# Conditional dynamics of optomechanical two-tone backaction-evading measurements

## TL;DR

This paper derives an exact theoretical framework for two-tone backaction-evading measurements in optomechanics, revealing new quantum squeezing and entanglement phenomena beyond common approximations, relevant for advanced quantum experiments.

## Contribution

It provides an exact expression for the conditional state in optomechanical systems beyond standard approximations, including numerical simulations and analysis of multimode entanglement.

## Key findings

- Conditional mechanical squeezing and intra-cavity squeezing predicted.
- Presence of optomechanical entanglement and tripartite entanglement shown.
- Results applicable to current backaction-dominated optomechanical experiments.

## Abstract

Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for state-of-the-art optomechanical experiments that have entered the backaction-dominated regime.