  The light-matter interaction can be utilized to qualitatively alter physical
properties of materials. Recent theoretical and experimental studies have
explored this possibility of controlling matter by light based on driving
many-body systems via strong classical electromagnetic radiation, leading to a
time-dependent Hamiltonian for electronic or lattice degrees of freedom. To
avoid inevitable heating, pump-probe setups with ultrashort laser pulses have
so far been used to study transient light-induced modifications in materials.
Here, we pursue yet another direction of controlling quantum matter by
modifying quantum fluctuations of its electromagnetic environment. In contrast
to earlier proposals on light-enhanced electron-electron interactions, we
consider a dipolar quantum many-body system embedded in a cavity composed of
metal mirrors, and formulate a theoretical framework to manipulate its
equilibrium properties on the basis of quantum light-matter interaction. We
analyze hybridization of different types of the fundamental excitations,
including dipolar phonons, cavity photons, and plasmons in metal mirrors,
arising from the cavity confinement in the regime of strong light-matter
interaction. This hybridization qualitatively alters the nature of the
collective excitations and can be used to selectively control energy-level
structures in a wide range of platforms. Most notably, in quantum
paraelectrics, we show that the cavity-induced softening of infrared optical
phonons enhances the ferroelectric phase in comparison with the bulk materials.
Our findings suggest an intriguing possibility of inducing a superradiant-type
transition via the light-matter coupling without external pumping. We also
discuss possible applications of the cavity-induced modifications in collective
excitations to molecular materials and excitonic devices.
