# Generation and stabilization of entangled coherent states for the vibrational modes of a trapped ion

## TL;DR

This paper presents a scheme to generate and stabilize entangled coherent states of vibrational modes in a trapped ion system using laser-driven interactions and spontaneous emission, enabling steady-state entanglement.

## Contribution

It introduces a novel method for preparing steady-state entangled coherent states of ion vibrational modes via laser control and dissipation effects.

## Key findings

- Steady two-mode cat states can be achieved for two-dimensional ion vibrations.
- The scheme can be extended to three vibrational modes in a 3D trap.
- The method leverages competition between unitary dynamics and spontaneous emission.

## Abstract

We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.