Fröhlich discovered the remarkable condensation of polar vibrations into the lowest frequency mode when the system is pumped externally. For a full understanding of the Fröhlich condensate one needs to go beyond the mean field level to describe critical behavior as well as quantum fluctuations. The energy redistribution among vibrational modes with nonlinearity included is shown to be essential for realizing the condensate and the phonon-number distribution, revealing the transition from quasithermal to super-Poissonian statistics with the pump. We further study the spectroscopic properties of the Fröhlich condensate, which are especially revealed by the narrow linewidth. This gives the long-lived coherence and the collective motion of the condensate. Finally, we show that the proteins such as bovine serum albumin and lysozyme are most likely the candidates for observing such collective modes in THz regime by means of Raman or infrared spectroscopy.