Many-body effects on atom-molecule conversion in a Floquet spin-boson model

We investigate the quantum many-body dynamics of ultracold atom-molecule conversion using a Floquet spin-boson model, where the periodic energy detuning between molecules and atomic pairs is utilized to explore various dynamical regimes. We find that the upper bound of the adiabatic driving frequency increases continuously with the strength of molecule-molecule interactions, indicating that many-body interactions are beneficial in meeting the requirement of the adiabatic condition, thereby facilitating the realization of adiabatic atom-molecule conversion. This enhancement of the fulfillment of the adiabatic condition is further evidenced by the stabilization of periodic oscillations in the mean molecule number over time, protected by these interactions, even when the frequency lies within the localized regime. Interestingly, in the diffusive regime, while the many-body interaction has little effect on the dynamical equilibrium of atom-molecule conversion, it significantly expands the diffusive regime. In the high-frequency limit, many-body interactions are found to completely suppress atom-molecule conversion. Our results shed light on how molecule-molecule interactions influence the boundaries between different dynamical regimes.