Phase Noise and the Stability of Floquet-Engineered Quantum States

Floquet engineering—the control of quantum materials through periodic driving—offers a versatile pathway to realizing non-equilibrium phases such as light-induced superconductivity, tunable magnetism, and topological transitions. However, the role of environmental noise, particularly fluctuations in the driving field, remains poorly understood and poses a major challenge for experimental realization. In this work, we investigate how phase noise in time-periodic drives influences the stability of Floquet-engineered states. Using a combination of model Hamiltonians and ab initio real-time simulations, we analyze how such noise alters non-equilibrium electronic structure. As a representative case, we examine photo-driven graphene to illustrate how both resonant and off-resonant gap openings and edge-state topology evolve under noisy driving conditions. Our results reveal characteristic signatures of phase-noise-induced spectral broadening, and allow us to both quantify and build intuition for the robustness of Floquet phases and their associated nontrivial topological states. We conclude by discussing implications of this work for a broad range of emerging platforms, especially those where bosonic modes, like excitons or cavity photons, are used to drive Floquet effects.