  The interaction of light and matter at the single-photon level is of central
importance in various fields of physics, including, e.g., condensed matter
physics, astronomy, quantum optics, and quantum information. Amplification of
such quantum light-matter interaction can be highly beneficial to, e.g.,
improve device performance, explore novel phenomena, and understand fundamental
physics, and has therefore been a long-standing goal. Furthermore, simulation
of light-matter interaction in the regime of ultrastrong coupling, where the
interaction strength is comparable to the bare frequencies of the uncoupled
systems, has also become a hot research topic, and considerable progress has
been made both theoretically and experimentally in the past decade. In this
review, we provide a detailed introduction of recent advances in amplification
of quantum light-matter interaction and simulation of ultrastrong light-matter
interaction, particularly in cavity and circuit quantum electrodynamics and in
cavity optomechanics.
