Wannier-Stark resonances in optical and semiconductor superlattices

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a non-separable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.

We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state problems. We develop the transformation theory mapping the wave equation to LTL and we apply the model to the case of a solid state periodic lattice. We extend the theory with an additional Wannier-Stark term and we show with results the f...

We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark ...

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.

The concept of Wannier-Stark ladders, describing the equally spaced spectrum of a tightly-bound particle in a constant electric field, is generalized to account for arbitrary slowly-varying potentials. It is shown that an abrupt transition exists that separates Wannier-Stark-like from effective-mass-like behavior when the depth of the perturbation becomes equal to the width of the band of extended states. For potentials bounded from below, the spectrum bifurcates above the cr...

The theoretical analysis of the ultrafast energy relaxation and transport phenomena in semiconductor superlattices is reviewed. In particular, we discuss the two equivalent quantum-mechanical pictures of Bloch oscillations and Wannier-Stark localization. A review of simulated experiments and their comparison with available experimental investigations is also provided.

Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most approaches adjust theories for infinite systems, which is acceptable for large but not small number of unit cells $n$. In the past 30 years, a theory based entirely on transfer matrices was developed, where the finiteness of $n$ is an essential condition. The theory of finite periodic systems (TFPS) is also valid for any number of propagating mo...

We analyze the Wannier-Stark spectrum of a quantum particle in tilted two-dimensional lattices with the Bloch spectrum consisting of two subbands, which could be either separated by a finite gap or connected at the Dirac points. For rational orientations of the static field given by an arbitrary superposition of the translation vectors the spectrum is a ladder of energy bands. We obtain asymptotic expressions for the energy bands in the limit of large and weak static fields a...

This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.

The physics of one dimensional optical superlattices with resonant $s$-$p$ orbitals is reexamined in the language of appropriate Wannier functions. It is shown that details of the tight binding model realized in different optical potentials crucially depend on the proper determination of Wannier functions. We discuss the properties of a superlattice model which quasi resonantly couples $s$ and $p$ orbitals and show its relation with different tight binding models used in othe...