Quantum dynamics of a model for two Josephson-coupled Bose--Einstein condensates

In this work we investigate the quantum dynamics of a model for two single-mode Bose--Einstein condensates which are coupled via Josephson tunneling. Using direct numerical diagonalisation of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalised and self-trapping phases. We show that these behaviours are dependent on both the initial state of the system as well as regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.