Nonlinear quantum metrology using coupled nanomechanical resonators

TL;DR

This paper proposes a nanomechanical nonlinear interferometer with coupled resonators to enhance measurement precision of nonlinearity strength, achieving a super-Heisenberg scaling even with dissipation.

Contribution

It introduces a nanomechanical analogue of a nonlinear interferometer with switchable coupling and demonstrates a super-Heisenberg scaling in parameter estimation.

Findings

Precision scales as 1/n^{3/2} with phonon number n.

Super-Heisenberg scaling persists despite dissipation.

Measurement of quadrature components is essential.

Abstract

We consider a nanomechanical analogue of a nonlinear interferometer, consisting of two parallel, flexural nanomechanical resonators, each with an intrinsic Duffing nonlinearity and with a switchable beamsplitter-like coupling between them. We calculate the precision with which the strength of the nonlinearity can be estimated and show that it scales as $1/n^{3/2}$, where $n$ is the mean phonon number of the initial state. This result holds even in the presence of dissipation, but assumes the ability to make measurements of the quadrature components of the nanoresonators.