NIST researchers have developed a universal method for calculating the lowest possible uncertainty in measuring resonance frequencies of harmonic oscillators. This method incorporates various factors including thermodynamic, quantum, and instrumental uncertainties, as well as whether the oscillator is driven by an external force or freely fluctuating.
The new approach provides a practical way to calculate resonance frequencies from measured motion and obtain the best possible precision. It applies to a wide range of resonators, including nanomechanical, optical, and atomic systems. The researchers tested their method with a nanoscale mechanical resonator and found they could estimate resonance frequencies with the predicted error, even for measurements as short as 30 millionths of a second.
The study also identifies factors like random atomic motion as sources of noise that actually provide valuable information about resonance. By including these factors in their calculations, researchers can avoid underestimating the precision of resonance measurements. The work extends to quantum-dominated systems where the uncertainty principle must be considered, and the researchers describe how to use quantum backaction to measure resonance frequencies.
Keywords: uncertainty, precision, resonance, frequency, oscillation
