Understanding Phonon-Induced Decoherence in Trapped Ion Floquet Simulations

Quantum systems under Floquet (periodic) drive allow for engineering non-trivial Hamiltonians and investigating non-equilibrium many-body dynamics. The controllable inter-ion spin coupling makes trapped-ion systems an ideal platform to study Floquet dynamics. Trapped-ion spins are typically controlled by Raman transitions mediated by off-resonant phonons. Here, we numerically and experimentally investigate unwanted phonon excitations during Floquet dynamics, whose evolution can leave the spin Hilbert space and manifest as a source of decoherence for the intended Hamiltonian. Understanding phonon-induced decoherence is essential for establishing trust in quantum simulators where the evolution is otherwise intractable.