Broadband Multidimensional Variational Measurement with Non-Symmetric Coupling

TL;DR

This paper proposes a broadband multidimensional variational measurement scheme that can eliminate quantum back action across a wide frequency band, enhancing force detection sensitivity beyond the Standard Quantum Limit, even considering optical losses.

Contribution

It analyzes a non-symmetric coupling scheme for multidimensional variational measurement, including optical losses, and demonstrates conditions for complete back action removal.

Findings

Back action can be fully eliminated in lossless asymmetric systems.

Optical losses limit the measurement sensitivity.

The scheme's practical implementation is discussed.

Abstract

A broadband multidimensional variational measurement allows overcoming the Standard Quantum Limit (SQL) of a classical mechanical force detection for a mechanical oscillator. In this measurement quantum back action, which perturbs the evolution of a mechanical oscillator, can be completely removed in a broad detection frequency band after post-processing. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other optical modes, which have the frequency separation with the central mode equal to the mechanical frequency. To realize such a scheme in practice one either needs to use a very long optical interferometer or should utilize optical modes belonging to different mode families. In the second case the modes have different geometries and their coupling with the mechanical mode is not identical. Here we analyze a general case of the non-symmetric measurement scheme, in which the coupling strengths with the light modes are not equal to each other, and take into account optical losses. We found that the back action can be completely excluded from the measurement result in the case of the asymmetric lossless system. The nonzero loss limits the sensitivity. An experimental implementation of the proposed scheme is discussed.