Multimode Motional Quantum State Tomography in a Trapped Ion System

We present a new method to determine an arbitrary motional state of multiple normal modes in a trapped ion chain. We use individual gate operations and state detection on multiple ions to quickly reconstruct the density matrix and Wigner function of a high-dimensional motional state. We apply this method in a room temperature trapped ion system with ¹⁷¹Yb⁺ ions and reconstruct a motional Bell state. The method offers a new approach to study complex motional states.