Violation of the Leggett-Garg inequality for dynamics of a Bose-Einstein condensate in a double-well potential

TL;DR

This paper investigates the violation of the Leggett-Garg inequality in Bose-Einstein condensates within a double-well potential, revealing conditions under which macrorealism is violated and how particle number influences this violation.

Contribution

It demonstrates the conditions for LGI violation in BEC dynamics, highlighting the roles of Josephson oscillations and self-trapping phenomena, and shows how particle number affects the violation.

Findings

LGI is violated due to Josephson oscillations.

LGI remains unviolated in the strong coupling regime.

Violation increases with particle number.

Abstract

The Leggett-Garg inequality (LGI) serves as a criterion to determine the adherence of macroscopic system dynamics to macrorealism, as introduced by Leggett and Garg. A violation of this inequality implies either the absence of a realistic description of the system or the impossibility of noninvasive measurement. In this Letter, we investigate the violation of the LGI for the system of bosons in a double-well potential. Specifically, we explore the violation of the LGI in the dynamics of bosons in a double-well potential in the Bose-Einstein-condensation (BEC) regime, where the system can be considered as two weakly coupled Bose condensates, and in the single-particle regime to establish the conditions under which the violation of the LGI occurs. Our analysis reveals that the LGI is violated due to Josephson oscillations, while it remains unviolated in the strong coupling regime, attributed to the self-trapping phenomena. Notably, we observe that the violation of the LGI becomes increasingly significant as the particle number increases. These findings provide valuable insights into the macrorealistic behavior of Bose condensates and highlight the effect of measurements on the dynamics of a macroscopic system.