Bose-Einstein condensates in coupled co-planar double-ring traps : a thesis presented in partial fulfillment of the requirements for the degree of Masterate of Science in Physics at Massey University, Palmerston North, New Zealand
This thesis presents a theoretical study of Bose-Einstein condensates in a doublering
trap. In particular, we determine the ground states of the condensate in the
double-ring trap that arise from the interplay of quantum tunnelling and the trap’s
The trap geometry is a concentric ring system, where the inner ring is of smaller
radius than the outer ring and both lie in the same two-dimensional plane. Due to
the difference in radii between the inner and outer rings, the angular momentum
that minimises the kinetic energy of a condensate when confined in the individual
rings is different at most frequencies. This preference is in direct competition with
the tunnel coupling of the rings which favours the same angular momentum states
being occupied in both rings.
Our calculations show that at low tunnel coupling ground state solutions exist
where the expectation value of angular momentum per atom in each ring differs by
approximately an integer multiple. The energy of these solutions is minimised by
maintaining a uniform phase difference around most of the ring, and introducing a
Josephson vortex between the inner and outer rings. A Josephson vortex is identified
by a 2p step in the relative phase between the two rings, and accounts for one
quantum of circulation. We discuss similarities and differences between Josephson
vortices in cold-atom systems and in superconducting Josephson junctions.
Josephson vortices are actuated by a sudden change in the trapping potential.
After this change Josephson vortices rotate around the double-ring system at a
different frequency to the rotation of the double-ring potential. Numerical studies
of the dependence of the velocity on the ground state tunnel coupling and interaction
strength are presented. An analytical theory of the Josephson vortex dynamics is
also presented which is consistent with our numerical results.