Using dark solitons from a Bose-Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas

• URL: http://arxiv.org/abs/2307.11803v1
• Date: Fri, 21 Jul 2023 11:35:18 GMT
• Title: Using dark solitons from a Bose-Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas
• Authors: Alain M. Dikande
• Abstract summary: A possible use of matter-wave dark-soliton crystal produced by a Bose-Einstein condensate with ring geometry is explored. The spectrum of bound states created in the free boson gas is shown to be determined by the Lam'e eigenvalue problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A possible use of matter-wave dark-soliton crystal produced by a Bose-Einstein condensate with ring geometry, to store soliton states in the quantum memory of a free boson gas, is explored. A self-defocusing nonlinearity combined with dispersion and the finite size of the Bose-Einstein condensate, favor the creation of dark-soliton crystals that imprint quantum states with Jacobi elliptic-type soliton wavefunctions in the spectrum of the free boson gas. The problem is formulated by considering the Gross-Pitaevskii equation with a positive scattering length, coupled to a linear Schr\"odinger equation for the free boson gas. With the help of the matter-wave dark soliton-crystal solution, the spectrum of bound states created in the free boson gas is shown to be determined by the Lam\'e eigenvalue problem. This spectrum consists of $\vert \nu, \mathcal{L} \rangle$ quantum states whose wave functions and energy eigenvalues can be unambiguously identified. Among these eigenstates some have their wave functions that are replicas of the generating dark soliton crystal.

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