# Emergence of Bloch oscillations in one-dimensional systems

## TL;DR

This paper investigates how Bloch oscillations emerge in finite one-dimensional systems under electric fields, revealing a transition from current flow to oscillations and proposing an experimental detection method.

## Contribution

It introduces a theoretical analysis of Bloch oscillations in finite systems and suggests a pump-probe scheme for experimental observation.

## Key findings

- Transition from direct current to Bloch oscillations with increasing system size or decreasing field strength.
- Numerical demonstration of Bloch oscillations in a 1D tight-binding model.
- Proposal of a pump-probe measurement scheme to detect oscillations.

## Abstract

Electrons in periodic potentials exhibit oscillatory motion in presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems where the electric field is confined to a finite region, like in typical electronic devices. We use a one-dimensional tight-binding model within the single-band approximation to numerically study the dynamics of electrons after a sudden switching-on of the electric field. We find a transition from a regime with direct current to Bloch oscillations when increasing the system size or decreasing the field strength. We propose a pump-probe scheme to observe the oscillations by measuring the accumulated charge as a function of the pulse-length.