Tunable light sources with sub-femtosecond to picosecond laser pulses offer intriguing opportunities in ultrafast materials science. Contrary to femtochemistry, where chemical processes are watched in real time, the difference is that in solids photodressing changes not only the state of the system, but even affects its effective Hamiltonian. This is due to the much smaller energy scales that govern collective modes in solids vis-a-vis large binding energies in small molecules.

Here we show how this photodressing tool to engineer Hamiltonians can be monitored.

In this paper we demonstrate how the photo-dressing of electrons in a solid leads to a rich non-equilibrium bandstructure and how the formation of quasiparticle bands of the combined photon-electron states can be directly observed in td-ARPES measurements.

We simulate the pump-probe photoemission process and angle reosolved measurement, as depicted in Fig. 1a, where the pump is a circularly polarized monochromatic pulse that is long enough to drive the electronic structure into a non-equilibrium but stationary state. The probe is typically much shorter but with a higher energy, large enough to ionize electrons from the sample (HH: here a bit more on how photoemission gives the electronic structure). The atomic structure of monolayer WSe\({}_{2}\), which crystalises in with hexagonal symmetry, is depicted in Fig. 1b, along with the Brillouin zone and the path across the \(K\) point that we are considering here. The observed photoelectron spectrum depends strongly on the overlap of the pump and probe pulses as shown in Fig. 1d. When the two pulses do not overlap one only measures the equilibrium bandstructure of WSe\({}_{2}\), but in case of overlapping pulses extra features occur in the spectrum. The non-equilibrium state of the driven monolayer consists of quasiparticles that are a combination of electrons from the material and photons from the driving field, so called photon-dressed electronic states. This dressing of the electronic bands leads to replicas of the equilibrium bands shifted by the photon energy. In case this energy is in resonance with the band gap these bands can hybridize with other equilibrium bands, as schematically shown in Fig. 1c. These dressed bands are directly obeservable in the ARPES spectra of Fig. 1d. When the overlap between pump and probe pulse, we can observe how the dressed bands collapse to the equilibrium bands. This means it is possible to directly observe the creating and destruction of the photon-electron quasiparticle by tuning the pump-prpobe overlap: the real-time dressing and undressing of an electron.