Degenerate ground state and quantum tunneling in rotating condensates

Abstract

Quantum tunneling introduces a fundamental difference between classical and quantum mechanics. Whenever the classical ground state is non-unique (degenerate), quantum mechanics restore uniqueness thanks to tunneling. A condensate in a rotating trap with a vortex can have such a degenerate classical ground state, a degeneracy that is excluded in the absence of rotation at least when the Gross-Pitaevskii equation applies. If the rotating trap has a center of symmetry, like a figure eight (a peanut), the vortex may be on either side with the same energy yielding a degenerate ground state, a degeneracy lifted by quantum tunneling. We explain how to compute the rate of tunneling in the WKB limit by estimating the action of the trajectory in the Euclidean version of the dynamics.