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

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