# Leggett-Garg tests of macro-realism for dynamical cat-states evolving in a nonlinear medium

## TL;DR

This paper demonstrates that single-mode and multi-component cat-states evolving in nonlinear media can violate Leggett-Garg inequalities, providing evidence against macro-realism and indicating mesoscopic quantum coherence.

## Contribution

It derives a generalized Leggett-Garg inequality for evolving cat-states and predicts violations in experimental setups like BEC and superconducting circuits, highlighting non-classical behavior.

## Key findings

- Violations of Leggett-Garg inequalities for cat-states in nonlinear media.
- Predicted violations in Bose-Einstein condensate and superconducting circuit experiments.
- Higher nonlinearity orders lead to stronger violations.

## Abstract

We show violations of Leggett-Garg inequalities to be possible for single-mode cat-states evolving dynamically in the presence of a nonlinear quantum interaction arising from, for instance, a Kerr medium. In order to prove the results, we derive a generalised version of the Leggett-Garg inequality involving different cat-states at different times. The violations demonstrate failure of the premise of macro-realism as defined by Leggett and Garg, provided extra assumptions associated with experimental tests are valid. With the additional assumption of stationarity, violations of the Leggett-Garg inequality are predicted for the multi-component cat-states observed in the Bose-Einstein condensate and superconducting circuit experiments of Greiner et al. (Nature 419, 51, (2002)) and Kirchmair et al. (Nature, 495, 205 (2013)). The violations demonstrate a mesoscopic quantum coherence, by negating that the system can be in a classical mixture of mesoscopically distinct coherent states. Higher orders of nonlinearity are also studied and shown to give strong violation of Leggett-Garg inequalities.