A two-state model for vortex nucleation in a rotating Bose-Einstein condensate

TL;DR

This paper introduces a two-state model for vortex nucleation in rotating Bose-Einstein condensates, revealing the quantum states at criticality can be controlled by trap shape and potential flatness, with implications for understanding vortex formation.

Contribution

It develops an effective two-state model for vortex nucleation in BECs, showing the ground state becomes a twin-like or Schrödinger cat-like state at large particle numbers.

Findings

Ground state at criticality is a twin-like or Schrödinger cat-like state.

Quantum state nature can be controlled by trap deformation and potential flatness.

Model agrees with exact numerical solutions within the lowest Landau level approximation.

Abstract

It is well-known that a rotating Bose-Einstein condensate forms vortices to carry the angular momentum. For a first vortex to nucleate at the trap center, the rotational frequency must become larger than a certain critical value. The vortex nucleation process, however, is sensitive to the trap shape. It was shown earlier that for a symmetry-breaking potential that preserves parity, at criticality the leading natural orbitals may become degenerate, giving rise to a maximally entangled quantum state, found from exact solutions for just a few bosons. Developing an effective two-state model, we here show that in the limit of large particle numbers, the many-body ground state becomes either a so-called twin-like or a Schr\"odinger cat-like state. We corroborate this finding by a direct comparison to the exact numerical solution of the problem, feasible for moderate particle numbers within the lowest Landau level approximation. We show that the nature of the quantum state at criticality can be controlled by both the quadrupolar deformation and the flatness of the confining potential.