  Optical cavities confine light on a small region in space which can result in
a strong coupling of light with materials inside the cavity. This gives rise to
new states where quantum fluctuations of light and matter can alter the
properties of the material altogether. Here we demonstrate, based on first
principles calculations, that such light-matter coupling induces a change of
the collective phase from quantum paraelectric to ferroelectric in the
SrTiO$_3$ groundstate, which has thus far only been achieved in
out-of-equilibrium strongly excited conditions[1, 2]. This is a
light-matter-hybrid groundstate which can only exist because of the coupling to
the vacuum fluctuations of light, a "photo-groundstate". The phase transition
is accompanied by changes in the crystal structure, showing that fundamental
groundstate properties of materials can be controlled via strong light-matter
coupling. Such a control of quantum states enables the tailoring of materials
properties or even the design of novel materials purely by exposing them to
confined light.
