Abstract
Micro and nano-mechanical oscillators are capable of ultra-sensitive force measurement, allowing precision spin, charge, acceleration, and field sensing [1, 2]. It is well known that feedback control can improve the precision of nonlinear mechanical sensors through the suppression of saturation, instabilities, and frequency mixing [3]. Feedback control also appears attractive as a technique to enhance the precision of linear sensors, since it allows, for example, suppression of thermal noise [4, 5], or increased mechanical response in the frequency band of the signal [6]. Such precision enhancement is prohibited for linear processes with stationary linear feedback and Gaussian noise by the well known principle of neutrality in linear control theory, which states that the uncertainty of a measurement is independent of the choice of feedback [7]. However, several force sensing techniques with linear oscillators fall outside the scope of the principle of neutrality. Prominent examples include stroboscopic measurement incorporating non-stationary feedback [8], and measurement of the variance of incoherent forces as applied in temperature sensing. In both of these cases, feedback cooling has been proposed as a means to enhance precision [8, 9]. However, neither proposal identifies an optimal estimation strategy. Consequently, the important question of whether the same, or improved, sensitivity enhancement might be achieved by applying a better estimation strategy, without the requirement of feedback, is left unresolved.
© 2013 IEEE
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