Determination of Multimode Motional Quantum States in a Trapped Ion System

Zhubing Jia, Ye Wang, Bichen Zhang, Jacob Whitlow, Chao Fang, Jungsang Kim, and Kenneth R. Brown

Phys. Rev. Lett. 129, 103602 – Published 31 August 2022

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 multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

Received 13 June 2022
Revised 12 August 2022
Accepted 15 August 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.103602

Physics Subject Headings (PhySH)

Coherent control Quantum control

Trapped ions

Atom & ion trapping & guiding Jaynes-Cummings model

Atomic, Molecular & Optical

Authors & Affiliations

Zhubing Jia ^1,2,*, Ye Wang ^1,3,†, Bichen Zhang ^1,3,§, Jacob Whitlow^1,3, Chao Fang^1,3, Jungsang Kim^1,2,3,4, and Kenneth R. Brown ^1,2,3,5,‡

¹Duke Quantum Center, Duke University, Durham, North Carolina 27701, USA
²Department of Physics, Duke University, Durham, North Carolina 27708, USA
³Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
⁴IonQ, Inc., College Park, Maryland 20740, USA
⁵Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

^*zhubing.jia@duke.edu
^†wang.ye.phy@gmail.com
^‡ken.brown@duke.edu
^§Present address: Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA.