Direct observation of zero modes in a non-Hermitian optical nanocavity array

Abstract

Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature π/2 phase jumps between adjacent cavities. Here, we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavities array containing quantum wells. Unlike the Hermitian counterparts, the observation of non-Hermitian zero modes upon single pump spot illumination requires vanishing sublattice detuning, and they can be identified through far-field imaging and spectral filtering of the photoluminescence at selected pump locations. We explain the zero-mode coalescence as a parity-time phase transition for small coupling. These zero modes are robust against coupling disorder and can be used for laser mode engineering and photonic computing.