  The interplay between charge density wave (CDW) order and superconductivity
has attracted much attention. This is the central issue of along standing
debate in simple transition metal dichalcogenides without strong electronic
correlations, such as 2H-NbSe$\_2$, in which twosuch phases coexist. The
importance of anisotropic electron-phonon interaction has been recently
highlighted from both theoretical and experimental point of view, and explains
some of the key features of the formation of the CDW in this system. On the
other hand, other aspects, such as the effects of anharmonicity, remain poorly
understood despite their manifest importance in such soft-phonon driven phase
transition. At the theoretical level in particular, their prohibitive
computational price usually prevents their investigation within conventional
perturbative approaches.Here, we address this issue using a combination of high
resolution inelastic X-ray scattering measurements of the phonon dispersion, as
afunction of temperature and pressure, with state of the art ab initio
calculations. By explicitly taking into account anharmonic effects, we obtain
an accurate, quantitative, description of the (P,T) dependence of the phonon
spectrum, accounting for the rapid destruction of the CDW under pressure by
zero mode vibrations - or quantum fluctuations - of the lattice. The low-energy
longitudinal acoustic mode that drives the CDW transition barely contributes to
superconductivity, explaining the insensitivity of the superconducting critical
temperature to the CDW transition.
