Geometric control theory for quantum back-action evasion

TL;DR

This paper develops a geometric control theory-based method to design controllers that enable quantum sensors to evade back-action noise and surpass the standard quantum limit, with applications to opto-mechanical systems.

Contribution

It introduces a novel geometric control approach for quantum back-action evasion, extending classical disturbance decoupling techniques to quantum sensor design.

Findings

Designed controllers that achieve back-action noise evasion.

Applied the method to practical opto-mechanical sensors.

Demonstrated robustness against experimental imperfections.

Abstract

Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present.