  We describe the measurement and modeling of amplitude noise and phase noise
in ultra-high Q nanomechanical resonators made from stoichiometric silicon
nitride. With quality factors exceeding 2 million, the resonators' noise
performance is studied with high precision. We find that the amplitude noise
can be well described by the thermomechanical model, however, the resonators
exhibit sizable extra phase noise due to their intrinsic frequency
fluctuations. We develop a method to extract the resonator frequency
fluctuation of a driven resonator and obtain a noise spectrum with dependence,
which could be attributed to defect motion with broadly distributed relaxation
times.
