Localization landscape and mobility edge in polaritonic lattices

Polariton systems have emerged as a promising and highly tunable platform to construct simulators for various condensed-matter models.

In this work, we present a protocol to design polariton lattices that capture 1D quasi-periodic tight-binding Hamiltonians with mobility-edge. This mobility edge defines an energy boundary between localized and extended states in the spectrum. In particular, we focus on the Generalised Aubrey-Andre model[1]. We study the localization properties of the model through the localization-landscape theory, which is a diagnostic of the localized low-energy state positions. This, in principle, can be used as a direct comparison with the real space imaging of the polariton lattice. Furthermore, we compare these predictions with numerical calculations. At the end, we say a few words on the expected condensate behaviour, through numerical simulations.

[1]S. Ganeshan et al, Phys. Rev. Lett. 114, 146601 (2015)