Degenerate ground state and quantum tunneling in rotating condensates

TL;DR

This paper explores how quantum tunneling lifts degeneracy in the ground state of rotating Bose-Einstein condensates with vortices, using WKB approximation to estimate tunneling rates.

Contribution

It provides a method to compute tunneling rates in degenerate rotating condensates by applying Euclidean dynamics and WKB approximation.

Findings

Quantum tunneling restores uniqueness in degenerate ground states.

Tunneling rates can be estimated via Euclidean action calculations.

Degeneracy is lifted in symmetric rotating traps with vortices.

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.