(3) 3 in Fig. ) at initial population time t 2 ≈ 0 fs. For both cases, SE and GSB, during t 1 the system is in the coherence state |G 0 ⟩⟨±| and during t 3 , the system is in the conjugate coherence state |±⟩⟨G 0 |. Thus, they have exactly the same lineshapes at t 2 = 0 fs for all the peaks. Fig. , we observe the negative ESA peaks to be a little bit shifted from along the ω 3 , when compared to the peak locations in panels (a) and (b). This is because the |G 0 ⟩ → |P 1 ⟩ transitions are slightly different frequencies compared to the |P 1 ⟩ → |P 2 ⟩ transitions. The overall addition of signals gives the diagonally elongated diagonal and cross-diagonal peaks in the total rephasing spectra in panel (d). We can observe the existence of negative features along the diagonal peaks due to the shifted contribution from the ESA signal. As we move down along each column, we see similar lineshape features when compared with the first row. On careful observation, we see that the SE transition peak intensities have reduced when compared to the GSB transitions at t 2 = 250 fs. This is due to the population decay associated with the cavity mode during population time t 2 . For the SE signal, the system is in the state |±⟩⟨±| (see Fig. ) which loses its intensity when evolving during t 2 due to cavity loss from the cavity mode (|G ⟩ → |G 0 ⟩). When compared to the GSB signal, where the system is in the state |G 0 ⟩⟨G 0 | during t 2 propagation, which increases in intensity due to the decay of photonic population to the ground state. The effect of difference in population between the |±⟩⟨±| and |G 0 ⟩⟨G 0 | during t 2 causes the cross-diagonal peaks to be significantly reduced in size for the SE signal, and thus the GSB pathway is the major contributor to the coherent energy transfer between the polariton eigenstates via rephasing mechanism.