  According to the principles of quantum mechanics the Hamiltonian describing a
closed system's energies must be Hermitian. This leads to an avoided crossing
on resonance, as coupling between states causes the energy levels to repel.
This concept lies at the heart of exciton-polariton physics, where coherent
exciton-photon interaction causes polariton branches to repel in momentum
dispersion. However, non-Hermitian physics predicts an opposite effect: level
attraction, which occurs when significant energy dissipation is present in the
system. Here, we show a manifestation of dissipative coupling in a high-quality
AlGaAs-based polariton microcavity, where two polariton branches attract,
resulting in an anomalous, inverted dispersion of the lower branch in momentum
dispersion. We observe the evolution of the level attraction with
exciton-photon detuning, leading to changes in anomalous dispersion shape
within a single sample. The dissipative coupling is explained by the
interaction with an indirect exciton, acting as a highly dissipative channel in
our system, and the observed dispersions are well captured within a
phenomenological model. Our results present a new mechanism of dissipative
coupling in light-matter systems and offer a tunable and well-controlled
AlGaAs-based platform for engineering the non-Hermitian and negative mass
effects in polariton systems.
