  We report the observation of parametric down-conversion of phonons in a
spherical Bose-Einstein condensate. The spherical symmetry, which is crucial
for observing this phenomenon, is experimentally demonstrated by measuring the
collective mode and expansion behavior of the condensate. The low-energy
monopole mode is excited by coupling with a high-energy mode with a nearly
twice eigen-frequency. The population of the low-energy mode becomes maximum
only when the high-energy mode is resonantly excited. Furthermore, we directly
observe the parametric down-conversion process in the driving process, through
simultaneously probing the two coupling modes. The experimental observation is
consistent with the perturbation theory including the gravity effect. This work
opens the challenge in related study of the condensate beyond mean-field theory
and has potential applications in quantum information.
