Squeezing and measurement of a mechanical quadrature via PID feedback

TL;DR

This paper explores how extending PID feedback to quantum optomechanical systems influences quadrature squeezing and control, offering new methods for quantum state manipulation and measurement enhancement.

Contribution

It introduces the application of derivative and integral feedback in quantum systems, showing their effects on squeezing and state control beyond standard proportional feedback.

Findings

Derivative feedback affects both conditional and unconditional squeezing.

Feedback can be used to drive a mechanical quadrature to follow a reference signal.

The approach offers new routes for improved quantum state control.

Abstract

Proportional-Integral-Derivative (PID) control is used for automatically regulating a measurable quantity to a desired setpoint. It is widely used in different types of classical control electronics. Here, we show how extending the feedback theory in quantum systems to include the derivative and integral parts influences both the transient and steady-state behavior of the amplitude and squeezing of a mechanical quadrature in an optomechanical system. We show that, in contrast to standard proportional feedback, derivative feedback affects both the conditional and unconditional squeezing. Furthermore, we demonstrate how feedback may be employed to drive a mechanical quadrature to track a desired reference signal. Our findings offer new routes for an improved quantum state control and measurement precision.