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

TL;DR

This paper explores using dark soliton crystals from a Bose-Einstein condensate to encode quantum states in a free boson gas, linking nonlinear matter-wave phenomena with quantum memory applications.

Contribution

It introduces a novel method to imprint soliton states into a free boson gas using BEC dark-soliton crystals, connecting nonlinear wave solutions with quantum spectral states.

Findings

Dark-soliton crystals can create bound states in a free boson gas.

The spectrum of these states is determined by the Lamé eigenvalue problem.

Some eigenstates replicate the original dark soliton crystal wavefunctions.

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.