Observation of quantum-classical transition behavior of LGI in a dissipative quantum gas

TL;DR

This paper investigates how dissipation affects the Leggett-Garg inequality in a non-Hermitian ultracold Fermi gas, revealing a transition from quantum to classical behavior at the exceptional point.

Contribution

It demonstrates the quantum-classical transition of LGI violation in a dissipative non-Hermitian quantum gas, highlighting the role of dissipation and time evolution.

Findings

LGI violation peaks at the exceptional point of dissipation.

Beyond a threshold, LGI violation diminishes, indicating a quantum-to-classical transition.

LGI violation decreases with longer evolution times, supporting the transition evidence.

Abstract

The Leggett-Garg inequality (LGI) is a powerful tool for distinguishing between quantum and classical properties in studies of macroscopic systems. Applying the LGI to non-Hermitian systems with dissipation presents a fascinating opportunity, as competing mechanisms can either strengthen or weaken LGI violations. On one hand, dissipation-induced nonlinear interactions amplify LGI violations compared to Hermitian systems; on the other hand, dissipation leads to decoherence, which could weaken the LGI violation. In this paper, we investigate a non-Hermitian system of ultracold Fermi gas with dissipation. Our experiments reveal that as dissipation increases, the upper bound of the third-order LGI parameter $K_3$ initially rises, reaching its maximum at the exceptional point (EP), where $K_3 = C_{21} + C_{32} - C_{31}$, encompassing three two-time correlation functions. Beyond a certain dissipation threshold, the LGI violation weakens, approaching the classical limit, indicating a quantum-to-classical transition (QCT). Furthermore, we observe that the LGI violation decreases with increasing evolution time, reinforcing the QCT in the time domain. This study provides a crucial stepping stone for using the LGI to explore the QCT in many-body open quantum systems.