  All known optical materials have an index of refraction of order unity.
Despite the tremendous implications that an ultrahigh index could have for
optical technologies, little research has been done on why the refractive index
of materials is universally small, and whether this observation is fundamental.
Here, we investigate the index of an ordered arrangement of atoms, as a
function of atomic density. At dilute densities, this problem falls into the
realm of quantum optics, where atoms do not interact with one another except
via the scattering of light. On the other hand, when the lattice constant
becomes comparable to the Bohr radius, the electronic orbitals begin to
overlap, giving rise to quantum chemistry. We present a minimal model that
allows for a unifying theory of index spanning these two regimes. A key aspect
is the treatment of multiple light scattering, which can be highly
non-perturbative over a large density range, and which is the reason that
conventional theories of the index break down. In the quantum optics regime, we
show that ideal light-matter interactions can have a single-mode nature,
allowing for a purely real refractive index that grows with density as
$(N/V)^{1/3}$. At the onset of quantum chemistry, we show how two physical
mechanisms (excited electron tunneling dynamics and the buildup of electronic
density-density correlations) can open up inelastic or spatial multi-mode light
scattering processes, which ultimately reduce the index back to order unity
while introducing absorption. Around the onset of chemistry, our theory
predicts that ultrahigh index ($n\sim 30$), low-loss materials could in
principle be allowed by the laws of nature.
