Nonclassical correlations in binary Bose-Einstein condensates: from double-well confinement to twin Schrödinger cat states.

We propose and numerically validate a scheme for the realization of Schrödinger cat-like states in a two-component Bose-Einstein condensate, emphasizing their twinning across components under tunable intra- and inter-species interactions within the miscibility regime. Wigner phase-space analysis reveals sub-Planck-scale interference fringes, confirming the nonclassical character of the states and their potential utility in quantum-enhanced metrology. The dynamical response of the system to a weak linear gravitational-like perturbation further demonstrates cooperative enhancement: while the directly perturbed component retains its cat-like features, the coupled partner exhibits a pronounced population imbalance and a distinct phase-space rotation, providing a sensitive detection channel absent in single-component condensates. These results establish binary condensates as a versatile platform for engineering macroscopic quantum superpositions and exploiting their twinning dynamics for precision measurements.