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