Quantum dynamics of a binary mixture ofBECs in a double-well potential: aHolstein–Primakoff approach

We study the quantum dynamics of a binary mixture of Bose–Einstein condensates (BECs) in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto an SU(2) spin problem together with a Holstein–Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunnelling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.