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In this work we investigate the quantum dynamics of a model for twosingle-mode Bose--Einstein condensates which are coupled via Josephsontunneling. Using direct numerical diagonalisation of the Hamiltonian, wecompute the time evolution of the expectation value for the relative particlenumber across a wide range of couplings. Our analysis shows that the systemexhibits rich and complex behaviours varying between harmonic and non-harmonicoscillations, particularly around the threshold coupling between thedelocalised and self-trapping phases. We show that these behaviours aredependent on both the initial state of the system as well as regime of thecoupling. In addition, a study of the dynamics for the variance of the relativeparticle number expectation and the entanglement for different initial statesis presented in detail.Comment: 15 pages, 8 eps figures, accepted in J. Phys.

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