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Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates

We study effects of tunnel coupling on a pair of parallel disc-shaped Bose–Einstein condensates with the self-attractive intrinsic nonlinearity. Each condensate is trapped in a combination of in-plane and transverse harmonic-oscillator potentials. It is shown that, depending on the self-interaction strength and tunnelling coupling, the ground state of the system exhibits a phase transition which links three configurations: a symmetric one with equal numbers of atoms in the coupled condensates, an asymmetric configuration with a population imbalance (a manifestation of the macroscopic quantum self-trapping), and the collapsing state. A modification of the phase diagram of the system in the presence of vortices in the disc-shaped condensates is reported too. The study of dynamics around the stationary configurations reveals properties which strongly depend on the symmetry of the configuration.