Minimum requirements for feedback enhanced force sensing

TL;DR

This paper demonstrates that feedback does not inherently improve force sensing beyond estimation when system dynamics are known, showing that nonlinearity is necessary for true enhancement, supported by theoretical proof and experimental validation.

Contribution

It proves that linear feedback cannot surpass estimation in force sensing unless nonlinearity is introduced, clarifying the fundamental limits of feedback-enhanced sensing.

Findings

Feedback alone cannot improve force sensing if dynamics are known.

Nonlinearity is essential for sensing enhancement beyond estimation.

Experimental reproduction of feedback-induced susceptibility modification.

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 or sensitivity. 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 non-stationary forces and feedback, and in the general case of non-Gaussian and correlated noise. Recently, feedback enhanced incoherent force sensing has been demonstrated [Nat. Nano. \textbf{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.