Influence of local fields on the dynamics of four-wave mixing signals from 2D semiconductor systems

Abstract

In recent years the physics of two-dimensional semiconductors was revived by the discovery of the class of transition metal dichalcogenides. In these systems excitons dominate the optical response in the visible range and open many perspectives for nonlinear spectroscopy. To describe the coherence and polarization dynamics of excitons after ultrafast excitation in these systems, we employ the Bloch equation model of a two-level system extended by a local field describing the exciton–exciton interaction. We calculate four-wave mixing (FWM) signals and analyze the dependence of the temporal and spectral signals as a function of the delay between the exciting pulses. Exact analytical results obtained for the case of ultrafast (δ-shaped) pulses are compared to numerical solutions obtained for finite pulse durations. If two pulses are used to generate the nonlinear signal, characteristic spectral line splittings are restricted to short delays. When considering a three-pulse excitation the line splittings, induced by the local field effect, persist for long delays. All of the found features are instructively explained within the Bloch vector picture and we show how the exciton occupation dynamics govern the different FWM signals.

Local field effects in ultrafast light–matter interaction measured by pump-probe spectroscopy of monolayer MoSe2

“…The delay between the pulses is 𝜏 and the pulses have phases 𝜙 1 and 𝜙 2 , pulse areas 𝜃 1 and 𝜃 2 , and the same duration Δt. Both pulses are resonant to the exciton transition which is additionally renormalized by the local field strength V in this model [13]. We identify the pulse with index 1 as the pump pulse and pulse 2 as the probe, meaning 𝜃 1 ≫ 𝜃 2 in agreement with the experiment.…”

“…In the limit of ultrafast laser pulses, treated as delta functions in time, the full system's dynamics can be solved analytically as shown in Ref. [13]. Based on the analytical expression derived in the following, we can explain the lineshapes and extract approximations for energy shifts and dynamics that we will later compare to our numerical simulations for nonvanishing pulse durations and the experimental findings.…”

“…Note that here V and W are real-valued, while in Ref. [13] the two quantities were summed in a complex-valued V.…”

“…In Ref. [13], we have shown that for a two-level system (2LS) the dynamics can be calculated analytically and brought into a compact form in the limit of ultrafast laser pulses. To carry out an equivalent analysis here we will reduce the three-level system (3LS) to a 2LS.…”

“…This is usually attributed to the extinction of the exciton polarization transient by the second pulse [8][9][10] or by EID [11,12]. Here, it is additionally related to a rapid change of the character of the pump-probe signal accompanied by a frequency shift introduced by the local field effect [13].…”