Generalized Anderson localization threshold in dissipatively coupled quasicrystals

The well-established delocalization-localization (DL) transition in Hermitian Aubry-Andr\'e-Harper (AAH) lattices with incommensurate on-site potentials provides a compelling illustration of the subtle localized behavior of eigenstates. Our study extends the Anderson localization (AL) threshold to the non-Hermitian scenario by focusing on an AAH lattice that incorporates both dissipative couplings and loss modulations, demonstrating that the DL transition behaviors observed in Hermitian quasicrystals represent merely special cases of this broader phenomenon. We rigorously confirm the validity of the generalized AL threshold by observing the remarkable consistency between the numerical mean inverse participation ratio and the analytical Lyapunov exponent. Meanwhile, we investigate the impact of dissipative couplings and system size on the DL transition. Moreover, we propose a novel scheme for constructing dissipatively coupled AAH lattices, which involves cavity fields weakly coupled to engineered resonators. Our work significantly advances the understanding of AL by extending its threshold from Hermitian to non-Hermitian systems, demonstrating their compatibility and the promising possibilities for exploring criticality in non-Hermitian quasiperiodic lattices.