document: the frequency response of the resonators was measured using a downmixing method , described in detail in . 
   the device was electrostatically actuated , and the driving voltage was applied to a side - gate parallel to the resonator . to reduce parasitic signals , 
   the drive signal was set to half the actuation frequency 2 , thus the amplitude of motion of the resonator was proportional to the square of the actuation voltage . 
   a bias voltage at (  +  ) through the gauges was used to down - mix their resistance change ( occurring at the actuation frequency  ) , and the low - frequency readout signal at  was detected using a lock - in amplifier . 
   typical measurement values were 1.5 v for the bias voltage at a measurement frequency of 500 khz . 
   all measurements were performed in a vacuum chamber at a pressure of 10 mbar and at room temperature . 
   thermomechanical noise was measured using the same set - up , with the drive electrode disconnected . 
   measurements were taken with a lock - in amplifier , which also generated the drive and bias signals . 
   the allan deviation was measured in open - loop configuration , and the frequency stability was extracted from the response of the resonator actuated at resonance frequency with a fixed driving frequency . 
   the phase of the measured signal , (t ) , was monitored for a certain amount of time , and then transformed into frequency fluctuations using the phase response of the resonator . 
   close to the resonance frequency , this phase response was linear , f2qf0 . using the complete phase response of the resonator instead of this linearization does not significantly alter the allan deviation . 
   harmonics appearing at the frequency of the electricity supply ( multiples of 50 hz ) were filtered out of data during post - processing . using this method , we obtained n samples of the resonance frequency of the resonator f1fn , each averaged over an integration time , 0 . the allan deviation for this integration time could then be defined as : 
   ( 2)a(0)=12(n1)1n1(fi+1fif0)2 to obtain the frequency stability for higher integration times from the same set of frequency samples , we followed the standard method . 
   initial samples were averaged in groups of n samples , and the allan deviation for the new array was calculated using equation ( 2 ) to determine a(n0 ) . 
   this process was repeated multiple times until the number of samples was too low to provide a statistically significant result . 
   correlation measurements were performed by simultaneously measuring the response of the resonator at different frequencies within the resonator s bandwidth . 
   the measurement set - up was based on the one described in supplementary section 3 , but here each signal was doubled , using two drive signals at different frequencies , two bias signals , and two measurement signals ( supplementary figure s9 shows a detailed measurement scheme ) . 
   particular care was taken when choosing the drive signal amplitudes so that the resonator remained in the linear regime . 
   moreover , the two measurement frequencies were chosen to avoid cross - talk ( e.g. 302 khz and 367 khz ) . 
   although here we used a down - mixing set - up , correlation could also be measured with a homodyne method . 
   the phase traces were converted to frequency traces corresponding to the different integration times , as described above . here , the complete phase response of the resonator was used rather than the linear approximation , as the frequencies for phase samples can be quite different from the resonance frequency . with this method we obtained two frequency sample arrays with an integration time 0 . 
   the graph in figure 4b shows the correlation of these frequency traces versus the integration time . we processed the signals so that the correlation for a given  only depends on frequency variations with characteristic time close to . for each  of the plot , we filtered the two frequency traces with a band - pass filter centered on . for a consistent correspondence between allan deviation and correlation integration times , we chose the allan deviation transfer function as the band - pass filter , defined as : 
   ( 3)ha(f)2=2sin4f(f)2 finally , the correlation coefficient of the filtered frequency traces f1 and f2 , each of length n , was defined by : 
   ( 4)corrf1f2=i=1n(f1,if1)(f2,if2)nsf1sf2 
   where f1 and f2 are the sample means of f1 and f2 , respectively , and sf1 and sf2 are their standard deviations . 
   the frequency response of the resonators was measured using a downmixing method , described in detail in . 
   the device was electrostatically actuated , and the driving voltage was applied to a side - gate parallel to the resonator . to reduce parasitic signals , 
   the drive signal was set to half the actuation frequency 2 , thus the amplitude of motion of the resonator was proportional to the square of the actuation voltage . 
   a bias voltage at (  +  ) through the gauges was used to down - mix their resistance change ( occurring at the actuation frequency  ) , and the low - frequency readout signal at  was detected using a lock - in amplifier . 
   typical measurement values were 1.5 v for the bias voltage at a measurement frequency of 500 khz . 
   all measurements were performed in a vacuum chamber at a pressure of 10 mbar and at room temperature . 
   thermomechanical noise was measured using the same set - up , with the drive electrode disconnected . 
   measurements were taken with a lock - in amplifier , which also generated the drive and bias signals . 
   the allan deviation was measured in open - loop configuration , and the frequency stability was extracted from the response of the resonator actuated at resonance frequency with a fixed driving frequency . 
   the phase of the measured signal , (t ) , was monitored for a certain amount of time , and then transformed into frequency fluctuations using the phase response of the resonator . 
   close to the resonance frequency , this phase response was linear , f2qf0 . using the complete phase response of the resonator instead of this linearization does not significantly alter the allan deviation . 
   harmonics appearing at the frequency of the electricity supply ( multiples of 50 hz ) were filtered out of data during post - processing . using this method , we obtained n samples of the resonance frequency of the resonator f1fn , each averaged over an integration time , 0 . the allan deviation for this integration time could then be defined as : 
   ( 2)a(0)=12(n1)1n1(fi+1fif0)2 to obtain the frequency stability for higher integration times from the same set of frequency samples , we followed the standard method . 
   initial samples were averaged in groups of n samples , and the allan deviation for the new array was calculated using equation ( 2 ) to determine a(n0 ) . 
   this process was repeated multiple times until the number of samples was too low to provide a statistically significant result . 
   correlation measurements were performed by simultaneously measuring the response of the resonator at different frequencies within the resonator s bandwidth . the measurement set - up was based on the one described in supplementary section 3 , but here each signal was doubled , using two drive signals at different frequencies , two bias signals , and two measurement signals ( supplementary figure s9 shows a detailed measurement scheme ) . 
   particular care was taken when choosing the drive signal amplitudes so that the resonator remained in the linear regime . 
   moreover , the two measurement frequencies were chosen to avoid cross - talk ( e.g. 302 khz and 367 khz ) . 
   although here we used a down - mixing set - up , correlation could also be measured with a homodyne method . 
   the phase traces were converted to frequency traces corresponding to the different integration times , as described above . here , the complete phase response of the resonator was used rather than the linear approximation , as the frequencies for phase samples can be quite different from the resonance frequency . with this method we obtained two frequency sample arrays with an integration time 0 . 
   the graph in figure 4b shows the correlation of these frequency traces versus the integration time . we processed the signals so that the correlation for a given  only depends on frequency variations with characteristic time close to . for each  of the plot , we filtered the two frequency traces with a band - pass filter centered on . for a consistent correspondence between allan deviation and correlation integration times , we chose the allan deviation transfer function as the band - pass filter , defined as : 
   ( 3)ha(f)2=2sin4f(f)2 finally , the correlation coefficient of the filtered frequency traces f1 and f2 , each of length n , was defined by : 
   ( 4)corrf1f2=i=1n(f1,if1)(f2,if2)nsf1sf2 
   where f1 and f2 are the sample means of f1 and f2 , respectively , and sf1 and sf2 are their standard deviations . 
   
summary: frequency stability is key to performance of nanoresonators . this stability is thought to reach a limit with the resonator s ability to resolve thermally - induced vibrations . 
   although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response , these fluctuations have recently attracted considerable theoretical interest . 
   however , their existence is very difficult to demonstrate experimentally . here , through a literature review , 
   we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise . 
   we studied a monocrystalline silicon nanoresonator at room temperature , and found a similar discrepancy . 
   we propose a new method to show this was due to the presence of frequency fluctuations , of unexpected level . 
   the fluctuations were not due to the instrumentation system , or to any other of the known sources investigated . 
   these results challenge our current understanding of frequency fluctuations and call for a change in practices .