Single-particle mobility edges in a one-dimensional bichromatic incommensurate potential

In this talk I will focus on a 1D mutually incommensurate bichromatic lattice system which has been implemented in ultracold atoms to study quantum localization. It has been universally believed that the tight-binding version of this bichromatic incommensurate system is represented by the well-known Aubry-Andre (AA) model. Here we establish that this belief is incorrect and that the AA model description generically breaks down near the localization transition due to the unavoidable appearance of single-particle mobility edges (SPME). As a result, for the full lattice system, an intermediate phase between completely localized and completely delocalized regions appears due to the existence of the SPME, making the system qualitatively distinct from the AA prediction. Our theoretical prediction is subsequently verified in an experiment using a one-dimensional quasi-periodic optical lattice. In particular, a regime is identified where extended and localized single-particle states coexist, in good agreement with our theoretical results. Our work thus presents the first realization of a system with an SPME in one dimension, and it opens up more research prospects in the context of many-body localization, including the question of many-body mobility edges.