# Generation of quasi-rectangle-states of the vibrational motion of an ion

## TL;DR

This paper presents a method to generate quasi-rectangle vibrational states of an ion using repeated laser interactions and measurements, enabling highly localized quantum states with tunable squeezing.

## Contribution

It introduces a novel approach to produce localized vibrational states of an ion through superpositions of squeezed states with adjustable parameters.

## Key findings

- Successful generation of quasi-rectangle states demonstrated.
- The method allows tuning of the localization via the squeeze parameter.
- States exhibit uniform probability distribution within a specific interval.

## Abstract

We show how to generate quasi-rectangle-states of the vibrational motion of an ion, this is, states that have the same probability in a given position interval. We produce those states by repeated ion-laser interactions followed by conditional measurements that generate a superposition of squeezed states. The squeeze parameter of the initial state may be tuned in order to obtain such highly localized rectangle states.