Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates

Michele Correggi (1) , Nicolas Rougerie (2)

1 Dipartimento di Matematica [Roma 3]
2 LPM2C - Laboratoire de physique et modélisation des milieux condensés

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R) (2004)] for the vortex distribution, a consequence of which is that the vortex distribution is strongly inhomogeneous close to the critical speed and gradually homogenizes when the rotation speed is increased. From the mathematical point of view, a novelty of our approach is that we do not use any compactness argument in the proof, but instead provide explicit estimates on the difference between the vorticity measure of the GP ground state and the minimizer of a certain renormalized energy functional.

Mots clés: Bose-Einstein condensates; quantized vortices; Gross-Pitaevskii energy; renormalized energy; vortex lattices

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Michele Correggi, Nicolas Rougerie. Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates. Communications in Mathematical Physics, 2013, 321 (3), pp.817-860. ⟨10.1007/s00220-013-1697-y⟩. ⟨hal-00696092v4⟩