Multicomponent solitons present an optical realization of parity-time-symmetric dynamical systems

A variety of physical systems, such as light beam propagation through optical waveguides and multi-species Bose-Einstein condensates (BECs), behave according to coupled nonlinear Schrödinger (CNLS) equations. Solutions to the CNLS equations can involve particlelike wave packets called multicomponent solitons. Although their shapes can change, solitons generally maintain their total energy and speeds even during collisions. In nonlinear optics as well as in BECs, localized solitary waves, which propagate with a constant shape, are also loosely referred to as solitons.

In Chaos, authors report finding such stable solitons — in the form of solitary waves — in a CNLS system that exhibits parity-time (PT) symmetry, in which the system behaves the same way under the combined action of space reflection and time reversal. The study, they said, opens the possibility to study multicomponent PT-symmetric systems, which arise in nonlinear optics and in BECs.

Optical and matter wave solitons can be bright or dark. Bright solitons are localized peaks while dark solitons are localized dips amidst a continuous wave background. A two-component CNLS system with defocusing and repulsive nonlinearity can have both bright-dark and dark-dark solitons.

The analysis proposes, as a hypothesis, a CNLS system that has PT-symmetry. The authors assumed specific patterns for the solutions and determined the potentials that could sustain those solution patterns and yield bright-dark and dark-dark solitons. Using numerical simulations, they confirmed that the solitons are stable, demonstrating a novel perspective of PT-symmetric systems.

Source: “Bright-dark and dark-dark solitons in coupled nonlinear Schrodinger equation with PT-symmetric potentials,” by Debraj Nath, Yali Gao, R. Babu Mareeswaran, Thambithurai Kanna, and Barnana Roy, Chaos (2017). The article can be accessed at https://doi.org/10.1063/1.4997534 .