  Optical refrigeration of solids with anti-Stokes fluorescence has been widely
explored as a vibration-free cryogenic cooling technology. A minimum
temperature of 87 K has been demonstrated with rare-earth ion doped crystals
using optical refrigeration. However, the depletion of the upper-lying energy
levels in the ground state manifold hinders further cooling to below liquid
nitrogen (LN$_2$) temperatures, confining its applications. In this work, we
introduce a Purcell enhanced optical refrigeration method to circumvent this
limitation. This approach enhances the emission of high energy photons by
coupling to a nearby nanocavity, blue shifting the mean emission wavelength.
Such Purcell enhanced emission facilitates cooling starting from a lower energy
level in the ground state manifold, which exhibits a higher occupation below
LN$_2$ temperatures. Using our experimentally measured optical coefficients,
our theoretical analysis predicts a minimum achievable temperature of 38 K for
a Yb$^{3+}$:YLiF$_{4}$ nanocrystal near a cavity under realistic conditions.
The proposed method is applicable to other rare-earth ion doped materials and
semiconductors, and will have applications in creating superconducting and
other quantum devices with solid-state cooling.
