Phonon Modes χ3 Non-linearity in Ion Chains

Trapped ions are one of the most promising systems suitable for quantum computation. In Coulomb crystals consisting of trapped ions, high-fidelity single-qubit and entangling gates have been demonstrated, and quantum simulations of long-range Ising spin chains have been performed. To generate couplings and create entanglement between different ions, collective vibrational excitations (phonon modes) of the Coulomb crystal are utilized. Due to intrinsic nonlinearity of the Coulomb interaction, there are various types of nonlinear interactions between the phonon modes. They are one of the sources of the gate’s infidelity in the ion chain, and they can also be used to perform quantum nondemolition measurements.