# Symplectic tomography of nonlinear coherent states of a trapped ion

## TL;DR

This paper explores the use of symplectic tomography to reconstruct the quantum states of a trapped ion, focusing on nonlinear coherent states and their quadrature distributions.

## Contribution

It introduces a method to explicitly express density matrices of nonlinear coherent states of a trapped ion via symplectic tomography.

## Key findings

- Derived marginal distributions for squeezed and correlated states.
- Expressed density matrices explicitly in terms of marginal distributions.
- Demonstrated the applicability of symplectic tomography to nonlinear coherent states.

## Abstract

Squeezed and rotated quadrature of an ion in a Paul trap is discussed in connection with reconstructing its quantum state using symplectic-tomography method. Marginal distributions of the quadrature for squeezed and correlated states and for nonlinear coherent states of a trapped ion are obtained and the density matrices in the Fock basis are expressed explicitly in terms of these marginal distributions.