Fig. 4: Calculated spectra, energy levels, and dynamics of the microcavities.

Calculated linear 1 − R spectra of the (6,5)- (a), (7,5)- (b) and mixed (6,5)/(7,5) (c) microcavities. In c, the diagonal slice from the measured two-dimensional white-light (2DWL) spectrum in Fig. 2f, top (light blue line) is overlaid with the calculated spectrum (black line) with J = − 10 meV and g = 42.9 meV, which yielded the best match. These J and g values were then applied to generate the spectra for the single-bandgap microcavities shown as black lines in a, b. The vertical bars plot the individual eigenstates with heights proportional to the transition dipole strength, color coded to illustrate the composition of each eigenstate. d–f Energy level diagrams. Bright states are shown with color codes as in a–c, and dark states (states with transition dipoles smaller than 0.01% of the maximum dipole strength in each case) are shown in gray. g–i Calculated population dynamics upon photoexcitation of the upper-polariton (UP) band. In g, h, the gray and the purple/green traces plot the dark-state and the UP-to-lower-polariton (LP) transfer dynamics, respectively. In i, the two traces plot the UP-to-LP transfer dynamics upon pumping states with high- (yellow) and low (purple) photon content, also illustrated as colored arrows in c. For comparison, the experimental UP/LP cross peak traces are overlaid as black open circles.