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 (BEC) 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 BEC, 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 $\vert \nu, \mathcal{L} \rangle$ 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.

Keywords

• dark soliton crystals
• Bose–Einstein condensate
• free boson gas
• quantum bits
• lame equation