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

Violation of the Leggett-Garg inequality challenges classical realism and noninvasive measurement and is often associated with Schr"odinger's cat-like phenomena. Using this framework, the authors show that Josephson oscillations of a Bose-Einstein condensate, well described by the semi-classical Gross-Pitaevskii equation, deviate from macrorealism, while self-trapping does not. Remarkably, in experimentally accessible parameter regimes, the Leggett-Garg inequality remains violated.