Abstract
The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth, sensitivity or resolution. We show that as long as the oscillator dynamics are known, there exists a real-time estimation strategy that reproduces the same measurement record as any arbitrary feedback protocol. Consequently some form of nonlinearity is required to gain any advantage beyond estimation alone. This result holds true in both quantum and classical systems, with nonstationary forces and feedback, and in the general case of non-Gaussian and correlated noise. Recently, feedback enhanced incoherent force resolution has been demonstrated [E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nano. 7, 509 (2012)], with the enhancement attributed to a feedback induced modification of the mechanical susceptibility. As a proof-of-principle, we experimentally reproduce this result through straightforward filtering.
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