Preparation of Schr\"odinger cat states with cold ions in a cavity beyond the Lamb-Dicke limit

TL;DR

This paper presents a method for generating Schrödinger cat states with cold trapped ions in a cavity without relying on the Lamb-Dicke approximation, enabling simpler initial state preparation and exact Hamiltonian diagonalization.

Contribution

The authors develop an approach using unitary transformation for exact Hamiltonian diagonalization, bypassing the Lamb-Dicke limit in preparing Schrödinger cat states.

Findings

Schrödinger cat states can be generated from simple initial states

The method avoids the Lamb-Dicke approximation

Exact diagonalization of the Hamiltonian is achieved

Abstract

We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity. We have used an approach for preparing the SC states of motion of ion. This approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke aproximation. We show that is possible to generate a SC states having rather simple initial state preparation, e.g., the vacuum sate for both cavity field and the ion motion.