Revealing and Characterizing Dark Excitons through Coherent Multidimensional Spectroscopy

Dark excitons are of fundamental importance in a broad range of contexts but are difficult to study using conventional optical spectroscopy due to their weak interaction with light. We show how coherent multidimensional spectroscopy can reveal and characterize dark states. Using this approach, we identify parity-forbidden and spatially indirect excitons in InGaAs/GaAs quantum wells and determine details regarding lifetimes, homogeneous and inhomogeneous linewidths, broadening mechanisms, and coupling strengths. The observations of coherent coupling between these states and bright excitons hint at a role for a multistep process by which excitons in the barrier can relax into the quantum wells.

Figure 1

(a) Diagram of the conduction band and valence band (HH and LH) potentials and typical calculated steady-state wave functions for QW electrons and holes. (b) Calculated exciton transition energy for the various detected states as a function of the QC, which coincide with the measured transition energies (horizontal dashed lines) at $\mathrm{QC}\approx 0.63$.

Figure 2

(a) Absolute value rephasing 1Q 2D spectrum with a logarithmic color scale. A number of CPs are observed due to the strong coupling of the bright and dark states. (b) An absolute value rephasing 3D spectrum. The amplitude of the detected peaks spans several orders of magnitude, so for clarity each region is plotted at the most appropriate isosurface level.

Figure 3

Projections of several 3D CPs onto the $E_1$ vs $E_3$ plane, which reveal details about the spectral broadening of the dark states, as discussed in the text.