Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the resonator to noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the frequency of eigenoscillations on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large vibration amplitudes. The spectral peak undergoes counter-intuitive narrowing when the noise intensity is increased. With the resonator serving as the frequency determining element in a feedback loop, the phase noise at the extremum amplitude is three times smaller than the conventional nonlinear regime. Zero dispersion phenomena open new opportunities for improving resonant sensors and frequency references.
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