Interference Pattern Formation between Bound Solitons and Radiation in Momentum Space: Possible Detection of Radiation from Bound Solitons with Bose–Einstein Condensate of Neutral Atoms

Abstract

We propose an indirect method for observing radiation from an incomplete soliton with a sufficiently large amplitude. We show that the radiation causes a notched structure on the envelope of the wave packet in the momentum space. The origin of this structure is the interference between the main body of oscillating solitons and the small radiation in the momentum space. We numerically integrate the nonlinear Schrödinger equation and perform Fourier transformation to confirm that the predicted structure really appears. We also show a simple model which reproduces the qualitative result. The experimental detection of the notched structure with the Bose-Einstein condensation of neutral atoms is discussed and suitable parameters for this detection experiment are shown.

Matter-Wave Fields for Double-Slit Atom Interferometry: Variational Versus Exact Solitons

“…In optical fibers, for instance, such structures originate from splitting 17,18 a single-pulse optical soliton using a quadratic chirp, which leads to a soliton molecule whose intensity profile exhibits * dikande.alain@ubuea.cm two temporal and spectral peaks with a finite phase difference between them. 8,16 Similar objects have been predicted and observed in Bose-Einstein condensate (BEC) systems, [19][20][21] where they result from a beam splitter acting on a bright matter-wave pulse, which creates two co-propagating matter-wave pulses.…”

“…[28][29][30] Still, the variational treatment is based on perturbation theory, both in the choice of the trial solution (despite its localized pulse shape, the Hermite-Gaussian mode is not a solution to the GP equation) and in the formulation of the time evolution of the variational soliton's collective coordinates. 31 In this work, we address the issue by considering two distinct variational solutions, namely, the super-sech and Hermite-Gaussian modes 19,[28][29][30] on one hand, and the exact one-soliton solution to the associated GP equation obtained by a non-isospectral inverse-scattering transform (NIST) method 32 on the other hand. A gravitational potential is included with the aim of taking into consideration the possible relative acceleration of one pulse in the post-created bisoliton with respect to the other due to the free-fall motion of atoms in the condensate fraction exposed to gravity.…”