل