Floquet engineering topological many-body localized systems

We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a topologically-protected qubit even at high energies. Floquet engineering - the idea that a periodically driven non-equilibrium system can effectively emulate the physics of a different Hamiltonian - is used to simulate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system emulated topology and disorder coexist which provides an intriguing inroad into the interplay of many-body localization, defying our standard understanding of thermodynamics, and topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology and many-body localization allows one to harvest the advantages (time-dependent control, topological protection and reduction of heating, respectively) of each of these sub-fields while protecting from their disadvantages (heating, static control parameters and strong disorder).