# Nonclassical and semiclassical para-Bose states

## TL;DR

This paper introduces a new basis for para-Bose states suitable for trapped-ion quantum simulations, revealing their nonclassical and semiclassical properties and how these can be controlled via system parameters.

## Contribution

It presents an overcomplete, nonorthogonal basis for para-Bose Hilbert spaces and demonstrates how these states can be realized and manipulated in trapped-ion experiments.

## Key findings

- States exhibit nonclassical and semiclassical statistics
- Asymmetric field quadrature variances observed
- Properties controllable by para-Bose order and evolution time

## Abstract

Motivated by the proposal to simulate para-Bose oscillators in a trapped-ion setup [C. Huerta Alderete and B. M. Rodr\'iguez-Lara, Phys. Rev. A 95, 013820 (2017)], we introduce an overcomplete, nonorthogonal basis for para-Bose Hilbert spaces. The states spanning these bases can be experimentally realized in the trapped-ion simulation via time evolution. The para-Bose states show both nonclassical and semiclassical statistics on their Fock state distribution, asymmetric field quadrature variances, and do not minimize the uncertainty relation for the field quadratures. These properties are analytically controlled by the para-Bose order and the evolution time; both parameters might be feasible for fine tuning in the trapped-ion quantum simulation.