Solitons Riding on Solitons: Hypersolitons and the Quantum Newton's Cradle

Abstract

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves. For appropriate conditions, the reduced dynamics derived from perturbation and variational techniques allows to describe a chain of dark or bright solitons as a chain of effective masses connected by nonlinear springs taking the form of a Toda lattice model on the soliton's positions. In turn, the Toda lattice possesses exact solitary travelling compression wave solutions corresponding to travelling compression waves in the original soliton chain. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. We corroborate our analytical results with direct numerical simulations of the nonlinear Schrödinger equation. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate description for the robust evolution of travelling compression waves. In contrast, bright soliton chains do not have such stable propagating solutions due to the desynchronization of the mutual phases between consecutive solitons during evolution. Finally, as an application to Bose-Einstein condensates trapped in a standard external harmonic trapping potential, we study the case of finite dark soliton chain confined at the center of the trap. We find that when the central chain is hit by a dark soliton initiated at the edge of the external trap, the energy is transferred through the chain as a hypersoliton. When the hypersoliton reaches the end of the central chain, a dark soliton is ejected away from the center of the trap and, as it returns from its excursion up the trap, hits the central chain producing again a hypersoliton. This periodic evolution is the equivalent of the classical Newton's cradle.

13 pages, 10 figures

References in corpus (6)

• Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Supersolitons: Solitonic excitations in atomic soliton chains
• Dark solitons in external potentials
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• Newton's cradle analogue with Bose-Einstein condensates

Cited by in corpus (7)

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• Observation of dense collisional soliton complexes in a two-component Bose-Einstein condensate
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Hyperchaos in a Bose-Hubbard chain with Rydberg-dressed interactions
• Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose-Einstein condensates
• Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup