Determination of Multimode Motional Quantum States in a Trapped Ion System
Complex bosonic states play an important role in quantum simulations, quantum computation and spin-boson interactions. While direct readout of multi-mode bosonic states can be challenging, the Jaynes-Cummings type interactions can coherently map the information of bosonic states onto spin states. In our recent paper (Z.Jia et.al., arXiv:2205.11444, collaboration with the MIST lab), we demonstrated a method to determine the Fock state distributions and density matrix of an arbitrary bosonic state, and experimentally verified it using motional modes in a 5-ion chain system. We show the measured Fock state distributions of various complex 2-mode and 3-mode motional states and the reconstructed density matrix of a 2-mode motional Bell state. This study offers a powerful tool for future experiments such as quantum simulations, boson sampling and bosonic error correction.