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 [Dagnino et al., Nat. Phys. 5, 431 (2009)] 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 show here that, in the limit of large particle numbers, the many-body ground state becomes either a so-called “twin”-like or a “Schrödinger 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.
- Received 25 October 2019
DOI:https://doi.org/10.1103/PhysRevA.100.063638
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