Fast Ground State to Ground State Separation of Small Ion Crystals

TL;DR

This paper presents a theoretical framework for rapidly separating small ion crystals into subsets, crucial for quantum computing, by describing their quantum evolution through classical equations of motion and designing suitable time-dependent potentials.

Contribution

It introduces a novel theoretical approach using Gaussian state evolution and classical equations to efficiently control ion crystal separation processes.

Findings

Framework accurately describes ion crystal separation dynamics.

Designed potentials enable separation on timescales comparable to Coulomb expansion.

Process can be reversed to recombine ions without energy gain.

Abstract

Rapid separation of linear crystals of trapped ions into different subsets is critical for realizing trapped ion quantum computing architectures where ions are rearranged in trap arrays to achieve all-to-all connectivity between qubits. We introduce a general theoretical framework that can be used to describe the separation of same-species and mixed-species crystals into smaller subsets. The framework relies on an efficient description of the evolution of Gaussian motional states under quadratic Hamiltonians that only requires a special solution of the classical equations of motion of the ions to describe their quantum evolution under the influence of a time-dependent applied potential and the ions' mutual Coulomb repulsion. We provide time-dependent applied potentials suitable for separation of a mixed species three-ion crystal on timescales similar to that of free expansion driven by Coulomb repulsion, with all modes along the crystal axis starting and ending close to their ground states. Three separately-confined mixed species ions can be combined into a crystal held in a single well without energy gain by time-reversal of this separation process.