Sympathetic Wigner function tomography of a dark trapped ion

TL;DR

This paper introduces a method for reconstructing the motional quantum state of a dark trapped ion by using a sympathetically coupled bright ion, enabling state measurement without direct optical access.

Contribution

It presents a novel protocol for sympathetic Wigner function tomography of dark ions, utilizing collective modes and sideband excitation for state reconstruction.

Findings

Protocol successfully reconstructs motional states for different mass ratios.

Mapping of dark ion's state onto collective mode is effective.

Scheme enables quantum state measurement without optical transitions.

Abstract

A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This "sympathetic tomography" of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer and read-out are derived, and the accomplishment of the scheme for different mass ratios is evaluated.