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

TL;DR

This paper experimentally demonstrates a significant violation of the Leggett-Garg inequality in a three-level trapped-ion system, highlighting quantum effects in temporal correlations and comparing state update rules.

Contribution

First experimental violation of LGI in a three-level system with direct comparison of Von Neumann and L"uders rules, achieving the most significant violation in natural three-level systems.

Findings

Maximum LGI value observed is 1.739, violating the L"uders bound by 17 standard deviations.

Demonstrates quantum violation of classical temporal correlations in a three-level system.

Provides insights into the role of state update rules in LGI violations.

Abstract

Leggett-Garg inequality (LGI) studies the temporal correlation in the evolution of physical systems. Classical systems obey the LGI but quantum systems may violate it. The extent of the violation depends on the dimension of the quantum system and the state update rule. In this work, we experimentally test the LGI in a three-level trapped-ion system under the model of a large spin precessing in a magnetic field. The Von Neumann and L\"uders state update rules are employed in our system for direct comparative analysis. The maximum observed value of Leggett-Garg correlator under the Von Neumann state update rule is $K_3 = 1.739 \pm 0.014$, which demonstrates a violation of the L\"uders bound by 17 standard deviations and is by far the most significant violation in natural three-level systems.