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

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 Schrödinger 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 Lamé eigenvalue problem. This spectrum consists of $|\nu ,\mathcal{L}⟩$ 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.

13 pages, 2 tables, 4 figures

References in corpus (4)

• Dark soliton dynamics in Bose-Einstein condensates at finite temperature
• Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains
• Stability analysis and attractor dynamics of 3D dark solitons with localized dissipation
• Soliton-mode proliferation induced by cross-phase modulation of harmonic waves by a dark-soliton crystal in optical media