When the coupling between light and matter becomes comparable to the energy gap between different excited states they hybridize, leading to the appearance of a rich and complex phenomenology which attracted remarkable interest in recent years. While the mixing between states with different number of excitations, so-called ultrastrong coupling regime, has been observed in various implementations, the effect of the hybridization between different single excitation states, referred to as very strong coupling regime, has remained elusive. In semiconductor quantum wells such a regime is predicted to manifest as a photon-mediated electron-hole coupling leading to different excitonic wavefunctions for the two polaritonic branches when the ratio of the coupling strength to exciton binding energy approaches unity. Here, we verify experimentally the existence of this regime in magneto-optical measurements on a microcavity with 28 GaAs quantum wells, showing that the average electron-hole separation of the upper polariton is significantly increased compared to the bare quantum well exciton Bohr radius. This manifests in a diamagnetic shift around zero detuning that exceeds the shift of the lower polariton by one order of magnitude and the bare quantum well exciton diamagnetic shift by a factor of two. The lower polariton exhibits a diamagnetic shift smaller than expected from the coupling of a rigid exciton to the cavity mode which suggests more tightly bound electron-hole pairs than in the bare quantum well.
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