Experimental observation of Floquet spectral sum rule

Time-periodic light-field can dress electronic states in quantum materials, resulting in hybrid states such as Floquet states. While the occupation of light-field dressed states is a fundamental quantity in determining the transient electronic and transport properties, so far there is limited information on the transient occupation of such hybrid states. In this talk, I will present our progress on revealing the occupation of light-field dressed states in black phosphorus and MoSe2 by TrARPES. In particular, we discovered an interesting spectral sum rule: while the intensity of each light-induced sideband strongly depends on the pump strength and light polarization, the Floquet spectral weight is conserved upon below-gap pumping. I will also discuss the conditions under which this robust Floquet spectral sum rule is violated. Our work reveals the occupation of light-field dressed states and establishes experimental conditions for the Floquet spectral sum rule, providing some insights for the light-induced ultrafast transport and opto-electronic properties of light-field dressed quantum materials.