Improved position measurement of nano electromechanical systems using cross correlations

TL;DR

This paper demonstrates that using cross correlations between two tunnel junction detectors in nano electromechanical systems can surpass the limitations of single detectors, significantly improving position measurement accuracy and reducing noise.

Contribution

It introduces a quantum approach to analyze cross-correlated measurements, showing how twin detectors with equal bias enhance measurement precision beyond traditional bounds.

Findings

Cross correlations overcome single-detector measurement bounds

Twin detectors with equal bias maximize cross-correlated output

Double-detector setup reduces added displacement noise

Abstract

We consider position measurements using the cross-correlated output of two tunnel junction position detectors. Using a fully quantum treatment, we calculate the equation of motion for the density matrix of the coupled detector-detector-mechanical oscillator system. After discussing the presence of a bound on the peak-to-background ratio in a position measurement using a single detector, we show how one can use detector cross correlations to overcome this bound. We analyze two different possible experimental realizations of the cross correlation measurement and show that in both cases the maximum cross-correlated output is obtained when using twin detectors and applying equal bias to each tunnel junction. Furthermore, we show how the double-detector setup can be exploited to drastically reduce the added displacement noise of the oscillator.