Determination of Multi-mode Motional Quantum States in a Trapped Ion System

TL;DR

This paper introduces a general method to directly determine and reconstruct complex multi-mode motional quantum states in trapped ions, verified experimentally with entangled states, advancing quantum state measurement techniques.

Contribution

The paper presents a novel, general approach for measuring and reconstructing multi-mode motional quantum states in trapped ions, extending capabilities for complex quantum state analysis.

Findings

Successfully reconstructed density matrices of multi-mode states

Verified method with entangled radial modes in a 5-ion chain

Method applicable to systems with Jaynes-Cummings interactions

Abstract

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multi-mode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a 5-ion chain. This method can be extended to any system with Jaynes-Cummings type interactions.