Modern mechanical sensors increasingly measure motion with precision sufficient to resolve the fundamental thermal noise floor over a broad band. Compared with traditional sensors—achieving this limit only near resonance—this capability provides massive gains in acquisition rates along with access to otherwise obscured transient signals. However, stronger measurements are naturally accompanied by increased back-action. Here we resolve the broadband thermal noise spectrum in the presence of measurement back-action, revealing back-action-induced correlations in noise from many mechanical modes, even those well separated in frequency. The observed spectra can deviate significantly from predictions using standard single-mode and (uncorrelated) multimode models over the broad band, notably even at the mechanical resonance peaks. This highlights the importance of these correlations in any system exhibiting strong back-action, even when the resonances are spectrally well isolated, and/or when the readout noise is high and the resonance peaks appear consistent with simpler models. These correlations advantageously allow the thermal noise spectrum to reach a minimum—equivalent to that of a single mode—in a band far from the resonance peak, where the mechanical susceptibility is comparatively stable against frequency noise.

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• Measurement back action
• Metrology
• Optomechanics
• Quantum fluctuations & noise
• Quantum sensing
• Micromechanical & nanomechanical oscillators
• Atomic force microscopy
• Scanning probe microscopy