Experimental violation of the Leggett-Garg inequality in a three-level trapped-ion system

This is the authors' abstract. We don't add key points for this paper.

Leggett-Garg inequality (LGI) is used to detect whether the macroscopic superposition state exists. Classical systems obey the LGI, but quantum systems may violate it. In the multilevel system, different state update rules determine different upper bounds of LGI. In this work, we experimentally test the LGI in a three-level trapped-ion system under the L\"uders and the von Neumann state update rules, respectively. The maximum observed value of the Leggett-Garg correlator under the von Neumann state update rule is K₃=1.739±0.014, which demonstrates a violation of the L\"uders bound by 17 standard deviations and is by far the most significant violation under the specific model. The method used in our experiment could also be used in other multilevel experiments in the trapped-ion system.