Optical pumping of solids creates a non-equilibrium 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 non-equilibrium quasiparticle bandstructure that can be directly measurable with photo-electron 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 the equilibrium bandstructure as the pump-probe overlap goes to zero. Additionally, we show how this time-dependent non-equilibrium quasiparticle structure can be understood to be the bandstructure underlying the optical Stark effect. The extension to spin-resolved PES can be used to predict asymmetric dichroic response linked to the valley selective optical excitations in monolayer transition metal dichalcogenides (TMDs).
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