Quantum-phase dynamics of two-component Bose–Einstein condensates: Collapse–revival of macroscopic superposition states

We investigate the long-time dynamics of two-component dilute gas Bose–Einstein condensates with relatively different two-body interactions and Josephson couplings between the two components. Although in certain parameter regimes the quantum state of the system is known to evolve into macroscopic superposition, i.e., Schrödinger cat state, of two states with relative atom number differences between the two components, the Schrödinger cat state is also found to repeat the collapse and revival behavior in the long-time region. The dynamical behavior of the Pegg–Barnett phase difference between the two components is shown to be closely connected with the dynamics of the relative atom number difference for different parameters. The variation in the relative magnitude between the Josephson coupling and intra- and inter-component two-body interaction difference turns out to significantly change not only the size of the Schrödinger cat state but also its collapse–revival period, i.e., the lifetime of the Schrödinger cat state.