Effect of even and odd numbers of atoms in a condensate inside a double-well potential

We study macroscopic quantum phenomena for an atomic condensate in a double-well potential as realized in recent experiments by Albiez [Phys. Rev. Lett. 95, 010402 (2005)] and Shin [Phys. Rev. Lett 95, 170402 (2005)]. By keeping the leading correction in the usually adopted mapping to an anisotropic spin model, we find that the topological Berry phase, a parity effect due to the even and odd atom numbers of a condensate, can be observed in the tunnel splitting. Our investigation suggests a cleaner, perhaps significantly improved, alternative for observing macroscopic quantum coherence (MQC) in large spin models.