  Quantum trapping potentials for ultracold gases change the landscape of
classical properties of scattered light and matter. The atoms in a quantum
many-body correlated phase of matter change the properties of light and vice
versa. The properties of both light and matter can be tuned by design and
depend on the interplay between long-range (nonlocal) interactions mediated by
an optical cavity and short-range processes of the atoms. Moreover, the quantum
properties of light get significantly altered by this interplay, leading the
light to have nonclassical features. Further, these nonclassical features can
be designed and optimised.
