Non-Hermitian trapping of Dirac exciton-polariton condensates in a perovskite metasurface
Massless Dirac particles avoid trapping due to their exceptional tunneling properties manifested in the so-called Klein paradox. This conclusion stems from the conservative treatment, but so far, it has not been extended to a non-Hermitian framework. Recently, driven-dissipative bosonic condensation of Dirac exciton-polaritons was demonstrated in metasurface waveguides. Here, we report an experimental observation of spatial binding and energy quantization of Dirac exciton-polaritons in a halide perovskite metasurface. A combination of spatially profiled nonresonant optical excitation and exciton-polariton interaction forms an effective non-Hermitian complex potential responsible for the observed effect. In the case of tightly focused pump spots spanning from 9 to 17~$\mu$m, several bound states simultaneously achieve macroscopic occupation, constituting a multi-mode bosonic condensation of exciton-polaritons. Our theoretical analysis based on the driven-dissipative extension of the Dirac equation reveals that the non-Hermitian character of the effective trap allows for confinement even in the case of the gapless Dirac-like photonic dispersion, both above and below the energy of the dispersion crossing.