Leggett-Garg Inequality for Bosons in a Double-Well Potential

Tsubasa Sakamoto, Ryosuke Yoshii, Shunji Tsuchiya

Published 2024-07-07Version 1

The Leggett-Garg inequality (LGI) serves as a criterion to determine the adherence of macroscopic system dynamics to macrorealism, as postulated by Leggett and Garg. A violation of this inequality implies either the absence of a realistic description of the system or the impracticality of noninvasive measurements. In this work, 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.