Flattening Floquet spectra of periodically driven quantum systems

Controlling the energy dispersion of quantum systems has many applications, ranging from enhancing dephasing times in qubit systems to realizing novel many-body phenomena. In this regard, obtaining a dispersionless spectrum is of special interest. So far, most conventional approaches have studied flat dispersion relations on a case-by-case basis. Here we will discuss how to use periodic drives to systematically flatten the quasi-energy spectrum of a given system. For the special case of systems with chiral symmetry, we show that exact flattening can be achieved by means of periodic kicks. We conclude with two case studies: first, we illustrate how the bulk energy bands of Majorana wires can be flattened without destroying their topology, opening the possibility for enhanced interaction and disorder effects in these systems;  second, we find that spectral flattening can help reduce the dephasing rate of superconducting qubits due to charge or flux noise.