  We report here the realization and commissioning of an experiment dedicated
to the study of the optical properties of light matter hybrids constituted of
crystalline samples embedded in an optical cavity. The experimental assembly
developed offers the unique opportunity to study the weak and strong coupling
regime between a tunable optical cavity in cryogenic environment and low energy
degrees of freedom such as phonons, magnons or charge fluctuations. We describe
here the setup developed which allows the positioning of crystalline samples in
an optical cavity of different quality factor, the tuning of the cavity length
at cryogenic temperatures and its optical characterization with a broadband
time domain THz spectrometer (0.2-6 THz). We demonstrate the versatility of the
setup by studying the vibrational strong coupling in CuGeO3 single crystal at
cryogenic temperatures.
