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~$μ$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.

💡 Research Summary

The authors investigate the possibility of trapping mass‑less Dirac particles in a non‑Hermitian setting, a problem that has traditionally been considered impossible due to Klein tunneling. They use a halide perovskite metasurface (MAPbBr₃) patterned with a sub‑wavelength grating to create a waveguide that supports Dirac‑like photonic dispersion with essentially no energy gap at the Γ point. By focusing a non‑resonant femtosecond pump onto a micron‑scale spot (9–17 µm), they generate a spatially localized incoherent exciton reservoir. The reservoir produces a complex‑valued potential U = (α + iβ)N, where the real part α induces a blueshift through exciton‑polariton repulsion and the imaginary part β provides position‑dependent gain. This non‑Hermitian potential acts as an effective trap for Dirac exciton‑polaritons despite the absence of a bandgap.

Experimentally, above a threshold fluence of ≈1.27 mJ cm⁻² the system exhibits a multi‑mode bosonic condensation. Real‑space imaging shows a speckled emission pattern confined within the pump region, while angle‑resolved spectroscopy reveals a ladder of well‑resolved energy levels (labeled A₁, S₁, A₂, S₂, etc.) with spacings of about 10 meV. The symmetry of each level in momentum space (maximum or minimum at k∥ = 0) allows classification into antisymmetric (A) and symmetric (S) states, reminiscent of particle‑in‑a‑box solutions. As the pump fluence increases, the dominant mode switches from A₂ to S₂ and eventually higher‑order states (A₃) appear. The quality factor of the dominant mode reaches ≈2450, confirming high coherence.

To interpret these observations, the authors extend the Dirac Hamiltonian to a driven‑dissipative (non‑Hermitian) form and couple it to a generalized Gross‑Pitaevskii equation that includes the reservoir dynamics. Numerical simulations based on this framework reproduce the measured real‑space profiles, momentum‑space emission patterns, energy shifts, and linewidth broadening across a wide range of pump powers. Crucially, the simulations demonstrate that the imaginary component of the coupling (Im V ≫ Re V) collapses the photonic gap, yet the complex potential still supports bound states both above and below the original Dirac crossing. This demonstrates that Klein tunneling does not preclude confinement when gain and loss are present.

The work provides four major contributions: (1) experimental proof that non‑Hermitian complex potentials can trap Dirac‑like polaritons without a bandgap; (2) observation of energy quantization and multi‑mode non‑Hermitian Bose‑Einstein condensation in a gapless system; (3) validation of a driven‑dissipative Dirac model as an accurate description of such photonic‑matter hybrids; and (4) insight into mode competition under ultrafast pulsed excitation, where multimode condensation persists because the reservoir lifetime is too short for single‑mode selection. These findings open new avenues for exploring relativistic phenomena, topological photonics, and nonlinear optics in non‑Hermitian platforms, suggesting that engineered gain‑loss landscapes can be used to control and manipulate Dirac quasiparticles in ways impossible in conservative systems.