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Journal Article

Effective three-body interactions for bosons in a double-well confinement


Nielsen,  Anne E. B.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Dobrzyniecki, J., Li, X., Nielsen, A. E. B., & Sowinski, T. (2018). Effective three-body interactions for bosons in a double-well confinement. Physical Review A, 97(1): 013609. doi:10.1103/PhysRevA.97.013609.

Cite as: https://hdl.handle.net/21.11116/0000-0000-C9DB-7
When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can, to a good approximation, ignore the high-energy states and thereby obtain an effective two-mode model. Here we show that the regime in which the two-mode model is valid can be extended by adding an on-site three-body interaction term and a three-body interaction-induced tunneling term to the two-mode Hamiltonian. These terms effectively account for virtual transitions to the higher-energy states. We determine appropriate strengths of the three-body terms by an optimization of the minimal value of the wave-function overlap within a certain time window. Considering different initial states with three or four atoms, we find that the resulting model accurately captures the dynamics of the system for parameters where the two-mode model without the three-body terms is poor. We also investigate the dependence of the strengths of the three-body terms on the barrier height and the atom-atom interaction strength. The optimal three-body interaction strengths depend on the initial state of the system.