  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).
