Blockade of phonon hopping in trapped ions in the presence of multiple local phonons

Driving an ion at a motional sideband transition induces the Jaynes--Cummings (JC) interaction. This JC interaction creates anharmonic ladder of eigenstates, resulting in suppression phonon hopping due to energy conservation. Here, we realize blockade presence multiple local phonons trapped-ion chain. Our work establishes key technological component for quantum simulation with bosonic particles, which can simulate classically intractable problems.