Coherent Coupling of Excitons and Trions in a Photoexcited CdTe/CdMgTe Quantum Well

We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

Figure 1

(a) Exciton and negative trion optical transitions accessible using circularly polarized light ($\sigma +$). (b) The exciton and trion nonlinear response is modeled using a six-level energy scheme consisting of a ground state ($|g⟩$), singly excited exciton ($|X⟩$) and trion ($|T^{-}⟩$) states, doubly excited exciton ($|2X⟩$) and trion ($|2T^{-}⟩$) states with an energy shift ${\mathrm{\Delta }}_X$ and ${\mathrm{\Delta }}_{T^{-}}$, respectively, and a doubly excited mixed exciton-trion state ($|X{T}^{-}⟩$) shifted from the $\text{exciton}+\text{trion}$ energy by ${\mathrm{\Delta }}_{X{T}^{-}}$. (c) Geometry of the incident beams and the FWM signal. The pulse time ordering and generalized double-sided Feynman diagrams are shown for the (d) rephasing zero- and one-quantum and (e) two-quantum sequences.

Figure 2

Normalized experimental rephasing (a) one-quantum spectrum of the exciton ($X$), trion ($T^{-}$), and their interaction ($LP$ and $HP$). Two-quantum coherences of the exciton ($2X$) and the mixed exciton-trion state ($LX{T}^{-}$ and $HX{T}^{-}$) appear in the experimental two-quantum spectrum shown in (b). $X$ and $T^{-}$ population peaks appear in the zero-quantum spectrum in (c). The excitation laser spectrum for all experiments is shown in the inset to (c). Panels (d)–(f) are the corresponding simulated spectra. The color bar indicates the normalized amplitude of each spectrum.