Multiphoton resonances to high-lying energy levels represent an unavoidable source of Floquet heating in strongly driven quantum systems. In this work, we extend the recently developed two-tone approach of “canceling” multiphoton resonances to shaken lattices in the Hubbard regime. Our experiments show that even for strong lattice shaking, the inclusion of a weak second drive leads to cancellation of multiphoton heating resonances. Surprisingly, the optimal canceling amplitude depends on the Hubbard interaction strength $U$, in qualitative agreement with exact diagonalization calculations. Our results call for novel analytical approaches to capture the physics of strongly driven, strongly interacting many-body systems.

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• Cold gases in optical lattices
• Floquet systems
• Feshbach resonance
• Hubbard model