# A macrorealistic test in hybrid quantum optomechanics

## TL;DR

This paper proposes a method to test macrorealistic theories using a hybrid optomechanical system, demonstrating how non-classical states can be generated and used to violate Leggett-Garg inequalities, advancing quantum foundations research.

## Contribution

It introduces a novel protocol for generating non-classical states in optomechanical systems and applies a theoretical test of Leggett-Garg inequalities with a hybrid setup involving a two-level system.

## Key findings

- The protocol can produce non-classical states in optomechanical cavities.
- Theoretical violation of Leggett-Garg inequalities demonstrated with a hybrid system.
- Potential to test macrorealism in macroscopic quantum systems.

## Abstract

We discuss a scheme for macrorealistic theories of the Leggett-Garg form [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)]. Our scheme is based on a hybrid optomechanical system. It seems reasonable to test these inequalities with an optomechanical system, since in an optomechanical cavity it is possible to create non-classical states of the mirror through a projective measurement on the cavity field. We will present the protocol to generate such non-classicality for a general optomechanical cavity and after we will carry out a theoretical test for one of the possible formulations of these inequalities using a hybrid optomechanical system. Specifically, the inequality will be investigated for an harmonic oscillator coupled to a two-level system, which replaces the light field of the cavity. The aim is to reproduce, with this system, the evolution of a single spin-1/2 for which the inequality is violated; this is achievable through the conditioning of the two-level system which will be used as an ancilla.