  We theoretically study a one-dimensional (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 model. Here we establish that this belief is
incorrect and that the Aubry-Andre model description, which applies only in the
extreme tight-binding limit of very deep primary lattice potential, generically
breaks down near the localization transition due to the unavoidable appearance
of single-particle mobility edges (SPME). In fact, we show that the 1D
bichromatic incommensurate potential system manifests generic mobility edges
which disappear in the tight-binding limit, leading to the well-studied
Aubry-Andre physics. We carry out an extensive study of the localization
properties of the 1D incommensurate optical lattice without making any
tight-binding approximation. We find that, 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 Aubry-Andre prediction. Using the Wegner flow
approach, we show that the SPME in the real lattice system can be attributed to
significant corrections of higher-order harmonics in the lattice potential
which are absent in the strict tight-binding limit. We calculate the dynamical
consequences of the intermediate phase in detail to guide future experimental
investigations for the observation of 1D SPME and the associated intermediate
phase. We consider effects of interaction numerically, and conjecture the
stability of SPME to weak interaction effects, thus leading to the exciting
possibility of an experimentally viable nonergodic extended phase in
interacting 1D optical lattices.
