Geometric phase in a Bose-Einstein-Josephson junction
The Institute of Mathematical Sciences, Chennai 600 113,
Corresponding author: a firstname.lastname@example.org
Revised: 12 January 2005
Published online: 24 May 2005
We calculate the geometric phase associated with the time evolution of the wave function of a Bose-Einstein condensate system in a double-well trap by using a model for tunneling between the wells. For a cyclic evolution, this phase is shown to be half the solid angle subtended by the evolution of a unit vector whose z-component and azimuthal angle are given, respectively, by the population difference and phase difference between the two condensates. For a non-cyclic evolution, an additional phase term arises. We show that the geometric phase can also be obtained by mapping the tunneling equations on to the equations of a space curve. The importance of a geometric phase in the context of some recent experiments is pointed out.
PACS: 02.40.Hw – Classical differential geometry / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005