Abstract. A model describing coherent quantum tunnelling between two trapped Bose–Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose–Einstein condensates and to characterize the degree of coherence in the system.

PACS numbers: 03.75.Fi, 05.30.Jp

Print publication: Issue 7 (21 February 2003)
Received 8 August 2002, in final form 12 December 2002
Published 5 February 2003