Few-femtosecond Limit of the Floquet Theory

The use of periodic light fields to induce new characteristics and functionalities in advanced materials is a remarkable example of how optical control of matter enables unforeseen developments. This recent field of research, named “Floquet engineering”, holds the potential to surpass the current paradigm and foster the opto-electronics and photonics of the future [1]. For example, the combination of Floquet engineering with short pulses can pave the way for the realization of ultrafast quantum switches of new concept and capable to operate with unprecedented speed. Despite the fascinating and important implications, the applicability of Floquet concepts to short light pulses is still highly debated since the Floquet formalism is strictly valid only for perfectly periodic (monochromatic) light [2]. Moreover, the shorter the light pulse, the less periodic it is and the more important the pulse envelope becomes. Therefore, so far, Floquet engineering has been based only on relatively long pulses (hundreds of femtoseconds), thus hindering the investigation of the ultimate speed limit at which the exotic properties of a quantum material can be manipulated with light.