Coherent excitonic quantum beats in time-resolved photoemission measurements

Coherent excitation of materials via ultrafast laser pulses can have interesting, observable dynamics in time-resolved photoemission measurements. The broad spectral width of ultrafast pump pulses can coherently excite multiple exciton energy levels. When such coherently excited states are probed by means of photoemission spectroscopy, interference between the polarization of different exciton levels can lead to observable coherent exciton beats. Here, we present the theoretical formalism for evaluating the time- and angle-resolved photoemission spectra (tr-ARPES) arising from the coherently excited exciton states in the regime of zero overlap between the pump and probe pulses. We subsequently apply our formalism to a simple model example of hydrogenic exciton energy levels to identify the dependencies that control the quantum beats. Our findings indicate that the most pronounced effect of coherent quantum excitonic beats is seen midway between the excited exciton energy levels and the central energy of the pump pulse provides tunability of this effect.

Figure 1

Schematic of the excited exciton levels by the ultrashort pump pulse (large spectral width).

Figure 2

Timeline of the pump-probe photoemission measurement. The pump acts at earlier times, creating a coherent state at time $t=0$, following which the probe pulse is used for measurements.

Figure 3

ARPES spectra at different delay times. The different time snapshots display the time dynamics of the coherent exciton state. The region where the beat oscillations are most pronounced is at the energies between the two exciton energies marked by dashed horizontal lines.

Figure 4

Momentum-integrated spectra at different delay times displaying the oscillation in the ARPES intensity which is most prominent in the energy range between the two exciton energies.

Figure 5

False color plot of the momentum-integrated spectra. The horizontal dashed lines are at the exciton energy levels considered. The momentum-integrated spectra clearly shows coherent excitonic quantum beats in the energy range between the exciton levels.