Monitoring Electron-Photon Dressing in WSe₂

Optical pumping of solids creates a nonequilibrium electronic structure where electrons and photons combine to form quasiparticles of dressed electronic states. The resulting shift of electronic levels is known as the optical Stark effect, visible as a red shift in the optical spectrum. Here we show that in a pump-probe setup we can uniquely define a nonequilibrium quasiparticle bandstructure that can be directly measurable with photoelectron spectroscopy. The dynamical photon-dressing (and undressing) of the many-body electronic states can be monitored by pump-probe time and angular-resolved photoelectron spectroscopy (tr-ARPES) as the photon-dressed bandstructure evolves in time depending on the pump-probe pulse overlap. The computed tr-ARPES spectrum agrees perfectly with the quasi-energy spectrum of Floquet theory at maximum overlap and goes to the equilibrium bandstructure as the pump-probe overlap goes to zero. Additionally, we show how this time-dependent nonequilibrium quasiparticle structure can be understood to be the bandstructure underlying the optical Stark effect. The extension to spin-resolved ARPES can be used to predict asymmetric dichroic response linked to the valley selective optical excitations in monolayer transition metal dichalcogenides (TMDs). These results establish the photon dressed nonequilibrium bandstructures as the underlying quasiparticle structure of light-driven steady-state quantum phases of matter.