A macro-realism inequality for opto-electro-mechanical systems

TL;DR

This paper demonstrates how to test macroscopic realism in opto-electro-mechanical systems near their quantum ground state by applying the Leggett-Garg inequality and discusses the implications of its violation.

Contribution

It introduces a method to apply the Leggett-Garg inequality to opto-electro-mechanical systems and identifies conditions for unambiguous violation indicating quantum behavior.

Findings

Leggett-Garg inequality can be violated in these systems

Measurements on the mechanical system yield unambiguous violations

Challenges exist with non-dichotomic unbounded observables

Abstract

We show how to apply the Leggett-Garg inequality to opto-electro-mechanical systems near their quantum ground state. We find that by using a dichotomic quantum non-demolition measurement (via, e.g., an additional circuit-QED measurement device) either on the cavity or on the nanomechanical system itself, the Leggett-Garg inequality is violated. We argue that only measurements on the mechanical system itself give a truly unambigous violation of the Leggett-Garg inequality for the mechanical system. In this case, a violation of the Leggett-Garg inequality indicates physics beyond that of "macroscopic realism" is occurring in the mechanical system. Finally, we discuss the difficulties in using unbound non-dichotomic observables with the Leggett-Garg inequality.