  The mobility edges (MEs) in energy which separate extended and localized
states are a central concept in understanding the localization physics. In
one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain
cases, the analytic results which allow for an exact understanding are rare.
Here we uncover a class of exactly solvable 1D models with MEs in the spectra,
where quasiperiodic on-site potentials are inlaid in the lattice with equally
spaced sites. The analytical solutions provide the exact results not only for
the MEs, but also for the localization and extended features of all states in
the spectra, as derived through computing the Lyapunov exponents from Avila's
global theory, and also numerically verified by calculating the fractal
dimension. We further propose a novel scheme with experimental feasibility to
realize our model based on an optical Raman lattice, which paves the way for
experimental exploration of the predicted exact ME physics.
