  Anharmonic decay of coherent optical phonons in semimetal Sb has been
investigated by using a femtosecond pump-probe technique. The coherent $A_{1g}$
mode is observed in time domain in a wide temperature range of 7 - 290 K. The
decay rate (the inverse of the dephasing time) systematically increases as the
lattice temperature increases, which is well explained by anharmonic
phonon-phonon coupling, causing decay of the optical phonon into two acoustic
phonon modes. The frequency of the $A_{1g}$ mode decreases with the
temperature, which is interpreted to the results of both thermal expansion and
anharmonic phonon-phonon coupling. The temperature dependence of the amplitude
of the coherent $A_{1g}$ mode exhibits a decrease with the lattice temperature,
which is well reproduced by considering the peaked intensity of spontaneous
Raman scattering assuming a Lorentzian line shape with the linewidth controlled
by the anharmonic decay, and this model can be applicable to other metallic
system, like Zn.
