Direct observation of zero modes in a non-Hermitian optical nanocavity array
F. Hentinger, Melissa Hedir, Bruno Garbin, M. Marconi, Li Ge, Fabrice Raineri, J. A. Levenson, A. M. Yacomotti
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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.