  Parametric resonances and amplification have led to extraordinary
photo-induced phenomena in pump-probe experiments. While these phenomena
manifest themselves in out-of-equilibrium settings, here, we present the
striking result of parametric amplification in equilibrium. In particular, we
demonstrate that quantum and thermal fluctuations of a Raman-active mode
amplifies light inside a cavity, at equilibrium, when the Raman mode frequency
is twice the cavity mode frequency. This noise-driven amplification leads to
the creation of an unusual parametric Raman polariton, intertwining the Raman
mode with cavity squeezing fluctuations, with smoking gun signatures in Raman
spectroscopy. In the resonant regime, we show the emergence of not only quantum
light amplification but also localization and static shift of the Raman mode.
Apart from the fundamental interest of equilibrium parametric amplification our
study suggests a resonant mechanism for controlling Raman modes and thus matter
properties by cavity fluctuations. We conclude by outlining how to compute the
Raman-cavity coupling, and suggest possible experimental realization
