  We discuss how complex-oxide heterostructures that include high-Tc
superconducting cuprates can be used to realize an array of sub-millimeter
cavities that support Josephson plasmon polaritons. These cavities have several
attractive features for new types of light matter interaction studies and we
show that they promote "ultrastrong" coupling between THz frequency radiation
and Josephson plasmons. Cavity electrodynamics of Josephson plasmons allows to
manipulate the superconducting order-parameter phase coherence. As an example,
we discuss how it could be used to cool superconducting phase fluctuations with
light.
